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1 A University of Susse PhD thesis Avilble online vi Susse Reserch Online: This thesis is protected by copyright which belongs to the uthor. This thesis cnnot be reproduced or quoted etensively from without first obtining permission in writing from the Author The content must not be chnged in ny wy or sold commercilly in ny formt or medium without the forml permission of the Author When referring to this work, full bibliogrphic detils including the uthor, title, wrding institution nd dte of the thesis must be given Plese visit Susse Reserch Online for more informtion nd further detils

2 Development of methodology for deriving Plsmspheric Electron Content from In-Situ electron density mesurements in highly eccentric equtoril orbits

3 Development of methodology for deriving Plsmspheric Electron Content from In-Situ electron density mesurements in highly eccentric equtoril orbits Aliyuthumn Sdhique School of Engineering nd Informtics University of Susse Submitted to the University of Susse for the degree of PhD. April 07 b

4 c

5 DECLARATION I hereby declre tht this thesis hs not been submitted, either in the sme or different form, to this or ny other University for degree. Aliyuthumn Sdhique i

6 DEDICATION I dedicte the gins of this reserch to my mother nd fther. ii

7 ACKNOWLEDGEMENTS I would like to epress my sincere grtitude to my min supervisor Dr Andrew Buckley for his concern, dvice nd guidnce on top of his supervision during ll these yers. I lso would like to thnk Prof. Pul Gugh for his encourgement nd resources. The inspirtion I received from my supervisors is priceless nd immense. I would like epress my specil grtitude nd pprecition towrds Dr Cmill Briult nd Dr Helen Prnce for fcilitting this. I lso thnk the University of Sheffield for providing the TC dt for the reserch. Lst not the lest, I would like to sy big Thnk you to my wife nd son, who scrificed lot for ll these yers nd my fmily members who helped immensely towrds this end. iii

8 ABSTRACT Stellite communiction nd nvigtion pplictions suffer due to spce wether phenomen. The effects re prticulrly pronounced in the equtoril regions, which re highly ionised nd more esily susceptible to spce wether effects thn the mid ltitude regions. Nevertheless, the bulk of the reserch on TEC profile nd behviour hs been crried out with respect to mid-ltitude regions. The contribution of the Upper Plsmsphere (the ltitudes bove semisynchronous orbit height up to the Plsmpuse height) to the Totl Electron Content t ny given loction hs been nd continues to be n un-quntified component. The PEACE instrument in the Chinese Europen Spce Agency Double Str TC stellite nd its highly eccentric equtoril orbit provides n ecellent opportunity to build Upper Plsmspheric Electron Content (UPEC) components in the Equtoril region from empiricl in-situ mesurements of electron density long the orbit in the 0000km to 40000km ltitude rnge. This work develops nd presents methodology for deriving Plsmspheric Electron Content from In-Situ, empiricl electron density mesurements in highly eccentric, elongted equtoril orbits, using the dt from the Double Str TC stellite. As such this thesis lso genertes dtbse of Upper Plsmspheric Electron Content (UPEC) long the orbitl pth of the TC. This work lso proposes dedicted mission to be lunched with highly eccentric orbits to generte comprehensive equtoril TEC dtbse bsed on this methodology. This works envisions tht future mission to be preferbly lunched in the equtoril belt, thus providing the opportunity to develop n rchive of dt s well s rel time source for better understnding of the Appleton nomly Effects on Plsmspheric Electron Content. iv

9 CONTENTS Chpter Section Pge No. Chpter : Introduction. Motivtion for the reserch nd the originl contribution of the reserch to knowledge.. Motivtion for the reserch.. Originl contribution to knowledge chieved by this reserch 3.. Totl Electron Content 4.. Why TEC is importnt? - Prcticl pplictions of TEC mesurements 4... Appliction tht require high precision electron content clcultions 4... Stellite communictions 4... Nvigtion Applictions 5.. Definition of Totl Electron Content (TEC) 7..3 Eqution for the Totl Electron Content (TEC) nd its unit 8..4 Verticl TEC nd Slnt TEC 9..5 Incident Angle 9..6 Verticl TEC nd Slnt TEC reltionship formul 0..7 Averge electron density versus height profile..8 Globl monthly verge verticl TEC profile 3..9 Geogrphic regionl vrition ptterns 4..0 Diurnl or Temporl vrition pttern of TEC 5 v

10 Chpter Section Pge No..3 Plsmspheric Electron Content (PEC or TECp) 9.4 Electron density nd TEC mesurement techniques.4. Ionosonde.4. Topside sounders.4.3 GPS Duel Frequency Techniques GPS System Description GPS TEC Derivtion 4 ) Pseudornge Method 4 b) Crrier Phse Method 6.5 GLONASS 7.6 Glileo GNSS 9.7 Descriptions of relevnt orbit types 9.7. Geo Synchronous Orbits 9.7. Semi (Geo) Synchronous Orbits Molny Orbit Geo Sttionry Orbit 3 Chpter : Ionospheric nd Plsmspheric effects 33. Introduction to Ionospheric nd Plsmspheric effects on rdio wves 33.. Amplitude nd phse scintilltion 33.. Amplitude scintilltion indices 34.. Phse scintilltion inde 35 vi

11 Chpter Section Pge No...3 Clssifiction of Scintilltions Reltionship between SI nd S4 indices Frequency dependence of scintilltions 36.3 Group Dely or Group Pth Dely 36.4 RF crrier phse dvnce Differentil crrier phse Second difference of crrier phse 39.5 Doppler Shift 39.6 Frdy Polriztion Rottion 40.7 Angulr Refrction 43 Chpter 3: Mission Overviews ATS-6, Cluster II, Double Str, nd C-NOFS Applictions Technology Stellite-6 ( ATS-6 ) The methodology employed in determining the Plsmspheric content 45 ) Frdy Rottion Technique 45 b) Dispersive Group Dely Technique Results obtined Observtions Conclusions The Cluster Mission 56 vii

12 Chpter Section Pge No. 3.. Orbitl prmeters The eperiments Double Str Mission Orbitl prmeters nd significnce of the mission Plsm Electron nd Current Eperiment (PEACE) The Instrument Resolutions: Opertion The Low Energy Electron Anlyser (LEEA): The High Energy Electron Anlyser (HEEA): DWP Instrumenttion The processor module Time resolution Prticle correltor Opertion of the Prticle correltor The Sptio-Temporl Anlysis of Field Fluctutions (STAFF) Objectives nd the instrument structure 7 Chpter 4 : TEC modelling nd Scintilltion modelling Interntionl Reference Ionosphere (IRI) Brief Description Prmeters 74 viii

13 Chpter Section Pge No. 4. Globl Ionospheric Scintilltion Model (GISM) Scintilltion fluctutions NeQuick Model Other models of interest 77 Chpter 5: Dt Etrction from TC DWP Correltor Double Str Dt dissemintion structure Double Str DWP Level dt cquisition Double Str L dt decommuttion Correltor DSD Heder definition for DWP Correltor science pcket formt Etrcting the Time Series nd the ACFs ACFTIMESBUILD 86 Chpter 6 Development of methodology for deriving the Upper Plsmspheric Electron Content (UPEC) long the orbitl pth of the TC from its empiricl, in-situ electron density dt The cse for this thesis Upper Plsmspheric Electron Content (UPEC) TC orbit nd the opportunity it provides Dt sources Electron Density Dt -Double Str UK Dt Centre Orbit Dt - NASA Stellite Sitution Centre 98 i

14 Chpter Section Pge No. 6.3 Orbitl elements nd Coordinte Systems -Primry bckground informtion Orbitl elements / Prmeters Geocentric Equtoril Inertil Coordinte Systems 05 ) J000 Frme Coordinte System (GEI /J000) 06 b) True of Dte Frme Coordinte System (GEI /TOD) The Methodology Dt cquisition nd input The Algorithm Mechnism for the determintion of the UPEC Notes on utomtion of the lgorithm 9 Chpter 7 Derivtions, Theories nd Clcultions 7. Deriving the plne eqution 7.. Clcultion of plne coefficients, b, c 7.. Clcultion of the Inclintion ngle Coordinte Trnsformtion theories Coordinte trnsformtion of two es Crtesin plne by n ngle of Coordinte Trnsformtion Mtri Trnsformtions to derive the orbitl plne coordintes Clcultion of the Longitude of the Ascending Node Trnsformtions through the Argument of Peripsis ( ) 8

15 Chpter Section Pge No. 7.5 Clcultion of n Orbitl Arc Length Ellipse eqution of the orbit with its centre t the origin of, y es nd Line of Apsides s the is Clcultion of the Arc Length of function Clcultion of the Arc Length of the orbitl ellipse with its centre t the origin nd the Line of Apsides s the iscu Clcultion of the TEC Br length Tngent Line Construction nd the determintion of the Incident Angle Clcultion of the UPEC length Summery of TEC Builder Clcultions Verifictions Verifiction : Line of Node intercept vlue close to zero Verifiction : Z coordinte close to zero Verifiction 3: Argument of Peripsis vlues re very close by vector nlysis method nd from the lgorithm Verifiction 4: The trnsformed coordintes produce 64 perfect ellipticl orbits Verifiction 5: Consistent inclintion ngle over the orbitl period, which grdully chnges in conformity with ctul GEI/J000 coordinte plots Notes on vector nlysis of this methodology 70 i

16 Chpter Section Pge No. Chpter 8 Anlysis of Results, Conclusions, Further Reserch nd Developments 7 8. Sptil vrition of the Upper Plsmspheric TEC component long the orbitl pth s function of continuous time Sptil vrition of the Upper Plsmspheric TEC component long the orbitl pth s function of rdil distnce Vrition of Upper Plsmspheric TEC component s function of longitude Observtions from the results of Upper Plsmspheric Electron Content (UPEC) generted by the TEC Builder methodology from TC dt Further Reserch nd Developments A dedicted mission to generte comprehensive equtoril TEC reserch bsed on this methodology 8.5. Development of n Interntionl GNSS System for trcking, communictions, rnging, serch nd rescue nd disster mngement pplictions Development of comprehensive TEC model nd Scintilltion model 3 ii

17 Chpter Section Pge No. Appendices 5 Appendi ACFTIMESBUILD.C 5 Appendi tlmdecom process 7 Appendi 3 tlmdecom.c 8 Appendi 4 tlmproc.c 33 Appendi 5 tlmproc.h 44 Appendi 6 Lest Squre Fit 46 Appendi 7 Deriving solution to by z c 0 formt 47 Appendi 8 Solving simultneous equtions with 3 unknowns 49 Appendi 9 Angle between two plnes 5 Appendi 0 Coordinte trnsformtion 53 Appendi PEACE energy rnge (ev) nd Correltor levels 56 Reference List 57 Bibliogrphy 6 iii

18 List of figures No. Figure Pge. Topside Ionosphere nd Plsmsphere 008. Single Lyer Model Ionosphere nd the Incident Angle 00.3 Electron density profile with height for Jicmrc sttion 0.4 Globl Verticl Monthly verge TEC Contours in TEC Units For 000UT Mrch 980 with Equtoril Anomly Regions Prominently feturing in the western hemisphere nd over Afric 03.5: Monthly overplots of TEC for Ascension Islnd 980 nd : Monthly overplots of TEC for Hmilton MS for The Molniy orbit digrm illustrting orbitl positions of the stellite with time 03. Vrition of Time Dely with frequency for vrious vlues of TEC 037. Vrition of Frdy Rottion with frequency for vrious vlues of TEC t northern mid ltitude sttion 04 3.: Vrition of Totl Electron Content up to geo-synchronous orbit height nd Ionospheric electron content (TECG nd TECI) t 5-minute intervls from 600 EDT, 3 July 974 to 0800 EDT 8 July 974 t Fort Monmouth, NJ, USA : Vrition of Plsmspheric electron content ( TEC P ) plotted for ech dy : Vrition of the rtio of Plsmspheric to Ionospheric electron contents in percentge : Vrition of the rtio of Plsmspheric electron content to Totl electron content to geo-sttionry height in percentge Orbitl plots of Double Str TC- spcecrft in three different dtes in 004, 005 nd PEACE FM07 Instrument in MSSL Clen Room A cross-section of the LEEA nlyser showing the structure of the input collimtor, the electrosttic nlyser nd the node pttern LEEA HEEA Sweep LEEA HEEA sweeps nd spin is 066 iv

19 3.0 LAR MAR HAR ENERGY TIME SPIN ANGLE : Double Str Science Dt System (DSDS) schemtic digrm Ground dt segment of Double Str Project The ltitudes, period, rdius nd speed of relevnt orbits Orbitl plne digrm showing Incident ngle being equl to the ngle the tngent to the orbit mkes with the line connecting the centre of the erth with the spcecrft in the ltitude rnge 3.5 Re to 6.5 Re Orbitl Plne digrm Orbitl elements / Prmeters Inclintion Angle, Longitude of the Ascending Node nd the Argument of Peripsis illustrted Longitude of the Ascending Node ( ) clcultion for the orbit on Argument of Peripsis ( ) clcultion for the orbit on Equtoril plne digrm showing Longitude of the Ascending Node ( ) being equl to the Grdient ngle of the Line of Nodes in GEI/J000 system for generl cse. The Z is is perpendiculr to the plne nd is pointing out Angle between the Orbitl plne nd the Equtoril plne being equl to the ngle between their Norml vectors n o nd n e, which equls Inclintion ngle 5 7. Coordinte trnsformtion of two es Crtesin plne by n ngle Trnsformtions to derive the orbitl plne coordintes with Line of psides s the is Trnsformtions through the Argument of Peripsis with Line of psides s the new y is Ellipse with centre t the origin of D Crtesin plne Arc length of function f () nd, y y between two points P, y P in D Crtesin plne Orbitl ellipse with its centre t the origin of, y es nd Line of Apsides s the is Descriptive digrm for Tngent Line construction nd the determintion of the Incident Angle Clcultion of the TEC Br length 50 v

20 7.0 Grph of GEI/J000 Z coordinte vlues nd z coordintes vlues fter the coordinte trnsformtions ginst Time strting t on 0/06/ Grph of GEI/J000 Z coordinte vlues nd z coordintes vlues fter the coordinte trnsformtions ginst Time strting t on 30/0/ Grph of GEI/J000 Z coordinte vlues nd z coordintes vlues fter the coordinte trnsformtions ginst Time strting t on 08/08/ Grph of GEI/J000 Z coordinte vlues nd z coordintes vlues fter the coordinte trnsformtions ginst Time strting t on /03/ Grph of GEI/J000 Z coordinte vlues nd z coordintes vlues fter the coordinte trnsformtions ginst Time strting t on /0/ Vector digrm for the perigee nd the Ascending Node Orbitl plot for 0/03/004 to 0/03/ Orbitl plot for 08/08/005 to 7/08/ Orbitl plot for /03/006 to 09/04/ Orbitl plot for /0/004 to 9/0/ Orbitl plot for 30/0/004 to 9// Orbitl stte vectors the position vector nd the velocity vector Plsmspheric TEC component generted for twenty dy between nd The X is is clibrted with minutes from midnight 00:00:00 on Plsmspheric TEC component generted for twenty dy between nd The X is is clibrted with minutes from midnight 00:00:00 on Plsmspheric TEC component generted for twenty dy between nd The X is is clibrted with minutes from midnight 00:00:00 on Plsmspheric TEC component generted for twenty dy between nd The X is is clibrted with minutes from midnight 00:00:00 on vi

21 8.5 Plsmspheric TEC component generted for twenty dy between nd The X is is clibrted with minutes from midnight 00:00:00 on Plsmspheric TEC component generted for twenty dy between nd The X is is clibrted with minutes from midnight 00:00:00 on Plsmspheric TEC component generted for twenty dy between nd The X is is clibrted with minutes from midnight 00:00:00 on Plsmspheric TEC component generted for twenty dy between nd The X is is clibrted with minutes from midnight 00:00:00 on Plsmspheric TEC component generted for twenty dy between nd The X is is clibrted with minutes from midnight 00:00:00 on Plsmspheric TEC component generted for twenty dy between nd The X is is clibrted with minutes from midnight 00:00:00 on Plsmspheric TEC component generted for twenty dy between nd for minutes 000 to Plsmspheric TEC component generted for twenty dy between nd for minutes 4500 to Plsmspheric TEC component generted for twenty dy between nd for minutes 600 to Plsmspheric TEC component generted for twenty dy between nd for minutes Plsmspheric TEC component generted for twenty dy between nd for minutes 9600= Plsmspheric TEC component generted for twenty dy between nd for minutes Plsmspheric TEC component generted for twenty dy between nd for minutes Plsmspheric TEC component generted for twenty dy between nd for minutes vii

22 8.9 Plsmspheric TEC component generted for twenty dy between nd for minutes Plsmspheric TEC component generted for twenty dy between nd for minutes Plsmspheric TEC component generted for twenty dy between nd for minutes Plsmspheric TEC component generted for twenty dy between nd for minutes Plsmspheric TEC component generted for twenty dy between nd for minutes Plsmspheric TEC component generted for twenty dy between nd for minutes Plsmspheric TEC component generted for twenty dy between nd for minutes The Vrition of Upper Plsmspheric TEC component generted between nd for minutes 000 to The Vrition of Upper Plsmspheric TEC component generted between nd for minutes The Vrition of Upper Plsmspheric TEC component generted between nd for minutes The Vrition of Upper Plsmspheric TEC component generted between nd for minutes The Vrition of Upper Plsmspheric TEC component generted between nd for minutes The Vrition of Upper Plsmspheric TEC component generted between nd for minutes The Vrition of Upper Plsmspheric TEC component generted between nd for minutes The Vrition of Upper Plsmspheric TEC component generted between nd for minutes The Vrition of Upper Plsmspheric TEC component generted between nd for minutes The Vrition of Upper Plsmspheric TEC component generted between nd for minutes viii

23 8.36 The orbit rrngement for dedicted mission to generte comprehensive equtoril TEC reserch bsed on this methodology. The two orbits for pir of stellites with the sme Line of Apsides 8.37 The orbit rrngement for dedicted mission to generte comprehensive equtoril TEC reserch bsed on this methodology. Plne view from the North pole. A9. Angle between the Orbitl plne nd the Equtoril plne being equl to the ngle between their Norml vectors n o nd n e, which equls Inclintion ngle 5 A9. Coordinte trnsformtion of two es Crtesin plne by n ngle of 53 i

24 List of Tbles No. Tble Pge. Civil Applictions of Stellite Nvigtion 006. Non - civil Applictions of Stellite Nvigtion Comprison between the orbitl nd stellite communiction prmeters of the GPS nd GLONASS systems 08 3.: List of Cluster II Eperiments : List of Equtoril Double Str (TC-) Eperiments : List of Polr Double Str (TC-) Eperiments PEACE energy rnge (ev) nd Correltor levels TED heder formt ACF + Time Series mode Science pcket dt structure Time Series only mode Science pcket dt structure DWP dt Pcket snippet for words 3 nd DWP dt Pcket snippet for the Fied energy ACF Offset nd Scle DWP dt Pcket snippet for the first eight fied energy time series in word DWP dt Pcket snippet for the Fied energy Zero lg ACF, Offset nd Scle Dt Pcket snippet for the first seven Fied energy ACFs NASA Stellite Sitution Centre TC Spcecrft coordintes: Units nd formtting options vilble for outputs nd the selected options NASA Stellite Sitution Centre TC spcecrft coordintes: Avilble output options nd the selected options Geocentric Coordinte Systems, their bbrevitions nd the es Definitions Orbitl dt elements, their formt nd units The coefficients of simultneous equtions, the summted equivlents nd their TECbuilder positions 3 7. Components of the Arc Length clcultion formul nd corresponding TEC Builder Columns Summery of TEC Builder Clcultions - TEC Builder Sheet b Summery of TEC Builder Clcultions - TEC Builder Sheet 53

25 7.3-c Summery of TEC Builder Clcultions - TEC Builder Sheet d Summery of TEC Builder Clcultions - TEC Builder Sheet Summery of TEC Builder Clcultions - TEC Builder Sheet Intercept vlues of the Line of Nodes eqution for smpled dtes Inclintion ngle for smpled periods 69 A PEACE energy rnge (ev) nd Correltor levels 56 i

26 Chpter : Introduction. Motivtion for the reserch nd the originl contribution of the reserch to knowledge.. Motivtion for the reserch Stellite communiction nd nvigtion pplictions suffer due to spce wether phenomen. These effects re prticulrly pronounced in the equtoril regions, which re highly ionised nd more esily susceptible to spce wether effects thn the mid ltitude regions (Biktsh, 005) As would be elborted lter, Totl Electron Content (TEC) mesurements, the primry mesure tht quntifies the number of therml, free electrons intercepted by trversing electromgnetic wve, yield very high vlues in the Ner-Equtoril regions. This region etends pproimtely ± on either sides of the mgnetic equtor (Bsu et l. 985) Ironiclly, bulk of the reserch on the TEC profile nd behviour hs been crried out with respect to mid-ltitude regions. Recently, efforts hve been undertook by the scientific community in the equtoril belt s well s the interntionl community to crry out reserch in this re, especilly so fter the dvent of the GPS nd its widespred usge. Nevertheless, much more studies need to be done.

27 The contribution of the Upper Plsmsphere (the ltitudes bove semisynchronous orbit height up to the Plsmpuse height) to the Totl Electron Content t ny given loction hs been nd continues to be n unquntified component. As Electron Content cnnot be mesured directly nd needs to be derived from other prmeters, it hs not been possible to derive this component from trditionl methods such s incoherent scttering rdrs, ground bsed ionosondes, stellite sounders nd GPS. GPS dul frequency mesurements cnnot be employed s the Upper Plsmspheric ltitudes re bove the GPS stellite orbit ltitudes. The PEACE instrument in the Chinese Europen Spce Agency Double Str TC stellite nd its highly eccentric equtoril orbit provides n ecellent opportunity to build Upper Plsmspheric Electron Content (UPEC) components in the Equtoril region from empiricl in-situ mesurements of electron density long the orbit in the 0000km to 40000km ltitude rnge. The methodology developed nd presented in this thesis genertes first time ever (comprehensive) dtbse of UPEC components long the orbitl pth of the TC. The resulting dtbse provides the opportunity for rnge of TEC nlysis s elborted lter in the thesis.

28 .. Originl contribution to knowledge chieved by this reserch The following section lists wht is new in this reserch nd wht re the min originl contributions to knowledge it effects:. For the first time, methodology hs been developed from first principles to quntify the Upper Plsmspheric Electron Content, from In-Situ electron density mesurements.. As the lst un-quntified component cn now be quntified, the stellite to receiver Totl Electron Content cn be fully nd precisely clculted, cusing improvements in stellite communictions, nvigtion nd rnging pplictions. 3. As this is from In-Situ mesurements, the errors re miniml, providing ccurte mesurements. 4. The equtoril Totl Electron Content behviour is very comple nd not well understood. The development of this methodology opens up wy to nlyse this in detil with precision. 5. The resulting Dtbse of Totl Electron Content is immensely useful in in stellite communictions, nvigtion nd rnging pplictions nd in Spce wether Totl Electron Content modelling nd forecsting. 6. This methodology cn be pplied on ny highly eccentric orbit in equtoril nd mid ltitude regions, generting globl Totl Electron Content dtbse. 3

29 7. This methodology cn be pplied for the entire Plsmspheric Electron Content (PEC) complementing, supplementing nd improving on the eisting methods for PEC mesurements... Totl Electron Content.. Why TEC is importnt? - Prcticl pplictions of TEC mesurements As would be detiled in Chpter, Plsmspheric nd Ionospheric wether impcts on rdio wves trversing through them by wy of mplitude nd phse scintilltion, Group pth dely, RF crrier phse dvnce, Doppler shift of the RF crrier, Frdy rottion of the plne of linerly polrised wves nd ngulr refrction of the wve pth nd distortion of the wveform of the trnsmitted pulses. Of these effects, ll the other effects ecept for the scintilltion effect re proportionl (t lest to the first order) to the Totl Electron Content (TEC).... Appliction tht require high precision electron content clcultions TEC vlues re of criticl importnce in stellite communictions, nvigtion, ltimeter, remote sensing nd militry pplictions. The following sections elborte on these impcts under respective hedings.... Stellite communictions: For stellite communiction pplictions, TEC mesurements re crucil, s the communiction signls re impired in multiple wys s listed bove. Hence, error corrections re progrmmed nd implemented in communiction lgorithms to compenste for the errors encountered in the stellite communiction link. 4

30 The correct quntifiction of electron content figure gretly improves qulity nd precision of the communiction link.... Nvigtion pplictions: Stellite nvigtion hs criticl dependency on the ccurcy of positioning. A Globl Nvigtion Stellite System (GNSS) is constelltion of stellites providing signls tht contin positioning nd timing dt to GNSS receivers, which in turn use these dt to determine their loction by wy of clculting the dely in receiving the signls. The dely stellite signl undergoes is severely ffected by the spce wether events nd the TEC ssocited with the signl pth, s elborted in Chpter. GNSS systems nd other dedicted stellite nvigtion systems re revolutionising eisting industries nd pplictions. At the mentime, entirely new technologies nd pplictions re being developed nd new industries re being formed bsed on these developments. Notble emples re drones, which re being etensively used in new pplictions such s serch nd rescue, surveying, utonomous trnsport, emergency services, security, defence nd delivery services. All these pplictions require high precision guidnce nd nvigtion nd they rely on stellites for these. Therefore, the mimum chievble precision in electron content quntifiction becomes criticl in reducing the errors for these sfety criticl pplictions. GNSS nd other regionl Stellite Nvigtion Systems or dedicted re widely used by wide spectrum of industries nd the pplictions cn be ctegorised s follows: 5

31 Rod Applictions Rod Nvigtion Tolling Emergency Services Trffic Mngement Fleet Mngement & Vehicle Trcking Personl Applictions Pedestrin Nvigtion Outdoor Nvigtion Socil Networking Photogrphy Geocoding Loction Bsed Services Avition Applictions Mritime Applictions Civil Applictions GNSS Augmenttion Systems o Aircrft Bsed o Ground Bsed o Stellite Bsed En Route Nvigtion Approch Attitude Determintion Air Trffic Control En Route Nvigtion Observing the chnges of se level, Dredging opertions, Wrecks loction, Lying pipe lines, Serch nd Rescue of sinking vessels, Dynmic positioning, Positioning of oil rigs nd Fiing of stellite se lunch pltforms Mritime Products Industry Applictions Precision Agriculture Pckge nd Continer Trcking Mining Ril Applictions Trffic Mngement nd Signlling Tble. Civil Applictions of Stellite Nvigtion (ESA, 0) 6

32 Surveying, Mpping nd GIS Lnd Surveying Mpping & GIS Aeril Survey GNSS-bsed Products Personl Products Rod Products Avition Products Scientific Applictions Erth Sciences Spce-time Metrology Fundmentl Physics Spce Applictions Precise Orbit Determintion Stellite Reltime Nvigtion Stellite Formtion Flying Autonomous Applictions Autonomous Driving Autonomous Flying Militry Applictions Militry Nvigtion Trget Acquisition Emergency, security nd humnitrin services Tble. Non - civil Applictions of Stellite Nvigtion (ESA, 0).. Definition of Totl Electron Content (TEC) Totl Electron Content is equl to the totl number of free, therml electrons in unit re (m ) column from the ground to height well bove the pek of ioniztion. This height is nominlly tken s the verge height of the Plsmpuse, bove which the corotting plsm doesn t eist. But s would be indicted in the eqution for TEC in the net prgrph, prcticlly the whole ry pth from the stellite to the receiver should be considered, s electron density long tht pth nd its vrition will ffect the rdio wves trversing the Ionosphere Mgnetosphere system (Breed nd Goodwin, 07; Klobuchr et l., 973). 7

33 Figure. Topside Ionosphere nd Plsmsphere (Rich nd Bsu 985: p.9-)..3 Eqution for the Totl Electron Content (TEC) nd its unit Totl Electron Content (TEC) is defined s the totl electron count in unit re column nd it is equl to the integrl of the electron density over the length of the column ie. r TEC n ( l dl. s e ) Here ne (l) is the electron density long the signl pth from the stellite (s) to the receiver (r). TEC Unit (TECU) is defined s 0 6 el/m 8

34 Here, the upper limit of the integrl is defined s the receiver height. Therefore, this mesure of Totl Electron Content is contetul, depending on the ltitude of the receiver. As such, it will differ for Low Erth Orbit, Medium Erth Orbit nd Geosttionry Orbit stellite...4 Verticl TEC nd Slnt TEC Verticl TEC (bbrevited VTEC, vtec or TECv) is the number of electrons in column of one unit re verticlly below the trnsmitting stellite. Slnt TEC (bbrevited STEC, stec or TECs) is the number of electrons in column of one unit re long the true trnsmission pth between the stellite nd the receiver...5 Incident Angle In single lyer model or thin lyer model, the incident ngle is defined s the ngle the Line of Sight (LoS) between the stellite nd the receiver in the ground mkes with the line connecting the centre of the erth with the Ionospheric Penetrtion Point (Also the zenith ngle t the Sub-Ionospheric Point C in figure.). The Ionospheric Penetrtion Point (IPP) is the point the Line of Sight between the stellite nd the receiver intersects the Centre of Mss column (Centroid) of the Ionosphere, vriously tken to be 300, 350, 400, 40 or 450 km. This height is sometimes considered s the men Ionospheric height too (Gormn nd Soicher, 973). 9

35 Figure. Single Lyer Model Ionosphere nd the Incident Angle..6 Verticl TEC nd Slnt TEC reltionship formul In Ionospheric Totl Electron Content nlysis, if the Ionosphere is considered to be single lyer or thin lyer model, then from the geometry illustrted in Figure.3, the reltionship between STEC nd VTEC is s follows in the net pge: 0

36 VTEC STEC R h R sin e m R e h e m. Where Re is the rdius of the erth is the incident ngle nd hm is the height of the Ionospheric Penetrtion Point (Grner et l., 008). But for the purpose of TEC clcultions, s the R e >>> h m, then Re hm R e Then, formul. cn be pproimted to VTEC STEC cos().3 This form of the reltionship STEC nd VTEC proves to be sufficient for TEC nlysis (Y cob, Abdullh nd Ismil, 00)...7 Averge electron density versus height profile In ny given geogrphic loction, the gretest contribution to the Totl Electron Content comes for the F region of the Ionosphere. The electron density increse drsticlly with height till the F lyer nd reduce eponentilly therefter. In mid ltitude regions, under quite solr conditions, up to two thirds of the TEC is generted by the F lyer (Bsu et l. 985; Wernik, Alfonsi nd Mterssi, 004).

37 Electron density profile with height for Jicmrc sttion 9 Jul 96 Figure.3 Electron density profile with height for Jicmrc sttion 9 Jul 96 (Bsu et l. 985: p0-6)

38 ..8 Globl monthly verge verticl TEC profile Figure.4 Globl Verticl Monthly verge TEC Contours in TEC Units for 000UT Mrch 980 with Equtoril Anomly Regions prominently feturing in the western hemisphere nd over Afric (Bsu et l. 985: p0-90) 3

39 The electron density profile of the Ionosphere (nd Plsmsphere by etension) hs the following vrition ptterns:. Loctionl - Vritions in reltion to geogrphic nd geomgnetic loctions. Diurnl Vritions throughout the dy (lrgely due to solr zenith ngle) 3. Solr ctivity- Vrition occurring due to chnges in solr ctivity; both long term nd disturbnces. 4. Sesonl - Vritions throughout the yer disturbnces 5. Height - Vrition long the ltitude in different lyers (Bsu et l. 985)..9 Geogrphic regionl vrition ptterns Electron density hs three distinctive ptterns of vritions geogrphiclly. The highest vlue for TEC is encountered in the Ner-Equtoril regions. This region is pproimtely bounded by ltitudes ±0 0 to ±5 0 on either sides of the mgnetic equtor. The highest vlue occurs in region pproimtely ± 5 from the Mgnetic Equtor, rther thn in the Equtor itself. This region is clled the Equtoril Anomly region, due to the occurrence of the Appleton Anomly. Mid-ltitudes yield moderte vlues for TEC nd the vritions re mostly predictble in quite solr conditions. The electron density profile nd behviour re well nlysed nd understood in this region thn in the Ner-Equtoril regions. Polr Regions re esily perturbed by CME events nd s such electron density vritions nd TEC vlues re unstble in those regions. 4

40 For sttion in Northern mid-ltitudes, the stndrd devition from monthly men diurnl TEC behviour is 0% -5%. For Ner-Equtoril regions nd the Polr/ Aurorl regions, the stndrd devition is very high. There re instnces where the TEC vlue hs been round 00 TEC units, ner Ascension islnds in the Equtoril Anomly region (Bsu et l. 985)...0 Diurnl or Temporl vrition ptterns of TEC In mid-ltitudes, electron density strts to increse in the morning sunlight nd reches its pek in lte evening. It flls stedily thorough out night hours through the Ryleigh- Tylor instbility mechnism (Li, Ning nd Yun, 007). This pttern holds for most of the sesons in quite solr conditions (Bsu et l. 985). This pttern differs in the Ner-Equtoril regions nd the Polr/ Aurorl regions. In the Ner-Equtoril regions, the electron density strts to rise with sunlight nd increses stedily throughout till sun set. After sunset, the electron density declintion is either slow due to recombintion of ions nd electrons or shows n increse just before midnight, sometimes surpssing the mimum TEC ttined during dytime. This nomly is referred to s the Appleton Anomly nd is more pronounced in high TEC yielding geogrphicl loctions such Ascension Islnd (7 56 S, 4 W). Appleton Anomly is cused by the effect of Ryleigh-Tylor instbilities from the bottom side Ionosphere. During this process, the depleted electron density bubble rises into the region bove the pek of the F lyer. This is cused by the E B drift of the post sunset F lyer, in response to the pre reversl electric field. 5

41 Temporl vrition of TEC in the equtoril nomly region cn be eplined by the vribility of equtoril electrojet strength during solr minimum periods, the dynmics re comple during solr mimum conditions. In Aurorl nd Polr regions, the night time behviour is highly vried nd unpredictble. In these regions, TEC vlues occsionlly surpss dy time mimum vlues. The chnges re rpid too. Specific lrge increses in TEC, unlike generl urorl ctivity re not individully predictble. Sttisticlly, they cn be chrcterised s function of mgnetic ctivity (Bsu et l. 985; Y cob, Abdullh nd Ismil, 00) The following plots indicte monthly diurnl vrition for two loctions in the Ner Equtoril region nd the Mid Ltitude region. 6

42 Figure.5: Monthly overplots of TEC for Ascension Islnd 980 nd 98 (Bsu et l. 985: p0-9) 7

43 Figure.6: Monthly overplots of TEC for Hmilton MS for 979 (Bsu et l. 985: p0-94) 8

44 .3 Plsmspheric Electron Content (PEC or TECp) Plsmspheric Electron Content cn be defined s the totl electron count in the Plsmsphere segment of column of m cross section, long the signl pth from the stellite (s) to the receiver (r). Plsmspheric Electron Content is bbrevited either s PEC (Mzzell 0) or TECp (Gormn nd Soicher, 973). Plsmspheric Electron Content becomes of consequence only in trns- Ionospheric stellite communictions nd nvigtions pplictions. As such geosttionry stellite communictions systems, semi-synchronous orbitl communictions systems such s Molny stellites, GPS, Russi s GLONASS, Europe s Glileo nd the Chinese nd Indin regionl nvigtions systems hve compelled towrds the wide spred use of the trns-ionospheric communiction nd nvigtion pplictions. With the prolifertion of these stellite systems, the need to quntify the Plsmspheric contribution to the TEC prmeter is gining importnce. This scenrio is prticulrly of importnt in the Ner-Equtoril regions, where ioniztion is very high nd where ll the geo-sttionry stellites re positioned. The Plsmsphere occurs from 000 km (the region bove the O+/H+ trnsition height) to the height of the Plsmpuse. The Plsmpuse demrctes the boundry of co-rotting plsm nd beyond which the electron density drsticlly depletes. Plsmpuse height vries with ll the spce wether vribles nd the mimum occurs in the equtoril belt t bout pproimtely bout 7 Re under quite solr conditions. As Plsmpuse reches such heights, Plsmspheric contribution to TEC lso gins significnce. Even though the ltitudes re mildly ionised, the mgnitude of the distnces mke the contribution from the Plsmsphere to be tken into ccount. 9

45 From the Frdy rottion nd dispersive group dely observtions conducted t Fort Monmouth Ocenport, NJ using the ATS-6, on the diurnl s well s dy-to-dy vritions of Plsmspheric content, its bsolute mgnitude ws found to be vrying from to 8 TEC units nd ws nerly lwys bove 50% of the Ionospheric content t night time nd on occsions eceeded 00%. This rtio verged 35% during dy times (Gormn nd Soicher, 973). At southern mid-ltitudes, the Plsmspheric contribution to the Ionosphere- Plsmsphere combined TEC is given t pproimtely 0% during dy time (when electron density in the Ionosphere is high) nd 40-50% during night time (when electron density in the Ionosphere is low). The understnding of the Plsmspheric contribution to TEC t the ner e equtoril region is still evolving study. This reserch strives to nswer prt of tht question by deriving the upper Plsmspheric (bove 000km) contribution from in-situ electron density mesurements from the Double Str TC mission. Plsmspheric contribution to the Electron Content should be nlysed in two prts, due to the fct tht the most prevlent method (with the eception of some geosttionery stellite missions such s ATS-6, which investigted the Plsmspheric content up to orbit height) of clculting the Plsmspheric contribution is GPS dul frequency method. The GPS system hs n orbitl ltitude of 0000 km. Therefore the TEC derived from these clcultions do not provide mesure for the electron popultion encountered bove tht ltitude. Erlier studies of the TEC in equtoril regions utilised Frdy rottion of the single frequency wves from geo sttionry stellites. As would be eplined lter, Frdy rottion of the rdio wve hs the integrl of the product of the electron density times the longitudinl component of the erth s mgnetosphere s its min component. 0

46 This component is negligible in ltitudes more thn 000 km, nd the resulting Frdy rottion is insignificnt for those ltitudes. Therefore, the resulting TEC clcultion only denoted Ionospheric TEC content. Top side sounding technique hs been pplied to Mgnetospheric plsm reserch with renewed interest during the lst decde nd fundmentl new results hd been obtined from Intercosmos-9, Cosmos-809 nd ISS-b missions (Beloff et l., 004). Geo-sttionry stellites nd semi-synchronous (such ds Molniy) orbitl systems hve orbitl ltitudes up to km. Therefore, it becomes impertive tht the upper Plsmspheric contribution to Electron Content should be determined, specilly in the ner equtoril region where the Plsmpuse occurs t up to 7 Re height (Li, Ning nd Yun, 007)..4 Electron density nd TEC mesurement techniques.4. Ionosonde Sounding the Ionosphere with ionosondes is the oldest nd one of most prevlent methods of Ionospheric investigtions. Ionosondes re vrible frequency rdrs tht mesure the time it tkes for the trnsmitted signl to be reflected from the vrious lyers of the Ionosphere. By sweeping its frequency, n ionosonde genertes ionogrms, plotting Ionospheric reflection height s function of frequency. Electron density of the respective lyer is deduced from the plsm frequency eqution; f N N e N e 0.40 f N 3 el / m.4

47 .4. Topside sounders As the ground bsed sounders could only get informtion bout the ionosphere up to the F lyer pek density, the topside of ionosphere informtion ws hrd to come by. Therefore, with the onset of the spce ge, stellite bsed sounders were used to mesure the ionosphere prmeters from bove. This technique is clled topside sounding. As with the ground bsed Ionosondes, topside sounders give informtion bout the criticl frequency of the highest ionised lyer, which is the F lyer normlly, nd hence its electron density. In the event the topside sounding spcecrft height is very close to the mimum ionised lyer height, the topside sounding techniques become complicted. Beloff et l (004) studied the TEC determintion methodology using the trces of the signls reflected from the erth from the ionosonde AI-840 in the MIR spce sttion. To determine the TEC below the orbitl height (hs) of 365 km, the plsm lyer below the stellite ws pproimted by the equivlent prbolic distribution; hs h f N h f m.5 H P Where f N is the electron plsm frequency; f m is the criticl frequency of the F region; hs is the stellite height nd HP is hlf thickness of the prbol. As the trces of the signls reflected from the topside of the ionosphere were recorded in nrrow bnd of frequencies nd the records presented were of low qulity due to strong deflective bsorption, it ws not possible to derive the electron density profile N(h) bove the F region mimum nd determine hmf. Therefore the methodology utilises mesurement of group pths of signls reflected from the erth to derive TEC below orbitl height.

48 The group pths reflected from the erth cn be given by: P hs f h ' f, f, dh ' 0 H.6 h s H p Where f is the sounding frequency; f H is the gyrofrequency; is the ngle between the verticl nd vector of intensity of the geomgnetic filed; h0 is the height of the equivlent bse lyer nd ' denotes the group refrctive indices for ordinry (o) nd etr-ordinry() polrised wves. The technique uses lest squres method nlysis to obtin the hlf-thickness of the prbol nd hence the TEC (Beloff et l., 004).. Integrting.4 with reference to.5 nd. gives: h s 0 TEC Ne hdh.40 f m H P From this, the men squre error of TEC cn be obtined s: s TEC s TEC f f sh p m m H p GPS Duel Frequency Techniques The TEC encountered long ry pth introduces time dely nd chnges to its phse. As GPS signls operte with two frequencies, the TEC cn be deduced by differencing these two quntities from the two frequencies GPS System Description The GPS system is Globl Nvigtionl Stellite System operting in si geosynchronous medium erth orbits with n inclintion of There re 30 stellites in 3

49 the constelltion, with five stellites operting in ech of the eqully spced si orbitl plnes nd one or two uiliry stellites in stndby. Due to this set up, ny geogrphic point on the surfce of the erth will be in Line of Sight (LOS) to 8-0 stellites or /3 of the constelltion t ny given time. The orbits hve period of siderel hours nd 58 minutes nd most importntly will remin within the ground receiver s field of view of 60 0 for 8 hours. The system hs typicl dt rte of 33.3 MHz corresponding to n ngulr difference of between djcent slnt pths. Due to the orienttion nd the period of the constelltion the GPS line of sight between the receiver nd prticulr stellite chnges only 5 0 within 5 minutes nd the system mkes 30 mesurements during tht period. Even though the time frme of 5 minutes is resonble for lrge scle Ionospheric nd Plsmspheric dynmics, the sptil chnge of 5 0 is not substntil enough. Therefore the resulting TEC mesurement cn detect temporl vritions within the Ionosphere nd Plsmsphere system not good enough for horizontl vrition. The GPS system works on two L bnd frequencies, L= MHz nd L 7.60 MHz (Grner et l., 008; Bsu, 003) GPS TEC Derivtion: The GPS duel frequency TEC Derivtion technique mkes use of the two components; the pseudornge ρ nd the crrier phse Φ. ) Pseudornge Method: The pseudornge method is the most stright forwrd TEC mesurement method of the two. The pseudornge eqution is s follows: b B e E Ct I v c D c t r t s.9 4

50 Where D is the true rnge, c is the speed of light, B nd b re the stellite nd receiver clock bises, E nd e re the electronics time dely within the stellite nd receiver, T is the dispersionless Tropospheric time dely, I is the Ionospheric time dely, vρ is the signl nd multipth noise, nd ts nd tr re the clock time t the stellite nd the receiver. The pseudornge cn be clculted t both frequencies nd thus the nondispersive components cn be removed. Thus we cn write: L L.0 c e e E E v v I I. L L L L L L L L This cn be rerrnged to: I e E v. c e nd E re referred to s the inter-frequency bis in the stellite nd the receiver. They re difficult to quntify nd re sensitive to locl temperture nd pressure vritions. Hence they re treted s noise terms. The Ionospheric time dely cn be determined from the first order Ionospheric inde of refrction: f P f. ds This is given by: I c e 8 c m 0 e f nds STEC.3 f 5

51 Where f P e n 4 m 0 e is the plsm frequency, f is the frequency of the rdio signl, e is the chrge of electron, n is the electron density, 0 is the permittivity of free spce, m e is the electron mss nd ds is the incrementl slnt pth. Using the first term in the binomil series for f P f f P f nd combining. nd.3, one gets: STEC 8 m f. f 0 L L e f L f L c e E v 3 m ce E 6 STEC v.4 The drwbck of deriving TEC from pseudornge method is tht there is quite lrge noise term v in the finl epression nd the inter- frequency bises cnnot be ignored. b) Crrier Phse Method: The crrier phse chnge in both frequencies is used to determine TEC long the signl pth. The reltionship of crrier phse is given by: b B e E T I v D c m.5 Where is the wve length, v is the noise in the phse nd m is whole number, representing the phse mbiguity. Applying this eqution in both frequencies the TEC cn be derived from: L L L L I e E v m f L f L e STEC.6 f. f 8 m L L 0 e It is significnt tht the crrier phse noise v much smller thn the pseudornge noise v typiclly by two orders of mgnitude. However, the phse 6

52 mbiguity m cretes significnt offset nd inter- frequency bises cuse errors nd cycle slips cretes more problems in this method too. But there hve been developments to remove these discrete discontinuities in the crrier phse before the TEC is computed. It should be noted tht the TEC vlued cn be deduced from GPS mesurements for only sub 000 km ltitudes (Grner et l., 008)..5 GLONASS With the need for stellite bsed nvigtion system for militry nd civilin uses rising, the Russi developed stellite nvigtion system bsed on one-wy rnge mesurements. This system, developed prllel to the United Sttes GPS, is clled GLONASS (Globl Nvigtion Stellite System) nd is continued by the Russin Federtion. GLONASS hs similr pplictions to those of GPS in precise nvigtion uses in lnd, se, ir nd low orbiting spcecrft. Besides this, GLONASS signls cn be used for the dissemintion of highly precise globl nd locl time scles nd estblishing globl geodetic coordinte systems nd locl geodetic networks. GLONASS provides stndrd precision (SP) nd high precision (HP) nvigtion signl, similr to the Stndrd Positioning Service (SPS) nd the Precise Positioning Service (PPS) of the GPS. These signls re lso referred to s Chnnel of Stndrd Accurcy (CSA) nd Chnnel of High Accurcy (CHA), respectively. The SP signl is vilble to ll civil users globlly on continuous bsis. GLONASS nvigtion systems re incresingly being incorported into stellite nvigtion receivers, smrt phones nd other ppliction either s stnd-lone systems or s complementry systems long with GPS (Rossbch, 00; Polischuk et l., 00). The GLONASS constelltion orbits in three co-plnr semi geo-synchronous, medium erth orbits with 64.8 degree inclintion nd period of hours nd 5 7

53 minutes. With eight stellites in ech plne spced 0 0 in longitude between the plnes, the constelltion chieves globl coverge with 4 stellites. The constelltion s orbitl prmeters mkes it especilly suited for usge in high ltitudes (north or south), where getting GPS signl cn be problemtic (Polischuk et l., 00). The following tble provides comprison between the orbitl nd stellite communiction prmeters of the GPS nd GLONASS systems: Prmeter GLONASS GPS Semi-mjor is 550 km 6580 km Orbitl height 930 km 000 km Orbitl period h 5.8 min h 58 min Inclintion Eccentricity Distinguishing between stellites FDMA ( code, multiple frequencies) CDMA ( frequency, multiple codes) Frequency L MHz MHz Frequency L MHz 7.60 MHz Signl polriztion RHCP RHCP Tble.3 Comprison between the orbitl nd stellite communiction prmeters of the GPS nd GLONASS systems (Rossbch, 00) According to Sergei Ivnov, the Kremlin Chief of Stff (04), the ltest genertion of GLONASS K stellites hve n ccurcy of.9 metres (Bodner, 04). 8

54 .6 Glileo GNSS The Glileo progrm is the GNSS progrm of The Europen Spce Agency. It is still under development, with only two eperimentl GIOVE (Glileo In-Orbit Vlidtion Element) stellites hving been lunched. Similr to GPS nd GLONASS, the orbits will be Medium Erth Orbits t n ltitude of 3 km with period of bout 4 hours. There will be three orbit plnes t n inclintion of 56 to the equtor. The constelltion will consist of 30 stellites with 0 stellites orbiting in ech plne. One stellite in ech orbitl plne will be stndby stellite. The system is interoperble with GPS nd the combined system will be of high relibility. GLONASS signls cn lso be utilised in receiver units nd such units will hve very high ccurcy stndrds owing to the fct tht they get input signl from three independent GNSS systems. Unlike GPS nd GLONASS, the Glileo is purely civilin project. Another mjor difference or upgrde from these two previous GNSS is the Serch nd Rescue cpbility, by which n orbiting stellite is ble to pick up distress signls from ground receiver nd rely it to serch nd rescue personnel on erth. (Hpgood, 99)..7 Descriptions of some relevnt orbit types.7. Geo Synchronous Orbits A Geo Synchronous orbit is n orbit round the Erth with n orbitl period equl to one siderel dy, (Erth's siderel rottion period which is pproimtely 3 hours 56 minutes nd 4 seconds). As the nme implies, the synchroniztion of the Erth s rottion nd the orbitl period mens tht n object in geosynchronous orbit returns to ectly the sme position in the sky fter period of one siderel dy for n observer on the surfce of the Erth. During the period of 9

55 siderel dy the object trces out the shpe of n nlemm. The reltionship between the semi-mjor is nd the period of n orbit is given by: 3 P where is the semi-mjor is, P is the orbitl period, nd μ is the Geocentric Grvittionl Constnt, which is equl to m 3 /s. As the orbitl period is the only vrible in the right hnd side of the bove eqution, ll orbits with the sme orbitl period hve the sme vlue for semi- mjor is. Therefore, ll Geo Synchronous orbits hve the sme semi-mjor is, irrespective of whether they re circulr or ellipticl in shpe, s they ll hve the sme orbitl period of one siderel dy..7. Semi (Geo) Synchronous Orbits A semi-synchronous orbit is defined s n orbit with hlf the period of the verge rottionl period of the body tht is being orbited nd rotting in the sme direction of the min body's rottion. For Erth, Semi (Geo) Synchronous Orbit is considered to be n orbit with period of hlf side rel dy, which is just below hours nd of n ltitude bout 0,000 kilometres bove se level (medium Erth orbit) (Bockstiegel, Benko nd Hobe, 005). The prentheses nd the word Geo re being used to indicte tht the orbit is n Erth orbit. Prcticlly, Semi (Geo) Synchronous Orbit is nerly circulr nd hs rdius of 6,560 kilometres from the centre of the Erth. As the Erth hs side rel period of rottion of pproimtely 4-hours (3 hours 56 minutes nd 4 seconds), stellite in Semi (Geo) Synchronous Orbit, crosses over the sme two spots on the equtor every dy. GPS stellites re deployed in this orbit. The orbitl pttern is simple, less comple nd highly predictble. 30

56 .7.3 Molniy Orbit Figure.7 The Molniy orbit digrm illustrting orbitl positions of the stellite with time (Ns Erth Observtory, 0) As much of the former Soviet Union s territory ws locted t high ltitudes, it ws imprcticl to brodcst to those ltitudes from geosttionry orbit due to the low elevtion ngles. Hence, the then Soviet spce scientists devised the Molniy orbit, which ws nmed fter series of communictions stellites by the sme nme, which hve been using this type of orbit since the mid-960s Molniy orbit is highly ellipticl orbit with n inclintion of 63.4 degrees. Its rgument of perigee is 90 degrees nd its orbitl period is one hlf of siderel dy. As such, it is specil type of Semi (Geo) Synchronous Orbit. As illustrted in Figure.7, stellite in this highly eccentric orbit spends most of its time in the neighbourhood of pogee. The sub-stellite point t pogee for 3

57 Molniy orbit stellite is t ltitude of 63.4 degrees North, therefore it spends most of its time in the high ltitudes of the Northern hemisphere,. Furthermore, s the pogee ltitude is very high 40,000 km, the orbit hs n ecellent visibility of the Northern hemisphere, including the former Soviet Union, Northern Europe, Greenlnd Cnd nd Alsk for considerble period of time round the pogee. Nevertheless, t lest three Molniy spcecrft re needed to get continuous high elevtion coverge of the northern hemisphere. In order to keep the rgument of perigee t 90, not perturbed by the J term of the grvittionl field of the Erth, the inclintion is computed to hve the vlue of (Ns Erth Observtory, 0; Piscne, 005).7.4 Geo Sttionry Orbit A Geo Sttionry Orbit is unique geosynchronous orbit which hs the Erth's equtoril pln s its orbitl plne nd is of circulr orbitl profile. Therefore its eccentricity is zero nd inclintion is 0 o. A Geo Sttionry Orbit hs rdius of pproimtely 4,64 km mesured from the centre of the Erth nd n ltitude of pproimtely 35,786 km bove men se level. A stellite in Geo Sttionry Orbit remins in the sme position reltive to the Erth's surfce nd hence it does not ehibit diurnl motion, Arthur C Clrke is widely credited with proposing the concept of globl telecommunictions coverge with three stellites positioned t equidistnce in the Geo Sttionry Orbit, though the ide of Geo Sttionry Orbit hd been proposed erlier. The Geo Sttionry Orbit is lso clled s Clrke Orbit in respect of the science fiction writer. 3

58 Chpter Ionospheric nd Plsmspheric effects. Introduction to Ionospheric nd Plsmspheric effects on rdio wves Electromgnetic wves trversing the Ionosphere nd the Plsmsphere encounter free, therml electrons. Chnges in the electron density long the signl pth nd differing dielectric qulities of the ionised plsm impct rdio wves in severl wys nd the resulting effects crete mny constrins nd problems on the qulity of communiction, nvigtion, surveying nd on rnging pplictions. The min effects Ionosphere nd Plsmsphere impct on rdio wves trversing through them re: ) Amplitude nd phse scintilltion ) Group pth dely 3) RF crrier phse dvnce 4) Doppler shift of the RF crrier 5) Frdy rottion of the plne of linerly polrised wves 6) Angulr refrction of the wve pth 7) Distortion of the wveform of the trnsmitted pulses Ecept for the scintilltion effect, ll the other effects re proportionl (t lest to the first order) to the Totl Electron Content (Bsu et l., 985). The bove effects re described briefly below:. Amplitude nd phse scintilltion Distortions in phse nd mplitude of rdio wve such s fding, phse devitions nd ngle of rrivl vritions re clled Scintilltions. These effects vry with signl 33

59 frequency, mgnetic nd solr ctivity, time of dy, seson nd ltitude. Indices hve been developed to quntify the mount of vritions in mplitude nd phse...6 Amplitude scintilltion indices Two indices re being utilised to quntify the intensity of Ionospheric scintilltions. They re: S4 Inde nd SI (Scintilltion Intensity) Inde The bove two indices re generlly used in two different scenrios. The mplitude or the intensity vrition is chrcterised by the vrince in the received power nd it is equl to the normlised second centrl moment of signl intensity fluctutions. This is denoted by the S4 inde: I I I S 4. Here the quntity I I denotes the vrince of the received power nd I denotes the men vlue of the received power (Bsu et l., 985; Béniguel, 0) The SI (Scintilltion Intensity) inde is less comple nd cn be used for dt deduced mnully from chrt records. The formul for the SI inde is given by SI P m Where Pm is the power level of the third pek down from the mimum ecursion of the scintilltions nd Pmin is the level of the third pek up from the minimum ecursion, mesured in db. 34 min m min. P P P

60 The S4 inde is used more often thn the SI inde s dt cn be deduced utomticlly with computer pplictions... Phse scintilltion inde The phse scintilltion inde or the stndrd devition of phse fluctutions cn be obtined from: Where eff irregulrities nd K f N e GF k N, p N.3 (Bsu, 003) is the effective scn velocity of the propgtion pth through the c is the dt intervl tht corresponds to /fc, where fc is the low frequency cut off of the detrend filter. S4 nd re sttisticl vribles computed over resonble time period. Here resonble time depends primrily on the effective velocity of the stellite ry pth nd it my vry from 0 to 00 seconds. Both these quntities re derived from detrended time series to nlyze only the fluctutions of the intensity nd phse. As mentioned erlier they depend on the density fluctutions in the medium. They cn be relted to physicl prmeters through phse screen theory (Rino, 979). In S4 clcultions, for irregulrity scle sizes less thn the Fresnel scle F, F hs vnishing mplitude nd F r is given by:. F r z.4 Where is the rdio signl wvelength nd z is the distnce from the observer to the Ionospheric phse screen (~350 km or more). For L frequency F r is typiclly r 35

61 meters; density fluctutions lrger thn this scle size will not cuse GPS mplitude scintilltions...3 Clssifiction of Scintilltions Scintilltions re generlly clssified into insignificnt, wek nd strong ccording to their S4 vlues, by the following criteri: Insignificnt: S4 < 0.3 Wek: 0.3 < S4 < 0.6 Strong: S4 > 0.6 Some rdio stronomy pplictions my suffer from effects such s imge degrdtion even during insignificnt scintilltions, ie S4 < Reltionship between SI nd S4 indices SI = 7.3 S Frequency dependence of scintilltions The S4 inde shows frequency dependence of f -.5 over the frequency rnge 00 MHz 3000 MHz, where f is the frequency of the signl being trnsmitted..3 Group Dely or Group Pth Dely The dditionl time dely, over the free spce trnsit time of signl trnsmitted from bove the Ionosphere to erth s surfce is given by 40.3 t TEC cf s.6 36

62 Where TEC s is the slnt totl electron content, c is the speed of light nd f is the frequency of the signl (Bsu et l., 985; Klobuchr et l., 973). For system operting t GHz, TEC vlue of 0 8 would mke time dely of 34ns nd rnge error of 40. m. For low frequency systems, the impct is very severe. A 00 MHz system would produce time dely of 3.4 ms nd rnge error of more thn 4 km, under the sme TEC circumstnces. The following grph illustrtes the vrition of Time Dely with frequency for vrious vlues of TEC: Figure. Vrition of Time Dely with frequency for vrious vlues of TEC (Bsu et l., 985: p0-84) 37

63 .4 RF Crrier Phse Advnce The phse of the crrier of the rdio wve is dvnced by the Ionosphere/Plsmsphere system when compred to free spce trnsmission. This effect is clled the RF Crrier Phse Advnce nd is etremely criticl in determining the velocity of the spce objects by wy of rnge rte mesurements. The phse increse is given by; TECcycles.7 f Where TEC totl electron content nd f is the frequency of the signl (Bsu et l., 985).4. Differentil crrier phse GNSS stellites trnsmit two coherently- derived crrier frequencies for differentil crrier phse mesurements. These re in ddition to the dul frequency identicl modultions trnsmitted. For GPS frequencies L nd L, the differentil crrier phse shift, referenced to the lower frequency is m TEC cycles L m 7 Where m= m f f.833, 4.30 TEC or / el / m per complete cycles of differentil crrier phse between L nd L, mesured t L. 38

64 .4. Second difference of crrier phse The second difference in phse between n RF crrier nd tht of its upper nd lower sidebnds cn be used to mesure bsolute vlues of TEC. For three coherently derived frequencies, f f m, f, f f m, the trnsmitted second difference of phse is: From.7 When U C C L U L C f. TEC( cycles ) m.0 f f f m f f m f. TEC( cycles ) 3 m f. [].5 Doppler Shift The chnging TEC in the pth of the wve propgtion dds to geometric Doppler Shift. This effect is cused s the frequency of ny signl is the time derivtive of its phse. The Doppler shift component due to the chnging TEC is given by: f d.340 dt f 7 d TEC dt (Hz). 39

65 Even though electron density vritions long the signl pth crete Doppler shifts, the results re not significnt. For high orbit stellites, where the diurnl chnges in TEC re greter thn geometric ones, the upper limit to the rte of chnge of TEC is pproimtely el.m -.s -. This results in n dditionl frequency shift of less thn 0. Hz for.6ghz nd for 400MHz the figure will be 0.3 Hz..6 Frdy Polriztion Rottion A linerly polrised rdio wve tht is trversing the ionosphere, undergoes rottion of the plne of polriztion nd it is clled the Frdy polriztion rottion. The TEC vlue cn be deduced from the mount of Frdy polriztion rottion undergoes while trversing the Ionosphere nd the technique hs long been used in mesurement of TEC. In high-frequency nd qusi-longitudinl pproimtions, the two mgneto-ionic modes re nerly circulrly polrized in opposite senses. A plne polrized wve trversing n ionised dielectric medi such s the Ionosphere cn be regrded s the vector sum of its ordinry nd etrordinry components. But these two components trvel t different phse velocities nd s result the plne of polriztion rottes continully long the signl's pth. This rottion is clled the Frdy Polriztion Rottion. The totl rottion from the signl source to the observer is relted to the totl electron content by the epression: B N edl f.cos..3 40

66 Where B is the locl mgnetic field flu density in gmms, is the ngle between the rdio wve norml nd the mgnetic field direction. Thus B. cos.n represents the product of electron density times the longitudinl component of the erth s mgnetic field integrted long the signl pth (Bsu et l., 985; Gormn nd Soicher, 973). e As the longitudinl mgnetic field density chnges much slower thn the electron density of the Ionosphere, the eqution cn be pproimted to: K BL TEC.4 f Where B L B.cos nd is tken t the men Ionospheric height, 5 K.360. One very importnt note bout the Frdy rottion technique in determining the TEC vlue is tht the technique does not give out vlue tht is representtive of the entire distnce trversed by the rdio wve. This is becuse, the term B. cos.n, which e represents the product of electron density times the longitudinl component of the erth s mgnetic field becomes insignificnt in heights bove the Ionosphere, becomes insignificnt bove Ionospheric ltitudes, since B decreses inversely with the cube of the geocentric distnce, nd the electron density decreses eponentilly with ltitude bove this region. Therefore, the integrl is hevily weighted in ner spce ltitudes nd the Frdy rottion technique is considered to provide TEC vlues t ltitudes below I00 km only (Gormn nd Soicher, 973). The following grph gives vlues of Frdy polriztion rottion ginst frequency for Northern mid ltitude sttion for different vlues of TEC. 4

67 Figure. Vrition of Frdy Rottion with frequency for vrious vlues of TEC t northern mid ltitude sttion: (Bsu et l., 985: p0-87) From the figure. t nominl commercil stellite trnsponder frequency bnd of 4GHz, the resulting Frdy rottion is round 0. rd nd this figure is well bove wht is required for dul, liner orthogonl chnnel seprtion. Frdy rottion is mjor hindrnce in stellite communiction s the receiver gets polriztion rottion of nerly n odd integrl multiple of 90 0 resulting in no signl received t the receiver s linerly polrised ntenn. As result, the receiver ntenn needs to be religned to obtin mimum received signl. Circulr polriztion techniques re used to overcome Frdy rottion problem, but t the cost of received signl power. 4

68 .8 Angulr Refrction Electromgnetic wves entering the Ionosphere get bent s in the optics. The refrctive inde of the ionosphere produces ngulr refrction incresing the pth length the signl ry tkes from the stellite to the receiver. The resulting rnge error is given by: E R r0 sin h i E0( r0 cos E0) R r h r sin E R 0 i Where: E0 is the pprent elevtion ngle, R is the pprent rnge, r 0 is the rdius of the Erth nd h i is the Centroid of the TEC distribution, normlly between 300 km nd 400 km. The R quntity is clculted from R (40.3/ f ) TEC 43

69 Chpter 3 : Mission Overviews ATS-6, Cluster II, Double Str, nd C-NOFS In this chpter, brief introduction is given to four missions; ATS-6 (974), Cluster II (000), Double Str (004) nd C-NOFS (008), which hve relevnce to this reserch. They re presented in the chronologicl order of their lunching nd effort hs been tken to briefly outline their eperiments relting to electron density profiles nd/or TEC. 3. Applictions Technology Stellite-6 ( ATS-6 ) ATS-6 ws NASA eperimentl stellite lunched in My, 974 nd decommissioned in July 979. Along with scientific eperiments, the mission lso hd other purposes including telecommunictions, Air Trffic Control testing, stellite ssisted serch nd rescue, pioneering direct TV brodcsting nd brodcsting eductionl progrmmes. It ws the most powerful telecommuniction stellite in orbit t the time of its lunch. It ws lso the first 3-is stbilized spcecrft in geosttionry orbit nd ws the first to use electric propulsion in geosttionry orbit with success. The mission crried out 3 eperiments, which included prticle physics eperiments. The first hevy ion detection in geosttionry orbit ws chieved by ATS-6. It lso crried n eperimentl rdiometer subsequently crried s stndrd instrument bord wether stellites. The Rdio Becon Eperiment (RBE) bord the ATS-6 offered the first opportunity to the western scientific community to determine the TEC nd/or the signl propgtion dely to geosttionry ltitudes. More importntly, the becon pckge provided the opportunity to conduct two relevnt eperiments. The first utilized the Frdy rottion 44

70 technique for determintion of TEC. The second utilized the dispersive group dely technique which is independent of the mgnetic field nd determined the TEC to geosttionry ltitudes. The difference between the vlues of the integrted electron content obtined by the two techniques yields the content from I00 km to geosttionry ltitudes, i.e., the Plsmspheric electron content. This is scenrio becomes possible due to the fct tht the Frdy rottion technique would yield the TEC vlue predominntly to the Ionospheric heights, s elborted in section.6. Gorrnn, Jr. nd Soicher of Communictions/Automtic Dt Processing Lbortory, U. S. Army Electronics Commnd (974) nlysed the ATS-6 RBE dt to determine the Plsmspheric TEC nd its vritions using the difference of results between the bove two methods (Gormn nd Soicher, 973). In generl, the observed Plsmspheric content ehibited diurnl s well s dy-to-dy vritions, with its bsolute mgnitude vrying from to 8 TEC units (0 6 el/m ). During night times, the Plsmspheric content ws nerly lwys bove 50% of the Ionospheric content nd on occsions eceeded 00%. During the dy, this rtio verged t 35%. Gorrnn, Jr. nd Soicher used the bbrevition TECp to denote the Plsmspheric Electron Content in their work. Therefore, the sme bbrevition hs been in the following sections, which present the methodology used by them nd the results obtined. 3.. The methodology employed in determining the Plsmspheric Electron Content ) Frdy Rottion Technique From.3, the totl rottion from the signl source to the observer is relted to the TEC by the epression 45

71 .360 f 5 s 0 B.cos. N ds 3. e.360 f 5 s 0 B.cos.sec N dh 3. e Where is the ngle between the wve norml nd the verticl, equl to incident ngle. Fort Monmouth (Monmouth County, New Jersey, US) from where the dt were tken is mid ltitude loction with coordintes N, W. Therefore the ngle vlue will be very significnt for rdio wve from geo sttionry stellite such s ATS-6. As mentioned erlier, the reltionship would yield the TEC vlue predominntly to the Ionospheric heights. The term B.cos. sec in the eqution 3. (denoted by M ) cn be tken out of the integrl sign nd replced by its vlue t "men" Ionospheric ltitude, h (40 km). This will give:.360 f 5 M s 0 N e dh f 5 M TEC I 3.4 Where TECI is the Ionospheric TEC mesured by the Frdy rottion technique. At Fort Monmouth, where the numericl vlue for ws 569, for TEC unit nd for f =40 MHz, Gorrnn, nd Soicher clculted to be equl to b) Dispersive Group Dely Technique Using the dispersive-group-dely technique, the phse of the modultion envelope between crrier nd its sidebnd ws compred t two frequencies 46

72 (nominlly f = 40 nd 360 MHz with sidebnd displcements of f = + MHz. As shown erlier, s the phse is insensitive to the erth's mgnetic-field, this technique yields the TEC long the entire pth from stellite to receiver. dely is: From eqution.6 for two signls t frequencies fl nd f, the differentil time 40.3 t c f f TEC If the two signls re modulted by sidebnd seprted by n equl s 3.5 f, then the modultion time dely tm is equl to the differentil group time dely, i.e., t t m. 360 f f 40.3 c f f t m TEC s 3.7 Where is the differentil modultion phse shift in degrees. From this, it cn be written: TEC G. 360 f c sec f f 3.8 Where TECG is the TEC up to geo-sttionry orbit height. At Fort Monmouth for TEC G = 0 6, phse difference of ws mesured. 3.. Results obtined The results of these mesurements were studied by the reserchers nd plotted grphiclly. The following grphs presented in the forthcoming pges provide some of the observtions: 47

73 Figure 3.: Vrition of Totl Electron Content up to geo-synchronous orbit height nd Ionospheric electron content (TECG nd TECI) t 5-minute intervls from 600 EDT, 3 July 974 to 0800 EDT 8 July 974 t Fort Monmouth, NJ, USA. Equivlent time-delys for.6 GHz signls re lso indicted (Gormn nd Soicher, 973: p448). 48

74 Vrition of Plsmspheric electron content Figure 3.: Vrition of Plsmspheric electron content ( TEC ) plotted for ech dy. The figures re from the sme dt of figure 3.. The P equivlent time delys re mrked s well (Gormn nd Soicher, 973: p449). 49

75 Vrition of the rtio of Plsmspheric to Ionospheric electron contents Figure 3.3: Vrition of the rtio of Plsmspheric to Ionospheric electron contents in percentge (Gormn nd Soicher, 973: p450). TEC TEC P I 00% The redings re from the sme dt s Figures 3. nd 3. nd tken in 5 minute intervls. 50

76 Plsmspheric electron content to TEC to geo-sttionry height in percentge Figure 3.4: Vrition of the rtio of Plsmspheric electron content to Totl electron content to geo-sttionry height in percentge, ie. TEC P TEC G 00%. (Gormn nd Soicher, 973: p45).the redings re from the sme dt s Figures 3., 3. nd 3.3 nd tken in 5 minute intervls. 5

77 3..3 Observtions Figure 3. shows the vrition of the totl electron contents mesured by the Frdy rottion nd group dely techniques, t 5-minute intervls for the time period 600 EDT on 3 July to 0800 EDT on 8 July. They provide the temporl vritions of nd TECI TEC G respectively nd were seen to be nerly prllel with most density vritions observed on both curves. It is very interesting to note the response to the two solr flres during the time period of observtion. The two prominent increses in TEC between 0945 EDT nd 000 EDT on 4 July, were due to the solr flres (Figure 3.). TECI cn be seen to be incresed by bout.5 TEC Units, while TEC G incresed by bout TEC Units. As the frequency of redings is 5 minutes, the Figure 3. is not ble to disply the fluctutions in better resolution. As result, the full increse of Strting t 0953 EDT, TECI nd TEC G re not displyed. TECI cn be seen to be incresed by bout 3.3 TEC Units in 3 minutes nd then decying to its previous vlue t 000 EDT. increse by pproimtely the sme mount, t the sme time. Units, while On 5 July between 730 EDT nd 745 EDT, t 740 EDT with similr increse. TECG cn lso be seen to TECI incresed by bout.9 TEC TECG incresed by.3 TEC Units. The rpid increses cn be seen strting TECI incresing by. TEC Units in 6 minutes. TECG displys It cn be noticed tht the equivlent signl-dely time corresponding to the VTEC distribution t.6 GHz (in the nvigtion frequency bnd) ws lwys below 5 nnoseconds for the time period nlysed. The following observtions cn lso be mde regrding the time dely: 5

78 On different dys, the time dely vried by s much s 60% between the mimum nd minimum on ny one dy nd the lrgest ws. Superimposed on the norml diurnl vritions of the content were qusisinusoidl vritions which usully occur ner the time period of mimum TEC in the dily cycle. 3 Mostly, these vritions were cused by Ionospheric irregulrities. As illustrted erlier, the dispersive-group-dely technique mesures the TEC from the receiver to the stellite ( TEC, wheres the Frdy rottion technique yields G the TEC only up to the Ionosphere ( TEC ). Therefore, the difference between the two yields the Plsmspheric Electron Content ( TEC ). Hence: I P TEC G TEC TEC 3.9 I P The Figure 3. ehibits the vrition of TEC P for the sme time intervls nd for the sme time period s tht of Figure 3.. It could be seen tht the Plsmspheric content ( TEC ) rnged from to 8 TEC units, or equivlently from bout 0.5 to over 4 P nnoseconds for.6 GHz signl. It could be generlised for this Figure tht the minimum of the Plsmspheric content ( TEC ) occurred close to Ionospheric sunrise while its mimum occurred P close Ionospheric sunset. It is lso noticeble tht during ny single dy, the diurnl vrition ws not s pronounced s the corresponding vrition of the totl or Ionospheric electron contents ( TEC or G TEC I ). The mimum vrition, by fctor of 53

79 3.4, could be observed on 5 July. This is compred to TEC G vrition by fctor of for the sme dy. The dy-to-dy vribility ehibited chnges of up to 300% during comprble locl time periods, for emple on 4 nd 7 July during night time hours. Figure 3.3 displys the rtio of Plsmspheric to the Ionospheric electron content, ie. TEC P TEC I 00%. The mesure is of gret importnce to the pplicbility of globl time dely models bsed on TEC dt obtined by the Frdy rottion technique, s it is of the sme mgnitude s the vrition of the rtio of Plsmspheric to the Ionospheric time delys. From the Figure 3.3 in could be seen tht this rtio shows diurnl s well s dy-to-dy vribility. Throughout the observtion period, the rtio ws nerly lwys bove 50% nd on occsions eceeded 00% between 000 nd 0700 EDT. After this time-period, the rtio decresed to its minimum t round 00 EDT, fter when it incresed with the time of dy. From EDT, the verge rtio incresed from round 30% to round 40 %. A similr rtio nlysis, with the rtio of the Plsmspheric to the Totl electron content up to the geo-sttionry height, ie. TEC P TEC G 00%, is provided in Figure 3.4. This rtio would lso give the sme quntity in rtio between the timedelys due to free electrons long the signl's pth long the two heights too. The diurnl nd dy-to-dy vribility of this rtio cn be observed to be similr to tht of TEC P TEC I. During the night the rtio is seen to be high, reching vlue up to 70%. During the dy, the rtio ws much lower, verging from bout 5 % to 30%. 54

80 3..4 Conclusions The reserchers (F. J. Gorrnn, Jr. nd H. Soicher) concluded tht the group pth dely of nvigtion signl due to free electrons in the Plsmsphere cnnot be neglected when it is compred to the dely due to the Ionosphere. They lso concluded tht the Group pth dely prediction models bsed on Frdy rottion dt lone would not dequtely compenste for the totl dely; t night, they my be differing by more thn 50%, nd during the dy by n verge of bout 35%. This is in ddition to other prediction errors, i.e., differences between observed nd predicted vlues of the dely times. Furthermore, they opined tht the Ionospheric Frdy rottion prediction models cnnot be corrected by dding constnt offset to ccount for the Plsmspheric dely, since the Plsmspheric content ehibited diurnl nd dy-to-dy vrition. Fortuntely, the highest rtio of Plsmspheric-to-Ionospheric dely time occurs t night, when the totl dely time is reltively smll. As this reserch ws crried out in 974, the bove conclusions cn be termed s being in the erly stges of understnding of the Plsmspheric Electron Content nlysis. The present stte of knowledge in the sector hs progressed substntilly nd the behviour of Plsmspheric Electron Content hs been nlysed in much more detil. Even then, the results obtined in the study re much more relevnt nd they provide bsolute vlues for thetec, its vrition nd the frctionl vlues reltive to TECInd TEC G. P The reserchers lso commented on future developments with regrd to rtios of Plsmspheric-to-Ionospheric delys from future dt t other geogrphic loctions under condition different from the mid-ltitude sttion (Fort Monmouth) nd under different conditions unlike the quiet phse of the solr cycle this set of dt ws tken from. During such phse nd t such loction, it is obvious tht the group dely 55

81 vlues re generlly smll. They noted tht it remins to be seen if the observed rtios will be mintined when dely times will be lrge, such s during the mimum phse of the solr cycle nd if such rtios re mintined during the mimum of the cycle, neglecting the Plsmspheric content will cuse errors eceeding the ccurcy requirement of the system. They opined tht the future modelling schemes should yield corrections within the ccurcy requirements of the proposed nvigtion systems. One very importnt drwbck of this nlysis is tht the Fort Monmouth sttion is mid-ltitude sttion nd rdio signl from geo-sttionry stellite mkes very lrge incident ngle. The suitbility of using thin lyer Ionospheric model in clcultions nd the resulting ccurcy is debtble. Moreover, the resulting TEC vlues cnnot be treted s verticl TEC vlues for the mid ltitude sttion s most of the Plsmspheric regions the rdio wve would be trversing would be bove ner equtoril regions, which ehibit very high electron density vlues thn mid ltitude regions. Nevertheless, the resulting percentges nd rtios re well in conformity with the previling knowledge bout Plsmspheric electron content behviour nd for tht reson this premier reserch nd its finding re impertive. 3. The Cluster Mission Cluster is constelltion of four spcecrft flying in tetrhedron formtion round the Erth in closely formed synchronous polr orbits. The min objective of the Europen Spce Agency progrm with NASA prticiption Cluster II progrmme is to study the smll-scle sptil nd temporl chrcteristics of the Mgnetospheric nd ner-erth solr wind plsm over the course of n entire solr cycle.. 56

82 The tetrhedron formtion fcilittes the three-dimensionl dt collection of how the solr wind intercts with the Mgnetosphere nd ffects ner-erth spce, including Aurore. The four Cluster spcecrft hve ccumulted more thn 7 yers of dt pssing in nd out of the Erth s Mgnetosphere, since their lunch in July-August 000. Cluster II is one of the longest serving missions in the history of humn spce eplortion. Cluster mission ws first proposed in November 98 nd pproved in 986 to study the 'cusp' nd the Mgnetotil regions of the Erth's mgnetosphere with polr orbiting mission. Along with the Solr nd Heliospheric Observtory (SOHO) progrm, the two missions were cornerstones of the ESA's Solr Terrestril Physics Horizon 000 missions progrmme. The originl Cluster spcecrft were destroyed in the eplosion of the Arine 5 rocket s first lunch in 996. The Cluster II is the follow up mission consisting of one spcecrft built from the spre prts of the initil progrm nd three newly built spcecrft lunched in two Soyuz rockets. The mission hs now been etended until Orbitl prmeters The Cluster II spcecrft were lunched in highly ellipticl djcent polr orbits with Perigee of 9000 km nd n pogee of 9000 km. The spcecrft hd n orbitl period of 57 hours. The spcecrft re now orbiting with much reduced perigee nd pogee vlues. 57

83 3.. The eperiments The tble below lists the eperiments of the Cluster mission, their cronyms nd brief description: No. Eperiment Description FGM Flugte Mgnetometer EDI Electron Drift Instrument 3 ASPOC Active Spcecrft Potentil Control eperiment 4 STAFF Sptio-Temporl Anlysis of Field Fluctution eperiment 5 EFW Electric Field nd Wve eperiment 6 DWP Digitl Wve Processing eperiment 7 WHISPER Wves of High frequency nd Sounder for Probing of Electron density by Reltion eperiment 8 WBD Wide Bnd Dt instrument 9 PEACE Plsm Electron And Current Eperiment 0 CIS Cluster Ion Spectrometry eperiment> RAPID Reserch with Adptive Prticle Imging Detectors WEC Wve Eperiment Consortium (DWP, EFW, STAFF, WBD, nd WHISPER) Tble 3.: List of Cluster II Eperiments (ESA, 04) 3.3 Double Str Mission The Chinese Ntionl Spce Administrtion ESA joint progrm Double Str ws continution of the Cluster II progrm nd it consisted of two stellites, one in equtoril orbit (TC) nd nother in polr orbit (TC). Primry im of the mission ws to investigte the Sun s effects on the ner spce. The generl region of interest ws the 58

84 Mgnetosphere with the Erth's Mgnetotil region, where electriclly chrged prticles (minly ions nd electrons) re ccelerted towrds the plnet's mgnetic poles by reconnection, being of specil focus. The stellite hd fifteen instruments, seven of which were identicl to the instruments on the four Cluster II spcecrft. Another eight eperiments were provided by Chinese institutes Orbitl prmeters nd significnce of the mission TC- ws lunched on highly ellipticl orbit, with very low perigee nd very high pogee. During its mission time, the orbitl prmeters hd been chnged continuously nd vried significntly, enbling the scientific community to study vrious combintions of spce wether prmeters. Just fter the lunch, the orbit of TC- hd perigee of 580 km nd pogee of 7895 km, (corresponding to n pogee/perigee of 3.37 RE/.09 RE.) n inclintion ngle of 8. 0 degrees to the equtor nd orbitl period of enbling TC to investigte the Erth's Mgnetic til nd the sunwrd boundry between the Mgnetosphere nd the solr wind. The polr orbitl stellite TC- hd perigee of 68 km, n pogee of 3879 km (corresponding to n pogee/perigee of 7.0 RE/.09 RE) nd n orbitl period of.7 hours. This orbitl rrngement enbled the smpling the polr cp nd cusp regions, the primry regions where energy from the Sun flows into the Mgnetosphere. Its instruments concentrted on the physicl processes tking plce over the mgnetic poles nd the development of urors (ESA, 03; Woolliscroft et l., 997) The Double Str mission ws conceived to operte in conjunction with the Cluster II mission. Its orbits hd been designed s such, so tht their Mgnetic Locl Times (MLT) of pogee would be ligned with ech other nd with those of the four 59

85 Cluster II stellites during the summer of 004, when ll si spcecrft would hd their pogee in the Mgnetotil. The polr orbiting Cluster II nd TC- spcecrft would mintin this coordinted phsing, but the MLT of pogee of TC- would drift prt from the other spcecrft. The NASA s Polr spcecrft s MLT of pogee ws similr to these nd s such could be phse locked with Cluster II. This prticulr orbitl coordintion would provide unique three point observtion point opportunity involving si spcecrft constelltion (if the four Cluster II stellites re treted s single observtion point, lbeit with specil smllscle multi-point mesurement cpbilities), well suited to simultneously emining Mgnetotil processes both close to nd fr from the Erth. Similrly it would lso llow emining the dyside cusps t multi points while lso mking mesurements t the low ltitude Mgnetopuse. Thus, this unique constelltion would be cpble of mking observtions with which the drivers of globl scle Mgnetospheric processes could be emined. The trough of dt could be used in conjunction with the other ctive upstrem monitors, Aurorl nd ring current imging stellites, nd sophisticted ground bsed Ionospheric monitors to provide detiled supporting observtions of the globl contet. A prticulr dvntge of the Cluster II-Double Str combintion is tht, s mentioned bove nd would be detiled lter, severl Double Str instruments, including the PEACE instrument re identicl or ner identicl copies of the Cluster II instrumenttion, which helps in crrying out comprtive dt nlysis studies. The project hd been rther cost-effective s significnt prts of the infrstructure (opertionl nd for science dt dissemintion nd nlysis) developed for Cluster II could be redily dpted for Double Str (Fzkerley et l., 005). 60

86 Figure 3.5 Orbitl plots of Double Str TC- spcecrft in three different dtes in 004, 005 nd 006 6

87 Out of the two spcecrft, the Equtoril spce crft TC is of relevnce to this reserch. Of the instruments, PEACE, STAFF nd DWP of the Wve Eperiment Consortium (WEC) del with electron density in the spce nd s such the dt nlysed here re from those instruments. Therefore, it is of importnce to nlyse the instruments in detils Plsm Electron nd Current Eperiment - PEACE The Instrument Figure 3.6: PEACE FM07 Instrument in MSSL Clen Room (MSSL, 000) The objective of the PEACE instrument is to mesure the distribution function of the electrons s ccurtely nd frequently s possible nd to provide the dt t the best resolution tht the spcecrft telemetry will llow (Johnstone et l., 997). The mesurements re used to nlyse the nture nd cuses of ccelertion, scttering, nd diffusion of electrons. 6

88 The PEACE instrument consists of two sensors with hemisphericl electrosttic energy nlysers. They contin position-sensitive microchnnel plte detectors positioned to scn rdilly on opposite sides of the spcecrft (Figure 3.3). Together both sensors cn cover the complete ngulr rnge in hlf spin of the spcecrft. PEACE mesures the three-dimensionl velocity distribution of electrons in the energy rnge from 0.59 ev to 6.4 kev in 88 levels. The first 6 energy levels re eqully spced linerly. (Rnge from 0.59 ev to 9.45 ev). The rest of levels re eqully spced logrithmiclly. (Fctor of.65 over the rest of the rnge). 63

89 Figure 3.7. A cross-section of the LEEA nlyser showing the structure of the input collimtor, the electrosttic nlyser nd the node pttern (Johnstone et l., 997: p. 357) 64

90 Resolutions: Intrinsic energy resolutions: Angulr resolutions:.7% nd 6.5% full width t hlf mimum..8º nd 5.3 º in n zimuthl direction 5 º in polr direction Opertion A voltge pplied to the inner hemisphericl plte sets the cceptnce energy of the detector. The direction of rrivl of the electron is determined from the position t which the electron strikes the detector. This is in reltion to the meridin plne of the spcecrft. Both sensors cn cover the full energy rnge from 0.59 ev to 6.4 kev but, the min difference between them is in their geometric fctor The Low Energy Electron Anlyser (LEEA): The Low Energy Electron Anlyser (LEEA) hs been designed to specilise in coverge of the very lowest electron energies (0.59 ev 9.45 ev). It hs the smller (by fctor 4) geometric fctor pproprite for the high flues to be found t low energy. This is chieved by reducing the field of view t the entrnce collimtor, nd reducing the size of the input perture, which lso help to improve the performnce for the mesurement of low energy electrons The High Energy Electron Anlyser (HEEA): The High Energy Electron Anlyser (HEEA) mesures the upper end of the electron energy spectrum. It hs lrger geometric fctor. This etends the dynmic rnge of the combintion of sensors. The pir of sensors re mounted opposite to ech other on the spcecrft so tht together they cover the complete ngulr rnge in hlf rottion of the spcecrft (Johnstone et l., 997) 65

91 Figure 3.8 LEEA HEEA Sweep (Johnstone et l., 997: p366) Figure 3.9 LEEA HEEA sweeps nd spin is (Johnstone et l., 997: p.374) 66

92 The sweep rte of the PEACE instrument is synchronized to the spin period of the spce crft to ensure n integrl number of sweeps during ech spin. The strting point for the spin is controlled by vrying the dely between the Sun pulse from the spcecrft nd the initition of the spin in the instrument. The instrument cn operte in four sweep modes. Their purpose is to vry the zimuthl ngulr resolution of the instrument: ) Low Angulr Resolution LAR; energy rnge 60 levels; 6 sweeps/spin;.5º resolution. ) Medium Angulr Resolution MAR; energy rnge 60 levels; 3 sweeps/spin;.5º resolution. 3) High Angulr Resolution HAR: energy rnge 30 levels; 64 sweeps/spin; 5.65º resolution. 4) Fied Energy FE; constnt energy for s long s required for energies up to 800 ev. Both sensors cn use ll four sweep modes nd they cn operte in different sweep modes, or strt from different levels simultneously. 67

93 Figure 3.0 LAR MAR HAR ENERGY TIME SPIN ANGLE (Johnstone et l., 997: p.36) 68

94 DWP Instrumenttion The Digitl Wve Processing Eperiment (DWP) is component of the Wve Eperiment Consortium (WEC). It is responsible for the coordintion of WEC s opertions, from providing electricl signls to synchronise instrument smpling to time tgging dt in consistent mnner nd fcilitting comple WEC modes by mens of mcros. As constrints on telemetry bndwidth re mjor problem for most spce instruments, dt compression techniques re utilised. The DWP instrument employs the following dt compression techniques: () Prticle Correltor Averging (b) STAFF Serch Coil (MWF) Differentil Encoding, (c) Widebnd instrument Digitl Filtering with Re-smpling, (d) WHISPER Dt Selection followed by Pseudo-Logrithmic Compression, (Woolliscroft et l., 997) The processor module of DWP instrument The processor of the DWP instrument is T5 trnsputer. It hs 3 Kbytes of eternl RAM nd the core of the ech module is formed by 3 Kbytes of PROM. Ech hs HS8C37A DMA controller, event multipleer nd instrument bus interfce. In order to increse rdition tolernce, the internl memory is disbled (Woolliscroft et l., 997). The DWP instrument hs been designed so s to llow the trnsputers to be operted t input clock frequencies of.5 or 5 MHz. This lower rnge enbles less power consumption. The system rchitecture of the instrument utilises 6 bit microprocessor rchitecture, gin to reduce power consumption. Higher order systems 69

95 such 3 bit rchitectures require more power. This is fcilitted from the fct tht fewer RAM nd ROM chips re ccessed in one cycle in 6bit system, reducing power consumption. Most other instruments too use 6-bit dt length Time resolution Accurte timing of dt is of prmount importnce in the study of polriztions nd phses of wve informtion. On the other hnd, the trnsducers (ntenns) cn mesure wve field prmeters over ll frequencies of interest. Dt cquired by the on-bord dt-hndling system re timed with n ccurcy of ± ms with respect to UTC for ech spcecrft. The ccurcy of compring dt from two spcecrft is of the order of ± 4 ms. The ccurcy within the DWP more shrper s the time differences cn be mesured to few microseconds. This is chieved by compring the time stmp of the ctive edge of the DWP 900 Hz clock with the spcecrft reset pulse, using trnsputer timer to precision of µs. But the interrupt ltency of the trnsputer plys mjor prt on the ccurcy of individul mesurements (Woolliscroft et l., 997) Prticle correltor The Prticle Correltor processing system within the DWP instrument performs prticle correltions, which fcilittes the study of wve/prticle interctions. Prticle correltion is bsed on forming utocorreltion functions of the time series of prticle detector counts s function of energy nd pitch ngle. The bsic opertions re crried out by the DWP resident softwre (Buckley et l., 00) The prticle correltor opertion fcilittes the following two results: 70

96 (i) The bility to detect bursts of prticle flu on shorter time scles short compred to the energy nd dwell time (ii) The bility to identify wve/prticle interctions occurring regions of velocity spce (Woolliscroft et l., 997) Opertion of the Prticle correltor The DWP Prticle Correltor tkes rw electron detection pulses from the PEACE instrument nd performs Auto-Correltion Functions (ACFs). The opertion for the Prticle Correltor is three stge process: Stge : The Prticle Correltor gets series of pulses s input from the PEACE HEEA electron sensor vi the PEACE-to-DWP Inter Eperiment Link (IEL), representing the number of individul electrons striking the sensor. Stge : The number of pulses is clculted in µs discrete time intervls by the lgorithm, forming time series of counts over prticulr energy intervl. Stge 3: These time series re put through the ACF lgorithm implemented by the DWP, producing the summed ACFs (Buckley et l., 000: Buckley et l., 00) The ACF would revel ny probble modultions in the electron popultion over tht prticulr energy rnge nd short time prticle bursts in the electron popultion s n indictor of wve-prticle interctions. The ACFs re constructed in of 5 Correltor electron contiguous energy bnds which correspond to either two or four PEACE energy levels, irrespective of the PEACE energy sweeping rte. Thus structure holds the frequency informtion but the phse informtion is lost. 7

97 The dt products from the Double Str Prticle Correltor re different form the Cluster II structure. This will be nlysed lte in the Double Str section. The ACFs re performed over 8 lgs including the zero lg. The lg time of is 45 µs gives modultion frequencies up to. khz. There re two dt rte ; High nd norml. At norml rte the summtion period is one spin (4s) nd t high rte it is /3 spin. The dt rte is constrined by the trnsmitting the summed ACF t two selected energy levels in summtion period nd third ACF tht is stepped in energy once per summtion period. This is repeted through the other 3 levels. Therefore, the two selected energies re covered with time resolution of 4 s in norml dt rte mode, nd the other energies hve time resolution of 5 s. In high dt rte these periods re correspondingly 0.5 s nd.65 s (Woolliscroft et l., 997) The Sptio-Temporl Anlysis of Field Fluctutions (STAFF) Objectives nd the instrument structure A prt of the WEC, the min objective of the STAFF eperiment is to chrcterise the wves nd ssocited turbulence. The STAFF instrument consists of boom-mounted three-is serch coil mgnetometer, digitl spectrum nlyser nd n on-bord signl-processing unit. The three-is serch coil mgnetometer cn mesure mgnetic field fluctutions t frequencies up to 4 khz nd the ltter permits the observtion of the three mgnetic wveforms up to either 0 Hz or 80 Hz, depending upon mode. The STAFF instruments hve dynmic rnge of bout 96 db in both wveform nd spectrl power. This rnge llows the study of wves ner plsm boundries (Cornilleu-Wehrlin et l., 997) 7

98 Chpter 4 : TEC modelling nd Scintilltion modelling Severl models hve been developed for the Ionosphere nd the Plsmsphere, for locl electron density distribution nd the resulting TEC nd scintilltion vritions for diurnl, sesonl, loctionl nd solr ctivity vritions. As some of the erlier ttempts become obsolete due to dvnces in scientific knowledge nd due to the vilbility of modern tools, newer models using bigger empiricl dtsets nd dvnced lgorithms hve come into plce. Still, the modelling efforts concerning TEC nd scintilltion behviours in globl scle re fr from being complete. In this section, the most importnt models re presented briefly. 4. Interntionl Reference Ionosphere (IRI) 4.. Brief Description: The Interntionl Reference Ionosphere (IRI) is n interntionl project, sponsored by the Committee on Spce Reserch (COSPAR) nd the Interntionl Union of Rdio Science (URSI). These orgniztions formed Working Group in the lte sities to produce n empiricl stndrd model for the ionosphere, bsed on ll vilble dt sources. Up to now, severl enhnced versions of the model hve been relesed. For given loction, time nd dte, IRI provides monthly verges of the electron density, electron temperture, ion temperture, nd ion composition in the ltitude rnge from 50 km to 000 km. Additionlly, prmeters provided by the IRI include the TEC, (for which user cn select the strting nd ending height of the integrl), the occurrence probbility for Spred-F nd the equtoril verticl ion drift. Worldwide network of ionosondes, powerful incoherent sctter rdrs (Jicmrc, Arecibo, Millstone Hill, Mlvern, St. Sntin), the ISIS nd Alouette 73

99 topside sounders nd the in-situ instruments on severl stellites nd rockets re the min dt sources for the IRI (Kenpnkho et l., 0). 4.. Prmeters: Electron density, electron temperture, ion temperture, ion composition (O +, H +, He +, NO +, O + ), ion drift, Ionospheric electron content (TEC), F nd spred-f probbility 4. Globl Ionospheric Scintilltion Model (GISM) The Globl Ionospheric Scintilltion Model genertes estimtions for both the men errors nd scintilltions due to propgtion through ionosphere. This model hs been ccepted by the Interntionl Telecommunictions Union (ITU) s reference code for scintilltions evlutions. Amplitude nd phse signl fluctutions re the result of propgtion through ionosphere electron density irregulrities. These signl fluctutions my occur specilly during equinoes, fter sunset nd lst for few hours. They re more intense during periods of high solr ctivity. These fluctutions result in signl degrdtion from VHF up to C bnd. They my ffect severl pplictions s nvigtion systems, communictions, remote sensing nd erth observtion systems. Two globl regions re impcted by such events: equtoril regions (-0 to +0 mgnetic ltitude) nd polr regions (> 60 ). Scintilltions re more intense t the equtor nd the resulting chrcteristics re different between these two regions. GISM llows ssessing both the men effects nd the scintilltions for propgtion through ionosphere for ny loctions of trnsmitter nd receiver. Two sub models re involved. The first one provides the men errors. It is bsed on resolution 74

100 of Hselgrove equtions. The second one provides the scintilltion effects. It is bsed on the resolution of prbolic eqution. The electron density in the ionosphere t ny given time nd loction, which is required input for both sub models, is provided by the NeQuick model. The NeQuick model hs been developed by the Universities of Grz nd Trieste. Inputs for the NeQuick model re the solr flu number, the yer, the dy of the yer nd the locl time. NeQuick is used s subroutine in the GISM model. The line of sight is determined by resolution of Hselgrove equtions. Men errors re subsequently provided for Rnge error, Angulr error nd Frdy rottion. The scintilltions re then clculted using split step technique bsed on Fst Fourier Trnsform clcultions (Béniguel, 0; IEEE, 0]. 4.. Scintilltion fluctutions The signl fluctutions, referred s scintilltions, re creted by rndom fluctutions of the medium s refrctive inde, which re cused by inhomogeneities inside the ionosphere. These inhomogeneities (or bubbles), or more generlly the turbulences, develop under severl deioniztion instbility processes. These processes strt fter sunset when the sun ioniztion drops to zero, consequently t night time. To produce signl scintilltion, the bubbles sizes should be below typicl dimension (typiclly one km) such tht the diffrcting pttern is inside the first Fresnel zone. The Fresnel zone dimension lso depends on the distnce from the Ionospheric Pierce Point (usully defined t bout 350 km height) to the receiver nd on the frequency. The Globl Ionospheric Propgtion Model (GISM ims to clculte these effects, in prticulr:. The Line of sight errors 75

101 . The Frdy rottion effect on polriztion: being n nisotropic medium, ionosphere lyers will impct liner polrized wve by rotting its polriztion plne. 3. The propgtion Dely: the rnging error is proportionl to the TEC nd to the inverse squre of the frequency. 4. The scintilltion effects: phse nd mplitude scintilltions, shorter correltion distnces with respect to spce, time nd frequency, cycle slips, loss of lock. GISM model uses the Multiple Phse Screen technique (MPS). With this technique, the medium is divided into successive lyers, ech of them cting s phse screen. The loctions nd ltitudes of both the trnsmitter nd the receiver re rbitrry. The link cn consequently go through the entire ionosphere or through smll prt of it. The whole clcultion for one prticulr link is composed of two steps:. The clcultion of the Line Of Sight (LOS). The clcultion of scintilltions The clcultion of the Line of sight is done using ry technique. GISM uses the NeQuick model to provide the vlue of the electron density inside ionosphere required t ny time nd loction. At the end of this clcultion the LOS errors, the Frdy rottion nd the delys re clculted. The LOS being determined, the scintilltions re then clculted. To do this, t ech screen loction long the line of sight, the prbolic eqution (PE) is solved. This clcultion requires the knowledge of the medium sttisticl chrcteristics. They re defined with respect to the ionosphere electron density men vlue t ll points long the LOS. 76

102 GISM model estimtes the scintilltion prmeters from the knowledge of the time series t receiver level using the signl intensity nd phse nd its correltion nd structure functions. In cse of strong scintilltions (typiclly S4 > 0.7), the phse my ehibit cycle slips with consequences on the receiver phse loop. It my lso in tht cse led to losses of lock for one or severl stellites. GISM model llows considering either trjectory described by list of successive points or constelltion (GPS, Glileo or GLONASS). An orbit genertor hs been introduced for this cpbility. The input in tht cse is the Yum file. GISM llows considering either links, from receiver to stellite or constelltion, or mps (Be niguel, 0, Be niguel nd Hmel, 0). 4.3 Nequick Model The NeQuick Model gives electron density s function of height, geogrphic ltitude, geogrphic longitude, solr ctivity (specified by the sunspot number or by the 0.7 cm solr rdio flu), seson (month) nd time. It lso llows the clcultion of electron density long rbitrrily chosen ry pths nd the corresponding TEC (IEEE, 0). 4.4 Other models of interest Other models of interest include the ITS 78 Model, the Bent Model, the Ionospheric Communiction Anlysis nd Prediction Progrm (IONCAP), the Brdley Model nd the WBMOD Model. 77

103 Chpter 5: Dt Etrction from TC DWP Correltor 5. Double Str Dt dissemintion structure The Double Str dt products re distributed to the scientific community through the Double Str Science Dt System (DSDS) mong mny other online nd offline distribution rrngements. The following digrm illustrtes the concept of DSDS. Figure 5.: The Double Str Science Dt System (DSDS) schemtic digrm (Torkr, 007: p4) The PEACE nd DWP dt re sent to nd stored in the University of Sheffield nd t the Mullrd Spce Science Lbortory, UCL. These institutions cted s the PI institutions for the PEACE & DWP projects. Figure 5. shows the flow of Level (L) dt from the Europen Double Str Dt System to the Europen PIs. 78

104 Figure 5. Ground dt segment of Double Str Project (Torkr, 007: p3) 79

105 5. Double Str DWP Level dt cquisition The full level dt sets of the entire TC mission were downloded vi ftp from the University of Sheffield Double Str Dt Archive t hoodie.shef.u.uk. The usernme, pssword, the relevnt literture nd relevnt instructions were provided by Dr Andrew Buckley. The level files hd been stored under the L folder further orgnised into yers, months nd dys. For ech dy there ws House Keeping file (hk_file) nd Science file (sci_file) nmed in the formt YYMMDDWH.NA nd YYMMDDWN.NA respectively. Here YY denotes the yer, MM denotes the month nd DD dy of the month. 5.3 Double Str L dt decommuttion The L dt ws needed to be decommutted in order to get Level ASCII output files, which re redble nd would provide useful dt. As the PI institution for the project, the University of Sheffield hd developed decommuttion progrm (Yerby et l., 004) clled TLMDECOM. According to its uthor, the TLMDECOM is simple progrm to decommutte the Double Str STAFF/DWP science telemetry like DECOM ( similr progrm for decommutting the Cluster II dt) does for Cluster. TLMDECOM will lso work on Cluster dt. The output file my be in decom or DSD formt, but some of the fields of the DSD heder my not be implemented. TLMDECOM is C progrm with two source files tlmdecom.c nd tlmproc.c. The eecutble tlmdecom.ee is compiled to run s 'console ppliction' (ie. in DOS window) under Microsoft Windows 9 or XP. In Linu environments, the progrm file is generted by: gcc -lm -o <eecutble file> tlmdecom.c tlmproc.c 5. 80

106 The resulting progrm is used to generte the Level output from the house keeping file, science file combintion. The commnd synt is: Tlmdecom hk_file sci_file output_file /f=4 /h= /i=n 5. Where n is for FFT, for MWF norml mode, 3 for MWF burst mode, 5 for correltor. The /h option controls the output heder formt. /h=0 outputs decom formt heders, whilst /h= outputs DSD formt heders. For Double Str correltor dt only the vlues /h= or /h=3 my lso be used for decom or DSD heders respectively. In tht cse the dt pckets re truncted to the Cluster size (the new summed counts nd time series re removed) nd the correltor mode word djusted to Cluster formt. The output file is binry nd hs heder followed by science dt s described in the formt document nd re provided in the following pges. 8

107 5.4 Correltor DSD Heder definition for DWP Words Bytes Comment 0 0 Softwre Version 0 Softwre Revision Softwre Ptch 3 Softwre User Ptch 4-5 Spcecrft ID Ground Sttion ID Source Instrument 5 0- Dignostics Word 6-3 Length of Science Dt SPRT Yer SPRT Month SPRT Dy of the Month 0 0- SPRT Hour -3 SPRT Minute 4-5 SPRT Second SPRT Millisecond SPRT Microsecond 5 30 DWP Mster Clock Pulse Count 5 3 OBDH Reset Pulse Count (modulus 8) 6 3 UDEF UDEF DWP Model Tg PEACE Flybcks per Spin PEACE Sun Reference Pulse Offset Correltor Disbled Flg 4-43 Correltion Processing Control Tble 5. TED heder formt (Susse Spce Science Centre, 00) 8

108 5.5 Correltor science pcket formt Unlike the Cluster II DWP correltor, the Double Str correltor could operte in two modes: Mode : The ACF mode which is similr to the Cluster correltor mode, plus the output of two unprocessed time series. Mode II: The time series only mode where no ACF clcultions re performed, but si unprocessed time series re output. In the ACF mode, the pcket descriptor nd time tg re followed by two sttus words nd two uto-correltion functions of 5 words ech (pcket length 34 words including pcket descriptor nd timetg). The sttus words contin count of the number of ACFs tht hve been summed to mke this pcket long with mode bits nd the PEACE energy level t which the ACF dt ws tken. Correct selection of the PEACE energy level depends on DWP being correctly informed by the telecommnd of the PEACE sweep mode nd offset. There is no on bord link for this informtion. One uto-correltion is clculted t fied energy level specified by the instrument processing word. This is referred to s the fied ACF. The other is clculted t n energy level tht steps through number of levels, t one step per spin. This is clled the stepped ACF. Ech ACF is clculted over 3 lgs, nd the rw ACF lgs re 4 bit integers. Only the zero lgs re output directly. For the other 3 lgs in ech ACF, the minimum vlue is output s 4 bit number, then the other lgs re output s: (Lg - Minimum) >> Scle 5.3 Where scle is the smllest number such tht the resulting vlues re less thn 63 nd cn be stored in 6 bits. The >> symbol is the shift right opertor, nd >> scle mens divide by to the power scle. The lrgest possible vlue for scle is 8 so it cn lso 83

109 be stored s 6 bits. Therefore, there re 3 6 bit vlues which re pcked into words. The loction of the correltor prmeters within the science pcket re given in the tbles below. Words Bytes Contents 0 0, Pcket descriptor (UDEF0 = 0, UDEF = 0), 3 Time tg for summed ACF dt (end of spin/sector) (bits 5..8) 4 Fied ACF count (bits 7..4) 5 (bits 7..4) Correltor mode bits (stepped energy limit for DSP) (bits 3..0) 5 (bits 3..0) Fied energy level 3 (bits 5..8) 6 Stepped ACF count 3 (bits 5..4) 7 (bits 5..4) PEACE mode bits (0 = fied, = LAR, = MAR, 3 3 (bits 3..0) 7 (bits 3..0) Stepped energy level 4, 5 (bits 7..0) 9, 8, Fied ACF zero lg, 4 bits 5 (bits 5..8), 6 0, 3, Fied ACF offset, 4 bits Fied ACF, scle + 3 lgs, 6 bits ech 9, 0 (bits 39, 38, 4 Stepped ACF zero lg, 4 bits 0 (bits 5..8), 40, 43, 4 Stepped ACF offset, 4 bits Stepped ACF, scle + 3 lgs, 6 bits ech 34 68, 69 Fied energy sum of counts 35 70, 7 Stepped energy sum of counts 36 7, 73 Time tg for time series dt selected sweep (end of sweep) fied energy nd stepped time series dt (compressed) Tble 5. ACF + Time Series mode Science pcket dt structure (Susse Spce Science Centre, 00) 84

110 Words Bytes Contents 0 0, Pcket descriptor (UDEF0 =, UDEF = 0), 3 Time tg for time series dt selected sweep (end of sweep) (bits 3..) 4 (bits 5..4) PEACE mode bits (0 = fied, = LAR, = MAR, 3 = HAR) (bits..8) 4 (bits 3..0) Stepped energy level (bits 7..4) 5 (bits 7..4) Stepped energy limit (bits 3..0) 5 (bits 3..0) Fied energy level fied energy nd 3 stepped time series dt (compressed) Tble 5.3 Time Series only mode Science pcket dt structure (Susse Spce Science Centre, 00) The compressed time series dt hs the sme formt in ech cse. Ech time series contins 6 smples, nd ech is stored s: (Smple - Offset) >> Scle 5.4 To etrct the dt it is first necessry to swp the bytes in ech word, so for the ACF mode dt the bytes should be ssembled in the order 75, 74, 77, 76, 79, 78, nd so on. Then divide the dt into 7 byte blocks ( in ACF mode, 6 in time series only mode). The first 5 bytes (numbered 0..4) contin the first 60 time series smples, bits ech, pcked with the first smple in the lest significnt end of the byte. Byte 5 contins the lst two smples in the lest significnt bits, plus the 4 bit offset. Byte 6 contins 6 bit clock counter in the lest significnt prt of the byte, plus the bit scle. 85

111 The clock counter counts DWP mster clock cycles from 0 to 35, nd my be used to check whether time series re cquired on djcent clock cycles. This counter is synchronised to the STAFF MWF smpling, with the NBR smple being tken on cycle 0 (TBC), nd HBR smples (when ctive) tken on ll odd numbered cycles. No correltor dt is tken on clock cycles used for STAFF smpling. 5.6 Etrcting the Time Series nd the ACFs ACFTIMESBUILD (This section is my own work) A bespoke etrctor progrm ws developed by the uthor of this thesis to etrct the heder informtion nd the science dt from the DWP correltor L output file from generted by running the decommuttion progrm TLMDECOM. The progrm is clled ACFTIMESBUILD nd it hs been developed in C. The code hs been provided in nneure I. The heder nd science combined dt pcket is essentil in progrmming the etrctor. The structure of the combined dt pcket is nneed in nneure II. The structure of the ACFTIMESBUILD progrm is detiled below; As the input is going to be level file, file pointer *fplv is declred Two 84 word long rrys {p[84] nd q[84]} re declred for storing the contents of the dt pcket. 3 As the time is given in hour, minute, second, millisecond nd microsecond, it needs to be built in suitble formt. As millisecond resolution is sufficient, the time is built in milliseconds. A vrible is declred for time in millisecond nd initited t timems = 0. 86

112 4 Si vribles re declred for Fied ACF count, Correltor mode bits, Fied Energy level, Stepped ACF count, PEACE mode bits nd Stepped energy level. 5 Vribles re declred for the Offset, Scle nd the 6 Fied energy Time series. 6 Similrly vribles re declred for the Offset, Scle nd the 6 Stepped energy Time series. 7 Vribles re lso declred for Fied energy Zero Lg ACF, Fied energy ACF Offset, Fied energy ACF Scle nd 3 Fied energy ACF Lgs 8 Similrly, vribles re lso declred for Stepped energy Zero Lg ACF, Stepped Energy ACF Offset, Stepped energy ACF Scle nd 3 Stepped energy ACF Lgs 9 Arry q[ ] is initited from 0 nd incremented. 0 Input file is opened nd red. The contents stored in q[ ]. Arry q[ ] is byte swpped in ech word nd result is sved in rry p[ ]. int m=0; for(m=0;m<84;m++){ p[m]=(((q[m] & 0FF) << 8) + ((q[m] & 0FFFFFF00) >> 8)); Time is clculted in milliseconds. Listing 5. Code snippet for byte swpping timems=(p[0]* ) + (p[]*60000) + (p[]*000) + p[3]; Listing 5. Code snippet for time clcultion in milliseconds 87

113 3 Fied ACF count, Correltor mode bits, Fied Energy level, Stepped ACF count, PEACE mode bits nd Stepped energy level re clculted by mnipulting bit-wise opertors. WORD WORD NO. IN HEADER / SCIENCE BYTE NO. IN HEADER / SCIENCE CONTENT BIT NO. VARIABLE / ARRAY ELEMENT 3 5 Fied Energy level Correltor mode bits (Stepped energy limit for DSP) p33 p3 4 Fied ACF count p Stepped energy level PEACE mode bits (0 = fied, = LAR, = MAR, 3 = HAR) p333 p33 6 Stepped ACF count p Tble 5.4 DWP dt Pcket snippet for words 3 nd 33 p3=((p[3] & 0FF00) >> 8); p3=(p[3] & 0F0); p33=(p[3] & 0F); p33=((p[33] & 0FF00) >> 8); p33=((p[33] & 030) >> 4); p333=(p[33] & 0F); Listing 5.3 Code snippet for the clcultion of Fied ACF count, Correltor mode bits, Fied Energy level, Stepped ACF count, PEACE mode bits nd Stepped energy level. 88

114 4 Fied energy offset nd scle re clculted by bit-wise opertions WORD WORD NO. IN HEADER / SCIENCE BYTE NO. IN HEADER / SCIENCE 88 CONTENT Fied energy Time series Smple 60 Fied energy Time series Smple 6 Fied energy Time series Smple 6 Fied energy Time series Offset BIT NO VARIABLE / ARRAY ELEMENT s60 s6 s6 offset Fied energy 6 bit Clock Counter Fied energy Time series Scle Stepped energy Time series Smple Stepped energy Time series Smple scle s0 s0 Tble 5.5 DWP dt Pcket snippet for the Fied energy ACF Offset nd Scle. offset=((p[74] & 0F0) >> 4); scle=((p[75] & 0C000) >> 4); Listing 5.4 Code snippet for fied energy offset nd scle clcultion. 5 The 6 fied energy time series re clculted implementing (Smple - Offset) >> Scle nd using offset nd scle. WORD WORD NO. IN HEADER / SCIENCE BYTE NO. IN HEADER / SCIENCE CONTENT Fied energy Time series Smple Fied energy Time series Smple Fied energy Time series Smple 3 Fied energy Time series Smple 4 Fied energy Time series Smple 5 Fied energy Time series Smple 6 Fied energy Time series Smple 7 Fied energy Time series Smple 8 BIT NO VARIABLE / ARRAY ELEMENT s0 s0 s03 s04 s05 s06 s07 s08 Tble 5.6 DWP dt Pcket snippet for the first 8 fied energy time series in word

115 s0=((((p[67] & 0300) >> 8) + offset) << scle); s0=((((p[67] & 0C00) >> 0) + offset) << scle); s03=((((p[67] & 03000) >> ) + offset) << scle); s04=((((p[67] & 0C000) >> 4) + offset) << scle); s05=(((p[67] & 03) + offset) << scle); s06=((((p[67] & 0C) >> ) + offset) << scle); s07=((((p[67] & 030) >> 4) + offset) << scle); s08=((((p[67] & 0C0) >> 6) + offset) << scle); Listing 5.5 Code snippet for the clcultion of the first eight fied energy time series 6 Stepped energy offset nd scle re clculted by bit-wise opertions 7 Stepped energy time series re clculted similrly s in Step 5 bove. 8 Fied energy Zero lg ACF, Fied energy ACF Offset, nd Fied energy ACF Scle re clculted by bit-wise opertions. fcflg0=((p[34] << 8) + ((p[35] & 0FF00) >> 8)); fcfoffset=(((p[35] & 0FF) << 6) + p[36]); fcfscle=((p[37] & 0FC00) >> 0); Listing 5.6 Code snippet for the clcultion of the Fied energy Zero lg ACF, ACF Offset nd Scle. 90

116 0 WORD WORD NO. IN HEADER / SCIENCE BYTE NO. IN HEADER / SCIENCE CONTENT BIT NO. VARIABLE / ARRAY ELEMENT Fied ACF zero lg, 4 bits fcflg Fied ACF offset, 4 bits fcfoffset Fied ACF Scle fcfscle Tble 5.7 DWP dt Pcket snippet for the Fied energy Zero lg ACF, Offset nd Scle 9 The 3 Fied energy ACFs re built by implementing (Lg Offset) >> Scle, the offset nd the scle. fcflg=((((p[37] & 03F0) >> 4) + fcfoffset) << fcfscle); fcflg=(((((p[37] & 0F) << ) + ((p[38] & 0C000) >> 4)) + fcfoffset) << fcfscle); fcflg3=((((p[38] & 03F00) >> 8) + fcfoffset) << fcfscle); fcflg4=((((p[38] & 0FC) >> ) + fcfoffset) << fcfscle); fcflg5=(((((p[38] & 03) << 4) + ((p[39] & 0F000) >> )) + fcfoffset) << fcfscle); fcflg6=((((p[39] & 0FC0) >> 6) + fcfoffset) << fcfscle); fcflg7=(((p[39] & 03F) + fcfoffset) << fcfscle); Listing 5.7 Code snippet for the clcultion of the first seven Fied energy ACFs 9

117 0 WORD WORD NO. IN HEADER / SCIENCE BYTE NO. IN HEADER / SCIENCE CONTENT BIT NO. VARIABLE / ARRAY ELEMENT 5 Fied ACF Scle 4 3 fcfscle Fied ACF Lg fcflg Fied ACF Lg fcflg 7 Fied ACF Lg fcflg Fied ACF Lg fcflg4 6 Fied ACF Lg fcflg Fied ACF Lg fcflg6 8 Fied ACF Lg fcflg7 7 Tble 5.8 DWP dt Pcket snippet for the first seven Fied energy ACFs 0 Stepped energy Zero lg ACF, Stepped energy ACF Offset, nd Stepped energy ACF Scle re clculted by bit-wise opertions. The 3 Fied energy ACFs re built by similrly s in Step 9 bove. The clculted vrible vlues, the time series nd the ACFs long with other most relevnt heder informtion re printed. 9

118 Chpter 6 Development of methodology for deriving the Upper Plsmspheric Electron Content component long the orbitl pth of the TC from its empiricl, in-situ electron density dt A new methodology is developed nd presented in this reserch, mking use of the electron density dt vilble from the TC mission to derive the Upper Plsmspheric TEC component (bove the semi-synchronous orbit height) long the orbitl trce of the spcecrft. 6. The cse for this thesis ((This section is my own work) As mentioned erlier in this thesis, the bsolute contribution of the Upper Plsmsphere to the Electron Content nd its vritions under loctionl, diurnl, sesonl nd solr ctivity vritions hve been nd continues to be unmesured quntities. The importnce of the Plsmspheric contribution to Electron Content in trns- Ionospheric stellite communictions hs been demonstrted in previous chpters. This thesis work clssifies the Plsmsphere into two prts; the Upper Plsmsphere nd the Lower Plsmsphere, demrcted by the semi synchronous orbit ltitude t round,000 kms. The Lower Plsmspheric TEC contribution hs been studied etensively by the scientific community using the GPS dul frequency techniques. As the GPS stellites hve globl footprint, it hs become possible to derive TEC figures (up to the Lower Plsmsphere ltitude) throughout the yer, building up huge dtbse of TEC figures. Comprehensive modelling of TEC vritions (up to Lower Plsmspheric ltitude) hs 93

119 become possible from these etensive sets of dt, wheres the Upper Plsmspheric contribution to the TEC remins unquntified. 6.. Upper Plsmspheric Electron Content (UPEC) Upper Plsmspheric Electron Content cn be defined s the totl electron count of the Upper Plsmsphere segment (the ltitudes bove semi-synchronous orbit height up to the up to geo-sttionry orbit height) in column of m cross section, long the signl pth from the stellite (s) to the receiver (r). Upper Plsmspheric Electron Content cn be bbrevited s UPEC. The quntifiction of Upper Plsmspheric Electron Content contribution to the Electron Content up to geo-sttionry orbit heights becomes of prcticl significnce in stellite communictions, nvigtion, rnging, remote sensing nd militry pplictions. Chpter lists the effects cused by the free electrons on rdio wves trversing the spce. Other thn these effects, it is of prime cdemic interest to nlyse this quntity, in order to thoroughly understnd the phenomen. In the stellite engineering pplictions listed bove, the effects introduced by the Upper Plsmspheric Electron Content re treted s errors nd noise terms. In the bsence of ccurte quntifiction, lrger tolernce llownces re used in overcoming the effects, thus ffecting the link budgets significntly. Geo- sttionry orbits stellites nd Molniy orbit stellites dwell in orbits higher thn 35,000 kms nd most of them hve pplictions ffected by the mount of TEC down to the ground receivers. In ddition, mny stellites in these orbits re used for the purpose of relying stellite signls cross the globe. The Chinese Nvigtion Stellite System (lso known s COMPASS or BeiDou-) nd the Indin Regionl Nvigtion Stellite System (IRNSS) use Geo- sttionry orbits stellites s prt of their constelltion for stellite nvigtion. As mentioned before, there re severe rnging nd 94

120 time dely implictions for nvigtion pplictions due to the mount of TEC encountered by the reference signls. Figure 6. illustrtes the reltive distnces of the Upper Plsmspheric content nd Lower Plsmspheric content s defined in this reserch. The upper limit of the Upper Plsmsphere is tken to be kms in order to ccommodte the TEC component encountered by the Molniy orbit stellites. Therefore it is logicl to ssume tht the Upper Plsmspheric TEC component will be of the sme order of the Lower Plsmspheric content which cn be clculted by the GPS Dul frequency method, s the distnces concerned re 0, 000 kms nd 8,000 kms respectively for the two components. When compring the etensive mount of reserch tht hs been under tken by the scientific community in reltion to the Lower Plsmspheric TEC content nd its ssocited effects in recent yers; the mount of reserch on the Upper Plsmspheric TEC content is lmost non-eistent. The bsence of suitble technology is the min reson for the inbility to quntify this component. This study firmly believes tht the methodology developed in this reserch using electron density dt for TC fills tht lcun, most probbly for the first time. 95

121 Figure 6. The ltitudes, period, rdius nd speed of relevnt orbits (Lee, 04) 6.. TC orbit nd the opportunity it provides The following points bout the TC Mission mke it pproprite for the development of this methodology: TC mission consists of the PEACE eperiment, which is equipped with Lngmuir Probe, enbling the in-situ mesurements of electrons long the orbitl pth nd the derivtion of the electron density. The orbit of TC is highly ellipticl. 3 It hs very low perigee nd very high pogee. 4 The high eccentricity nd the low perigee, high pogee of the TC orbit nd the resulting smller incident ngle the orbitl trce mkes while in the km ltitude rnge resulting from it provide the idel geometric opportunity to build the methodology nd utilise the in-situ electron density mesurements for the clcultion of the Upper Plsmspheric TEC component. 5 The inclintion ngle rnge of the TC mission mkes it n equtoril mission tht ws confined to the Ner-Equtoril region pproimtely ± on either sides of the mgnetic equtor. As the most pronounced bsolute TEC 96

122 vlues nd vritions re within this region, TC dt offers n ecellent opportunity to build TEC dtbse of this region. It is note-worthy tht the TC mission is unique mong ll the known spce wether reserch missions, when one considers the bove chrcteristics tht fcilitte the development of this methodology. Figure 6. Orbitl plne digrm showing Incident ngle being equl to the ngle the tngent to the orbit mkes with the line connecting the centre of the erth with the spcecrft in the ltitude rnge 3.5 Re to 6.5 Re ( Digrm not to scle) 6. Dt sources Electron density nd spcecrft time dt from the Double Str UK Dt centre nd the orbitl position nd spcecrft time nd dte dt from the NASA s Stellite Sitution Centre needs to be combined to form the input dt file for the methodology. These two sets of dt were downloded seprtely nd combined s would be eplined lter. 97

123 6.. Electron Density Dt -Double Str UK Dt Centre Electron density dt is sourced from the Double Str Science Dt System, UK Dt Centre, hosted t On the selection of TC, PEACE the dte rnge, output formt (CDF/CEF/ ASCII/Plot) nd the dt prmeter (electron density), the listing is generted. The listing tbultes intervl centred time tg rounded to nerest millisecond with electron density. The dte is given in DD-MM-YYYY formt nd the time is given in HH:MM:SS.MS formt. The electron density is given in Ne/cm 3. If the electron density ws outside the tolernce level of the instrument or if the instrument hd been turned off, figure of E+3 is output. Density dt ws downloded for 0 dys t time nd sved s spredsheet, rrnged under yer of opertion. 6.. Orbit Dt - NASA Stellite Sitution Centre The NASA Stellite Sitution Centre, run under the Spce Physics Dt Fcility of the Goddrd Spce Flight Centre provides spcecrft coordinte informtion for rnge of missions. The coordinte dtsets for TC nd TC re included in the dtbses. The dt is vilble t In order to downlod the coordintes one needs to select the spcecrft, the dte nd time rnge, output units / formtting nd the output options. 98

124 The tble 6. on the net pge gives the formtting nd units options vilble for outputs nd the selected options. Dte Time yyyy ddd yy/mm/dd yy-mmm-dd yy-mmm-dd hh.hhhh hh:mm:ss hh:mm Distnce Degrees Formt with R E - Erth Rdii km - Kilometers km - Integers km - Scientific Nottion deciml plces with -dd.ddd... deciml plces -ddd dd' -ddd dd ' dd" Direction/Rnge Lt (-90,+90), Long(0,360) Lt (-90,+90), Long (-80,+80) Lt (90S,90N), Long (80W,80E) Output Formt Options CDF Tet line(s) per pge Tble 6. NASA Stellite Sitution Centre TC Spcecrft coordintes: Units nd formtting options vilble for outputs nd the selected options. The tble 3. on the net pge gives the output options vilble nd the selected options. 99

125 X Y Z GEI/TOD GEI/J000 GEO GM GSE GSM SM LAT LON X Y Z LAT LON LOCAL TIME Additionl Options Regions Vlues Distnce From Spcecrft Regions Rdil Distnce T95 Neutrl Sheet Rdil Trced Footpoint Regions B Field Strength P93 Bow Shock North B Trced Footpoint Regions Dipole L Vlue RS93 MPuse South B Trced Footpoint Regions Dipole Inv Lt B GSE X-Y-Z B Field Trce Output Options Footpoint Ltitude Footpoint Longitude Field Line Length GEO NORTH GEO SOUTH GM NORTH GM SOUTH Tble 6. NASA Stellite Sitution Centre TC spcecrft coordintes: Avilble output options nd the selected options 00

126 0 dys of dt ws downloded in GEI/J000 coordintes in ASCII formt. As would be elborted lter in section 6.3., GEI/J000 re inertil coordintes, therefore re not ffected by the rottion of the erth. It is importnt tht the coordinte system selected should be ble to provide the elliptic shpe in order to crry out the geometric constructions. The rdil distnce is lso downloded long with the coordintes, fcilitting the clcultion of pogee nd perigee vlues. 6.3 Orbitl elements nd Coordinte Systems -Primry bckground informtion This section gives the primry bckground informtion bout the Orbitl elements nd Coordinte Systems used in the nlysis 6.3. Orbitl elements / Prmeters Primrily five prmeters uniquely define n orbit. They re: Semimjor is ( ) Eccentricity ( ) 3 Inclintion ngle ( i ) 4 Longitude of the Ascending Node ( ) 5 Argument of Peripsis ( ) The definitions for the orbitl elements re given below: Semimjor is ( ) Hlf the sum of the Peripsis nd Apopsis distnces. From Figure 6.3 r r 6. p 0

127 Eccentricity ( ) The eccentricity of n ellipse is the mesure of its elongtion compred to perfect circle. From Figure 6.3 r rp e 6. r r p The following two elements define the orienttion of the orbitl plne with respect to the reference (equtoril) plne nd the reference direction: 3 Inclintion ngle (i ) - Angle of the Ascending node, countered positively (counter clockwise) in the forwrd direction between 0 0 nd 80 0 between the norml (directed towrds the est) to the line of nodes in the equtoril plne nd the norml (in the direction of the velocity) to the line of nodes in the orbitl plne. 4 Longitude of the Ascending Node ( ) The ngle between the reference direction (Vernl Equino) nd tht of the Ascending Node in the Line of Nodes (the intersection of the orbitl plne nd the equtoril plne) mesured positively (counter clockwise) from 0 0 to 80 0 in the forwrd direction. 5 Argument of Peripsis ( ) - The orienttion of the orbitl ellipse in the orbitl plne is determined by this ngle, which is defined s the ngle mesured positively from 00 to 3600 in the direction of the motion of the stellite between the Line of Nodes from direction of the Ascending Node to the direction of the Peripsis.[59] 0

128 Figure 6.3 Orbitl Plne digrm 03

129 Figure 6.4 Orbitl elements / Prmeters Inclintion Angle, Longitude of the Ascending Node nd the Argument of Peripsis illustrted 04

130 6.3. Geocentric Equtoril Inertil Coordinte Systems The following tble lists the min Geocentric Coordinte Systems, their bbrevitions nd the es definitions: System Geocentric Equtoril Inertil Geogrphic Geocentric Solr Ecliptic Geocentric Solr Mgnetospheric Solr Mgnetic Geomgnetic GEI GEO GSE GSM SM MAG Definition of Aes X = First Point of Aries Z = Geogrphic North Pole X = Intersection of Greenwich meridin nd geogrphic equtor Z = Geogrphic North Pole X = Erth-Sun line Z = Ecliptic North Pole X = Erth-Sun line Z = Projection of dipole is on GSE YZ plne Y = Perpendiculr to plne contining Erth-Sun line nd dipole is. Positive sense is opposite to Erth s orbitl motion. Z = Dipole is Y = Intersection between geogrphic equtor nd the geogrphic meridin 90 0 Est of the meridin contining the dipole is Z = Dipole is Tble 6.3 Geocentric Coordinte Systems, their bbrevitions nd the es definitions (Hpgood, 99: p7) In the tble bove, the undefined third is completes the right hnded Crtesin Trid system. 05

131 In order to eecute the methodology, it is essentil to construct the true elliptic shpe of the orbit. Of these Geocentric Coordinte Systems, only GEI systems re suitble for this nlysis, s tht system does not chnge with the rottion of the erth nd therefore, the ellipse of the orbit cn be constructed. In the GEI system, the X is points towrds the First Point of Aries nd the Z is points to the Geogrphic North Pole with the erth s centre s the origin. This direction is lso the intersection of the Erth's equtoril plne nd the ecliptic plne. It points towrds the Sun in Vernl Equino. The Z is, which is the rottion is pointing towrds the North Pole of the Erth nd Y is completes the right-hnded orthogonl set. The norml GEI coordinte system chnges slowly in time owing to the effects of stronomicl precession nd the nuttion of the Erth's rottion is. Therefore it is importnt to stndrdise the epoch dte nd time, in order to hve unique reference point (Hpgood, 99). Multiple GEI coordintes systems hve been estblished nd utilised by reserchers. The NASA Stellite Sitution Centre for spcecrft coordinte dt is vilble in the J000 Frme Coordinte System (GEI /J000) nd the True of Dte Frme Coordinte System (GEI /TOD), which re two of the GEI coordintes systems utilised (Tble 6.). ) J000 Frme Coordinte System (GEI /J000) The most commonly used Geocentric Equtoril Inertil Coordinte Systems frme is the J000 frme. It is defined with the -is being ligned with the men equino t :00 Terrestril Time on Jnury 000 nd the erth's Men Equtor on tht dte. The system is lso referred to s the EME

132 b) True of Dte Frme Coordinte System (GEI /TOD) The True of Dte (TOD) frme is defined using the true equtor nd equino on the dte, when the coordintes re generted. Out of the two, the GEI /J000 is selected for this reserch, s coordintes from more thn one dtes re involved in the nlysis. 6.4 The Methodology ((This section is my own work) As demonstrted in previous chpters, the orbit of TC hs been constntly chnged over the mission lifetime. The declred inclintion, pogee nd perigee informtion t the beginning of the mission re not fctully holding. Therefore, ech orbit needs to be nlysed on its own merit nd the orbitl prmeters nd the other relevnt figures should be derived for ech individul orbit Dt cquisition nd input From the NASA Stellite Sitution Centre TC dt set, the orbitl coordintes nd the ssocited dt re downloded in 0 dys of dt sets blocks. This dt is clled the Spcecrft Position Dt Set nd is provided in one minute intervls. The dt elements, their formt nd units re given in tble 6.4 in the net pge. 07

133 Dt element Formt Unit Yer YYYY - Dy of yer DDD - Time HH:MM::SS - X GEI/J000 Kilometres Y GEI/J000 Kilometres Z GEI/J000 Kilometres Ltitude Lt (-90,+90) dd.dd Longitude Long (-80,+80) dd.dd Rdil Distnce - Kilometres Tble 6.4 Orbitl dt elements, their formt nd units. From the Double Str UK Dt Centre Spcecrft dte nd time nd the one minute verged electron density dt is obtined either in CDF/CEF formt or in ASCII formt for the sme 0 dys period. The dte is in DD/MM/YYYY nd the time is in HH.MM.SS.MS formt. The unit of electron density is Ne/cm 3. 3 From the Spcecrft Position Dt Set, one orbit long sets of dt (usully round 630 sets of dt) re selected nd loded into the sheet of the progrmmed spredsheet TEC Builder in columns B to J. 4 The corresponding electron density dt set is selected for the sme time rnge nd loded into the sheet of the TEC Builder spredsheet. The dte 08

134 dt is loded in column B, the time dt is loded in column D nd the density dt is loded in column G. 5 On loding these sets of dt, the progrm utomticlly crries out ll of the clcultions ecept the Line of Nodes nd the Argument of Peripsis clcultions. 6 The Ascending Node nd the Descending Node coordintes should be mnully loded in the TEC Builder. For tht the vlues of the Z is should be nlysed nd the two points where the sign chnge occurs should be mrked nd the respective X, Y coordinte long with the Z coordinte should be copied nd loded. The TEC Builder clcultes the Grdient nd the Intercept vlues of the line eqution of the Line of Nodes in the Equtoril plne nd thus the Longitude of the Ascending Node ( ). 7 The Argument of Peripsis should be clculted from the X nd Y coordinte vlues of the Peripsis nd Apopsis points in the orbitl plne. These vlues re clculted in the W nd Z columns in the TEC Builder. The Peripsis nd Apopsis points in the originl coordintes re mrked their respective trnsformed is coordintes in the orbitl plne re used for the clcultion of the Argument of the Peripsis. 09

135 LINE OF NODES y z A B A y0a B y0b m c Ω Figure 6.5 Longitude of the Ascending Node ( ) clcultion for the orbit on ARGUMENT OF PERIAPSIS Xp X Yp Y Yp/Xp X/Y w Figure 6.6 Argument of Peripsis ( ) clcultion for the orbit on With these clcultions, the TEC Builder completes the whole procedure. 0

136 6.4. The Algorithm After the dt entry, the TEC Builder spredsheet hs the spcecrft position dt nd the density dt in two different sheets, Sheet nd Sheet respectively. As both dt sets need to be merged, ech dt line needs to be given unique time stmp. To chieve this, in Sheet the dy of the yer in column C is multiplied by 4 nd dded with the time dt in column D. The result is stored in column A nd formtted to deciml numbers. The formul is: A = (C*4) + D In density dt in Sheet, column B contins dte in DD/MM/YYYY formt. It is converted to dy of the yer formt nd stored in column C by the formul below: C = B-DATE(YEAR(B),,0) In density dt, the electron density is verged for one minute nd the verged figure is given ginst the verge time. Therefore the time informtion is 30 seconds pst the minute. As the spcecrft position dt is time stmped t the beginning of the minute, the 30 seconds need to be deducted, in order to synchronise the time stmp. This is chieved by entering 00:00:30 seconds in column E nd deducting E from D nd storing the result in F. The formul is: F = D E 6.5 As the density dt is verged for the minute, it does not hve ny effect if the time stmp denoted t the beginning of the minute.

137 5 The unique time stmp is chieved by multiplying dy of the yer in column C by 4 nd dding it with the new time dt in column F. The result is stored in column A nd formtted to deciml numbers. The formul is: A = (C*4) + F From point 7 till point 35, the lgorithm determines the ellipse eqution of the orbit in the formt: b y 6.7 For tht, it is necessry to crry out is rottions to bring the GEI/J000 bsed coordintes to the orbitl is, then rotte the X is to the semi mjor is of the ellipse nd then move the origin to the centre of the ellipse from the centre of the erth which is focus of the ellipse. 7 For these mnipultions, it is necessry to clculte the orbitl elements from the vilble coordinte set. 8 As the first step, the eqution of the orbitl plne needs to be determined. As there is big set of X, Y nd Z coordintes, the best fitting plne eqution hs to be determined. This is chieved by wy of pplying the Lest Squres Fit method. The theory used, the clcultions mde nd the progrmming re described in Appendi 6. The constnts of the orbitl plne eqution re determined by TEC Builder spredsheet.

138 9 As the orbitl plne eqution is determined, the ngle between this plne nd the reference (which is the equtoril plne) cn be determined. As the equtoril plne consists of the X nd Y es nd the Z is coordintes re zero in tht plne, the eqution of the equtoril plne is: Z = The ngle between the two plnes bove is equl to the Inclintion ngle (i). The theory nd clcultions re given in section The resulting Inclintion ngle (i) is tbulted in Column Y of the TEC Builder The Ascending Node nd the Descending Node coordintes re determined by locting the Z = 0 points. As the coordintes re downloded in kilometres, it is etremely unlikely to get 0 vlue. Therefore, the coordinte vlues where the Z is undergoes sign chnges re locted. As eplined in Section 6.4. previously, the corresponding X, Y coordintes re loded to the TEC Builder spredsheet nd the progrm clcultes the coordintes for the Ascending Node nd the Descending Node by interpolting for the zero vlues of Z coordintes. The corresponding rtio interpolted X, Y coordintes re clculted nd they yield the coordintes for the Ascending Node nd the Descending Node. The Ascending Node nd the Descending Node re differentited by the sign chnge of the Z coordintes. A Plus to Minus sign chnge denotes the Descending Node nd Minus to Plus sign chnge denotes the Ascending Node. 3 The Line of Nodes is the intersection line of the orbitl plne nd the reference plne. By definition the Longitude of the Ascending Node ( ) is the ngle 3

139 between the reference direction (Vernl Equino) nd tht of the Ascending Node in the Line of Nodes mesured positively from 0 0 to 80 0 in the forwrd direction. If the line eqution of the Line of Nodes is determined from the GEI/J000 coordintes of the Ascending Node nd the Descending Node, the Grdient of tht line will be equl to the Longitude of the Ascending Node ( ) s the reference X is direction is the direction of Vernl Equino. Z coordintes in tht line eqution will be equl to (or very close to) zero. Figure 6.7 Equtoril plne digrm showing Longitude of the Ascending Node ( ) being equl to the Grdient ngle of the Line of Nodes in GEI/J000 system for generl cse. The Z is is perpendiculr to the plne nd is pointing out. 4 The clcultion of the Longitude of the Ascending Node ( ) is shown in Figure 6.6 nd detiled in the following sections. 4

140 The formul for the clcultion is: = (ATAN(P703))*80/PI() 6.9 Where P703 denotes m the grdient of the Line of Notes. The vlue of the Longitude of the Ascending Node ( ) is tbulted in Column V. 5 The first is trnsformtion is crried out by rotting the reference plne by the Longitude of the Ascending Node ( ) ngle in the clockwise direction. The Z is vlues remin the sme s the reference plne consists of X nd Y es nd only those es re rotted. 6 The Longitude of the Ascending Node ( ) vlue is tbulted in the Column V of TEC Builder. The clcultions for the rottion of of the new X nd Y es re s follows: X = ((E*(COS(V*PI()/80))) + (F*(SIN(V*PI()/80)))) 6.0 Y = ((F*(COS(V*PI()/80))) - (E*(SIN(V*PI()/80)))) 6. The theory of is rottion is detiled in the following sections. 7 The new X is is Line of Nodes, towrds the Ascending Node. The Z is is the previous Z is, which is the erth s is of rottion tht goes through the Geogrphic North pole. The origin is the centre of the erth nd the Y is completes the right hnd trid. 5

141 8 Now the second coordinte trnsformtion would tke plce. In this trnsformtion, the coordintes Y nd Z re rotted positively (counter clockwise) through the Inclintion ngle (i ). Therefore the X is remins the sme from the previous trnsformtion nd the Y nd Z es re rotted. The coordintes re nmed Y nd Z nd re tbulted in Columns Z nd AA. The Inclintion ngle ( i ) is tbulted in Column Y. 9 The clcultions for the rottion of the new X nd Y es re s follows: Y = ((X*(COS(Y*PI()/80))) + (G*(SIN(Y*PI()/80)))) 6. Z = ((G*(COS(Y*PI()/80))) - (X*(SIN(Y*PI()/80)))) Now the new coordintes system hs its X nd Y es in the orbitl plne nd the X is points towrds the Vernl Equino. As elborted in section 6.3., the with these two is trnsformtions through the Longitude of the Ascending Node ( ) nd the Inclintion ngle ( i ), the orbitl plne is defined nd fied. As the new X nd Y es s re in the orbitl plne now, the Z coordintes should be zero. This is verified by Z vlues in Column AA, which re either zero or negligible vlues. Net, the Argument of Peripsis ( ) needs to be clculted. The dt input procedure ws detiled in section 6.4. nd the Figure The new coordintes of the orbit re derived from the Input Dtset. All the z vlues should be equl to zero in the new, trnsitory coordintes. 6

142 4 Now, the distnce between strting point nd the origin is clculted. 5 The procedure is repeted for ll points in the orbit. 6 The mimum nd the minimum distnces re mrked. 7 The corresponding coordintes re mrked. They re the Apopsis nd Peripsis points. 8 The line connecting these points is the semi mjor is. 9 The semi mjor is line eqution is determined using these points. 30 The Argument of Peripsis is determined by the ngle between this line eqution nd the Line of Nodes line eqution. 3 Now the coordinte system is turned nti clockwise through this ngle bout the new Z is. 3 The new coordintes of the orbit re determined. 33 The Apopsis nd Peripsis points new coordintes re determined. 34 Now the semi mjor is is the new X is nd the centre of the erth is the focus. 7

143 35 The D Crtesin ellipse eqution of the orbit cn now be determined by the Peripsis nd Apopsis informtion. 36 From this new nd finl coordinte system trnsformtion, the true nomly of ny stellite position cn be determined. 37 From here onwrds the, the mechnism for the determintion of the UPEC vlues cn be implemented, s detiled in the following methodology Mechnism for the determintion of the UPEC The methodology is devised s below: The orbitl trce through the ltitude 0000km to 40000km is considered (bout 3.5 Re to 6.5 Re). The spcecrft psses this region in hour nd 7 minutes (400 seconds) 3 Men electron densities re clculted every 60 seconds, equlling 5 spins. 4 The distnce covered in every 60 second is clled UPEC Br 6 If the electron density vrition turns out to be more thn 0% within tht br, hlved sub brs re considered. 8

144 7 The orbitl rc distnce covered by the UPEC br in 60 seconds is clculted. 8 The men point long tht pth is clculted. The tngent line t this ment point is determined. 9 The ngle the tngent line to the orbit t this point mkes with the line to the centre of the erth is clled the incident ngle. 0 Numericl integrtion is performed on electron density long the UPEC br orbitl distnce. The resulting vlue is tken s the STEC t the tngent point, the incident ngle being clculted in point 9 bove. The VTEC for tht rc is derived from the STECs nd the incident ngles. 3 This vlue is proportiontely multiplied by the rtio of the.5 Re divided by the rc distnce clculted in point 7 bove nd the UPEC br is derived Notes on utomtion of the lgorithm. The 37 point lgorithm elborted bove is utomted ecept for one step. The coordintes of the Ascending Node nd the Descending Node need to be mnully loded in TEC Builder for the rest of the clcultions to be utomticlly eecuted. This is done in Step of the lgorithms bove. 9

145 Even this step cn be utomted by wy of locting the sign chnge in the Z coordinte. If there is sign chnge, the following logic will pply: For positive to negtive chnge: Zn Z (n+) > Zn 6.4 Where Zn is the n th reding nd Z (n+) is the (n+) th reding For negtive to positive chnge: Zn Z (n+) > Zn 6.5 Where Zn is the n th reding nd Z (n+) is the (n+) th reding Therefore, commonly for sign chnge in Z coordintes: Zn Z (n+) > Zn 6.6 Where Zn is the n th reding nd Z (n+) is the (n+) th reding By implementing this in the progrm, the Z coordinte sign chnge cn be locted nd consequently the coordintes of the Ascending Node nd the Descending Node cn be found utomticlly. 0

146 Chpter 7 Derivtions, Theories nd Clcultions ((This Chpter is completely my own work) During the course of the reserch, further nlysis of the TEC clcultion methodology hs resulted in few chnges to the initil procedure. The most significnt being the correction introduced to clculte the hypotenuse length in the imginry right ngled tringle long the orbitl pth from the orbitl rk length. As there is wy to clculte the incident ngle directly from the ellipse eqution in the orbitl plne, the need to construct the imginry tringle does not rise. 7. Deriving the plne eqution The generl 3d eqution 7.0 below needs to be solved nd the coefficients determined to derive the plne eqution. by z c The Appendices 6 nd 7 demonstrtes the mthemticl derivtions utilised nd the resulting plne coefficient reltionships re s follows: yb c z 0 y y b yc yz 0 yb c z 0

147 7.. Clcultion of plne coefficients c b,, From the Spcecrft Position Dt Set, one orbit long sets of dt (usully round 630 sets of dt) re selected nd loded into the sheet of the progrmmed spredsheet TECbuilder in columns B to J. The summted versions of the plne coefficient reltionships 7.0, 7.03 nd 7.4 re used to generte the three simultneous equtions needed for the determintion of the plne eqution. The corresponding summted formts respectively re: 0 i n i i n i i i n i i n i i z c b y i n i i n i i n i i i n i i z y c y b y y n i i n i i n i i z c b y The corresponding three simultneous equtions with coefficients 3 3 3,,,,,,,, o n m o n m o n m nd constnts 3,, d d d s shown in Appendi 8 re: 0 d o c n b m 0 d c o b n m d c o b n m The following Tble 7. on the net pge gives the coefficients of simultneous equtions, the summted equivlents nd their TecBuilder Positions.

148 Coefficient/Constnt Summted quntity TEC Builder Position m m 3 m 3 4 n 5 n 6 n 3 7 o 8 o n i i L654 n i y P656 i i n i i S658 n i y P656 i i n y i i M656 n y i i T658 n i i S654 n y i i T656 9 o 3 O658 0 d d d 3 n i z R654 i i n y i z Q656 i i n z i i U658. Tble 7. - The coefficients of simultneous equtions, the summted equivlents nd The plne coefficients equtions in Appendi 8. their TECbuilder positions, b nd c re clculted using these summted vlues, s per the 3

149 4 ) )( ( ) )( ( ) )( ( ) )( ( ) ( m n m n m o m o m n m n m o m o m n m n m d m d m n m n m d m d c ) ( ) ( ) ( m n m n m d m d c m o m o b d c o n b m The corresponding TecBuilder clcultions re: c ((((L664*M66) -(L66*M664))*((L666*P66)-(L66*P666))) - (((L666*M66) - (L66*M666))*((L664*P66) - (L66*P664))))/((((L666*M66) -(L66*M666))*((L664*N66) - (L66*N664))) - (((L664*M66) - (L66*M664))*((L666*N66)- (L66*N666)))) 7.05 b ((N664*L66*Q670) + (P664*L66) - (N66*L664*Q670) - (P66*L664))/((M66*L664) - (M664*L66)) 7.06 (-)*((M66*Q673)+(N66*Q670)+(P66))/(L66) 7.07 The vlues of the plne coefficients b, nd c re clculted t the TecBuilder positions Q 676, Q673 nd Q670 respectively.

150 7.. Clcultion of the Inclintion ngle The Inclintion ngle is derived s described in Appendi 8. Therefore: 0 b 0 Cos( i) b i Cos 7.09 b In the TEC Builder, Cos(i) is clculted in the cell Q679 by the following eqution: Cos (i) =/(SQRT((Q673)*(Q673) + (Q676)*(Q676) + )) 7.0 Consequently, Inclintion ngle i is clculted in the cell Q68 by the following eqution: i (ACOS(Q679))*80/PI() Coordinte Trnsformtion theories 7.3. Coordinte trnsformtion of two es Crtesin plne by n ngle of New coordintes of two dimensionl coordinte system, fter rottion by given by: 0 re ' ( Cos ysin ) 7. y ' ( ycos Sin ) 7.3 5

151 7.3. Coordinte Trnsformtion Mtri The trnsformed coordintes cn be represented by the following mtri eqution: ' Cos ysin ' y ycos Sin 7.4 ' Cos ' y y Sin Sin Cos 7.5 Therefore, the rottion mtri is given by: Cos Sin R Sin Cos Trnsformtions to derive the orbitl plne coordintes '' z z 0 i '' y 0 i 0 y ' 0 ' y Figure 7.3 Trnsformtions to derive the orbitl plne coordintes with Line of psides s the is 6

152 Trnsformtions to derive the orbitl plne coordintes with Line of psides s the is re crried out in two stges: Trnsformtion : Trnsformtion through the Longitude of the Ascending Node ( 0 ) Trnsformtion : Trnsformtion through the Inclintion ngle ( 0 i ) 0 Trnsformtion : Trnsformtion through the Longitude of the Ascending Node. ( ) This trnsformtion genertes ' from nd ' y from y. In this trnsformtion tke plce in the orbitl plne, the z coordintes don t chnge. The resulting coordintes system will hve the Line of Nodes s its is Clcultion of the Longitude of the Ascending Node 0 ( ) 7., 7.3 ' 0 0 ( Cos ysin ) 7.7 ' 0 0 y ( ycos Sin ) 7.8 In the TEC Builder, Cos(i) is clculted in the cell Q679 by the following eqution: Cos (i) =/(SQRT((Q673)*(Q673) + (Q676)*(Q676) + )) 7.9 Trnsformtion : Trnsformtion through the Inclintion ngle ( 0 i ) bout the Line of Nodes - This trnsformtion genertes '' y from. y nd,, z from z. As the trnsformtion is bout the new is, which is the Line of Nodes, the is coordintes, (which re ' ) do not chnge, during this trnsformtion. The resulting coordintes re: 7

153 7., 7.3,, ' 0 0 y ( y Cos( i ) zsin( i )) 7.0 z,, 0, 0 ( zcos( i ) y Sin( i )) Trnsformtions through the Argument of Peripsis Line of Nodes '' z A '' y O ( 90 ) 0 0,,, y 0 Apopsis B ( X P, YP ),,, ' Figure 7.4 Trnsformtions through the Argument of Peripsis with Line of psides s the new y is The trnsformtion is crried out by rotting the clockwise direction., nd,, y es by 0 ( 70 ) in the 8

154 In Figure 7.4, considering the tringle ABO :,, AO y 7., AB AO Tn( ) 7.4 AB,, y 7., 7.3, 7.4 Tn( 0 ),,, 0 y Tn 7.5, The trnsformed coordintes will be given by: ' o '' o Cos(70 ) y Sin( ''' ) y ''' ) '' o ' o y Cos(70 ) Sin( Clcultion of n Orbitl Arc Length In the Section 6.4.3, Mechnism for the determintion of the TEC in the Methodology, the point 7 stipultes tht the orbitl rc distnce covered by the TEC br in 60 seconds is clculted. This is chieved by determining the ellipse eqution of the orbit with its centre t the origins of the, y es nd pplying the Arc Length formul derived from the following section

155 7.5. Ellipse eqution of the orbit with its centre t the origin of, y es nd Line of Apsides s the is y b O(0,0) Figure 7.5 Ellipse with centre t the origin of D Crtesin plne Considering n ellipse with its centre t the origin of D Crtesin plne (Figure 7.5), if it s Semi Mjor Ais is nd Semi Minor Ais isb, then the ellipse eqution gives: b y 7.8 y b Clcultion of the Arc Length of function y f (). P, y.. P, y y Figure 7.6 Arc length of function f (), y P in D Crtesin plne y between two points 30 P nd, y

156 The Arc Length of ny given function in D Crtesin plne, of the form y f () is given by: PP dy d 7.30 d Clcultion of the Arc Length of the orbitl ellipse with its centre t the origin nd the Line of Apsides s the is y B, y b A, y O(0,0) Figure 7.7 Orbitl ellipse with its centre t the origin of, y es nd Line of Apsides s the is A, y ) nd B, y ) re two points long its Perimeter, then the Arc Length of the ( rc AB is given by: ( dy 7.30 Arc Length AB = d d 7.3 3

157 3 7.3 b y b y b y Differentiting both sides with respect to, we get: d d b y d d 0 d dy b y d dy b y b y d dy 7.3 b b d dy b d dy 7.33 b d dy b d dy 4 b d dy 7.34

158 Arc Length AB = d d dy d b AB 4 4 d b AB 4 4 d b AB 4 d b AB 4 d b AB 7.35 Substitute Sin 7.36 Cos d d Also Sin Cos ) ( Cos ) ( Cos 7.38

159 The limits of the integrl re nd, which re the coordintes of the points A nd B. For the bove substitution, the new limits need to be clculted. Let nd be the new limits. Then; 7.36 Sin Sin 7.39 Similrly Sin 7.40 Sin Substituting 7.55,7.56 nd 7.57 in 7.58, we get, Arc length; b Sin 4 AB Cos. d Cos b Sin AB Cos d 4 Cos 4 AB AB b Sin 4 d b Sin b Sin d AB. 4 d

160 But, from the properties of ellipse Eccentricity e b 7.4 b e , 7.43 Arc length AB e Sin. d 7.44 This function cnnot be integrted directly. Therefore it needs to be converted into series using the binomil theorem nd then cn be integrted. The binomil theorem gives: n n nk k p q p q k 0 n k , 7.45 Arc length AB e Sin. d Evluting this integrl cn be esier if it s evluted s n Indefinite Integrl nd the limits pplied fter the finl solution is derived. Therefore, the length AB cn be epressed in terms of the Constnt of IntegrtionC. e Sin. d C AB 35

161 36 Applying Binomil theorem; 4 Sin e Sin e AB C d Sin e Sin e Sin e Sin e AB C d Sin e Sin e Sin e Sin e AB C d Sin e Sin e d Sin e d Sin e d AB C d Sin e d Sin e d Sin e d Sin e d AB C d Sin e d Sin e

162 As these integrls re of the form Sin n. d, they cn be integrted using the following Reduction Formul. Reduction Formul gives: If n I n Sin. d, n Then, ni n Sin. Cos n I n 7.47 I n Sin n n n. Cos n I I Sin. d 0 I.d I C 7.48 () n Sin. d Sin. Cos I C Sin d Sin. Cos I 0. C Sin d Sin. Cos 3. C (4) n Sin. d Sin. Cos 4 I 4 C Sin. d Sin. Cos 3I C Sin. d Sin. Cos 3 Sin. d C

163 n 5 6 ) ( C I Cos Sin d Sin C I Cos Sin d Sin C d Sin Cos Sin d Sin n 6 8 ) ( C I Cos Sin d Sin C I Cos Sin d Sin C d Sin Cos Sin d Sin 7.53 Substituting 7.59, 7.60, 7.6, 7.6 nd 7.63 in 7.56 gives us the solution for the length AB. 7.49, 7.50, 7.5, 7.5 nd 7.53 in 7.46 Cos Sin e AB. d Sin Cos Sin e d Sin Cos Sin e C d Sin Cos Sin e

164 39 Cos Sin e AB. d Sin Cos Sin e d Sin Cos Sin e C d Sin Cos Sin e 7.54 The vlue of the integrl cn be determined in terms of by bck-substituting the vlues of Cos Sin,, nd e Sin Sin Sin Sin Cos ) ( Cos b e

165 , 7.54 & 7.55 ) (. Sin e Sin AB 3 4 ) (. 3 ) (. 4 4 Sin e ) (. 3 ) (. 5 ) ( Sin e ) (. 3 ) (. 5 ) (. 7 ) ( C Sin e 7.56 The terms succeeding the third term in the bove integrl re insignificnt due to the lrger denomintors nd very high powers of e. Therefore they cn be neglected nd the length AB cn be equted to the first three terms for ll relistic clcultions with high degree of confidence.

166 4 ) (. Sin e Sin AB ) (. 3 ) (. 4 4 C Sin e 7.57 The bove integrl provides the Arc Length of the orbitl ellipse s n Indeterminte Integrl. The Determinte Integrl cn hve the limits nd, respective to nd. Therefore the rc length between the coordintes nd cn be given s: Sin e Sin AB ) (. 3 4 ) ( 3 ) (. 4 4 Sin e 7.58 The technique used in TEC Builder clcultes the length of the rc from the origin to the position of the stellite on every row. Therefore the upper limit of the integrl is the coordinte '''' in the new trnsformed coordinte system nd the lower limit is 0. Therefore the rc length from 0 or the y is cn be clculted by substituting 0 nd ''''.

167 Sin e Sin AB ) (. Sin e 3 4 ) (. 3 ) (. 4 4 Sin e Sin ) (. Sin e 3 4 ) (. 3 ) ( Substituting 0 nd '''' Sin e Sin AB '''' '''' '''' '''' ) (. Sin e '''' '''' '''' '''' 3 '''' 4 ) (. 3 ) (. 4 4 Sin e Sin 0 ) 0 (. 0 0 Sin e 0 ) 0 (. 0 3 ) 0 (

168 43 Sin e Sin AB '''' '''' '''' '''' ) (. Sin e '''' '''' '''' '''' 3 '''' 4 ) (. 3 ) ( ) 0 ( 0. 0 Sin e Sin 0 ) 0 ( 0. 3 ) 0 ( Sin e Therefore: Sin e Sin AB '''' '''' '''' '''' ) (. Sin e '''' '''' '''' '''' 3 '''' 4 ) (. 3 ) ( e e Sin e Sin AB '''' '''' '''' '''' ) (. 0 ) (. 3 ) (. 4 4 '''' '''' '''' '''' 3 '''' 4 Sin e

169 44 Sin e Sin AB '''' '''' '''' '''' ) (. Sin e '''' '''' '''' '''' 3 '''' 4 ) (. 3 ) ( The bove epression hs been used in clculting the rc length from the 0 or the y is in column AP in TEC Builder. The TEC Builder clcultes the bove epression in prts. The prts clculted nd their corresponding TEC Builder Columns re given below: Clcultion prt TEC Builder Column AK ' ''' AG 3 Sin '''' AN 4 Sin '''' '''' '''' ) (. AO 5 e AM Tble 7. Components of the Arc Length clcultion formul nd corresponding TEC Builder Columns

170 As the integrl component '''' '''' '''' ( ). Sin is repeted twice in the formul 7.0. Therefore, it is seprtely clculted in column AO nd used in the finl clcultion of the formul. The following Ecel formul is used for it s clcultion: AO=(AN -(AG*(SQRT((AK*AK) - (AG*AG)))/(AK*AK))) 7.6 The Arc length from the from 0or the y is in column AP using the following Ecel formul: AP=(AK)*((AN) - (((AM)/4)*(AO)) - (((AM*AM)/3)*((3*(AO)) - ((AG*AG*AG)*(SQRT((AK*AK) - (AG*AG)))/(AK*AK*AK*AK))))) 7.6 The finl Arc length the stellite trces between two subsequent redings (ie. between two coordintes) is determined by clculting the difference between the successive Arc lengths from y is clculted in column AP. The following Ecel formul gives the Arc Length between two subsequent redings: AQ=ABS(AP-AP) 7.63 Clcultion of the TEC Br Length 45

171 7.6 Clcultion of the UPEC Br length 7.6. Tngent Line Construction nd the determintion of the Incident Angle Y S α P (X,Y) (90- α) (90- α) θ (ß -90) α T ß (80- ß ) ß F (-f,0) O (0,0) R Q (X,0) F (f,0) X Figure 7.8 Descriptive digrm for Tngent Line construction nd the determintion of the Incident Angle 46

172 Considering the figure 7.8: Let P (, y) be ny point in the orbitl ellipse nd the line SPT be the Tngent t tht point; Let F(-f, 0) nd F(f, 0) be the foci of the ellipse. Either one of them could be the centre of the erth. By the definition of ellipse, SPF = TPF 7.64 This ngle is equl to the Incident ngle. If the lines connecting the stellite nd the foci mke ngles nd respectively with the is, the perpendiculr line to the is from the stellite meets the is t Q, the perpendiculr line to the tngent line meets the is t R nd the ngle between PR nd PQ ( QPR ) is, then: PF Q QPF (80 ) QPF 90) 7.66 ( SPT RP 7.64 SPF = TPF 47

173 RPF RPF QPF RPQ 7.69 QPF QPR RPF RPQ QPF RPF 7.67, 7.68 & 7.69 ( 90 ) (90 ) ( ) 7.68 RPF RPQ QPF RPQ RPF QPF 7.67, 7.68 & 7.69 ( 90 ) ( 90) 80 ) 7.69 ( 7.68 & 7.69 ( ) (80 ) ( 80) ( 80) 7.70 In PQF, Tn PQ F Q Tn 48 f y

174 y Tn 7.73 f In PQF, Tn( 80 ) PQ F Q Tn f y 80 Tn f y y Tn f, & re clculte in columns AH, AI & AJ in the TEC Builder. The formule used re: AH=ATAN(AE/(AF+AG))*80/PI() 7.75 AI=(80 - ATAN(AE/(AF-AG))*80/PI()) 7.76 AJ=(AH-AI+80)/ Clcultion of the UPEC Br length If the eqution for n ellipse in given s b y Then, the eqution of the Tngent line to tht ellipse t point P 0, y ) in the ellipse is given by: ( 0 49

175 0 b yy B A Considering the Figure 7.9 bove: Figure 7.9 Clcultion of the UPEC Br length The orbitl position dt nd the electron density dt re provided in per minute bsis. The distnce between two points in stright lie is given by: d y y b b 7.79 The line eqution of tngent line t point P3(3, y3) is given by: 3 b yy b yy3 b y b y b

176 5 3 3 ) ( y b y 7.8 Any point on the tngent line cn be given by * ) ( y b y * 5 ) ( y b y 7.79 * * 5 5 y y d ) ( ) ( y b y b d ) ( ) ( y b y b d ) ( ) ( y b d y b d y b d y b d b y y d ) ( ) ( y b y d 7.8 Here '''' nd ''' y y

177 7.7 Summery of TEC Builder Clcultions TEC Builder Sheet No. TEC Builder Column Ecel Formul. A. A=(C*4) + D. B. Direct Input 3. C. Direct Input 4. D. Direct Input 5. E. Direct Input 6. F. Direct Input 7. G. Direct Input 8. H. Direct Input 9. I. Direct Input 0. J. Direct Input. K. Empty. L. L=E*E Tble 7.3- Summery of TEC Builder Clcultions - TEC Builder Sheet 5

178 No. TEC Builder Column Ecel Formul 3. M. M=F*F 4. N. N=G*G 5. O. 6. P. P =*E*F 7. Q. Q =()*F*G 8. R. R =()*E*G 9. S. S =*E 0. T. T =*F. U. U =()*G. V. V =P W. W =((E*(COS(V*PI()/80))) + (F*(SIN(V*PI()/80)))) 4. X. X =((F*(COS(V*PI()/80))) - (E*(SIN(V*PI()/80)))) 5. Y. Y =Q68 6. Z. Z =((X*(COS(Y*PI()/80))) + (G*(SIN(Y*PI()/80)))) Tble 7.3-b Summery of TEC Builder Clcultions - TEC Builder Sheet 53

179 No. TEC Builder Column Ecel Formul 7. AA. AA =((G*(COS(Y*PI()/80))) - (X*(SIN(Y*PI()/80)))) 8. AB. AB=SQRT((W*W) + (Z*Z)) 9. AC. AC=P AD. AD=((W*(COS(AC*PI()/80)))+(Z*(SIN(AC*PI()/80)))) 3. AE. AE=((Z*(COS(AC*PI()/80))) - (W*(SIN(AC*PI()/80)))) 3. AF. AF=P AG. AG=((AD) - (AF)) 34. AH. AH=ATAN(AE/(AF+AG))*80/PI() 35. AI. AI=(80 - ATAN(AE/(AF-AG))*80/PI()) 36. AJ. AJ=(AH-AI+80)/ 37. AK. AK=P AL. AL=P AM. AM=((AK*AK) - (AL*AL))/(AK*AK) 40. AN. AN=ASIN(AG/AK) Tble 7.3-c Summery of TEC Builder Clcultions - TEC Builder Sheet 54

180 No. TEC Builder Column Ecel Formul 4. AO. AO=(AN -(AG*(SQRT((AK*AK) - (AG*AG)))/(AK*AK))) 4. AP. AP=(AK)*((AN) - (((AM)/4)*(AO)) - (((AM*AM)/3)*((3*(AO)) - ((AG*AG*AG)*(SQRT((AK*AK) - (AG*AG)))/(AK*AK*AK*AK))))) 43. AQ. AQ=ABS(AP-AP) 44. AR. AR=VLOOKUP(A,Sheet!A:G,7,FALSE) 45. AS. AS=(AQ*AR)* AT. AT=(AS+AS+AS3+AS4) 47. AU. AU=AQ+AQ+AQ3+AQ4 48. AV. AV=(AT/AU)/ AW. AW=P AX. AX=P AY. AY=((AG-AG5)/(((AW)^)*AE3))*(SQRT(((AG3*((AX)^))^)+((AE3*((AW)^))^))) 5. AZ. AZ=AV*AY/(0^3) 53. BA. BA=((AZ/AY)*0000) 54. BB. BB=IF(BA>0.0000,BA*00%,0%) 55

181 Tble 7.3-d Summery of TEC Builder Clcultions - TEC Builder Sheet TEC Builder Sheet TEC No. Builder Clcultion Ecel Formul Column. A. A=(C*4) + F. B. Vlue Only Direct Input 3. C. C=B-DATE(YEAR(B),,0) 4. D. Vlue Only Direct Input 5. E. Vlue Only Direct Input 6. F. F=D - E 7. G. Vlue Only Direct Input Tble 7.4 Summery of TEC Builder Clcultions - TEC Builder Sheet 56

182 7.8 Verifictions Verifiction of the multitude of clcultions crried out in TEC Builder cn be crried out by mens of the following evidences: Verifiction : Verifiction : Verifiction 3: Verifiction 4: Verifiction 5: Line of Node intercept vlue close to zero Z coordinte close to zero Argument of Peripsis vlues re very close by both methods The trnsformed coordintes produce perfect ellipticl orbits. Consistent inclintion ngle over the orbitl period, which grdully chnges in conformity with ctul GEI/J000 coordinte plots The principles behind the bove verifictions nd evidences for them re provided in the following sections: 7.8. Verifiction : Line of Node intercept vlue close to zero In the lgorithm, the Step 3 sttes the Line of Nodes is the intersection line of the orbitl plne nd the reference plne. By definition the Longitude of the Ascending Node ( ) is the ngle between the reference direction (Vernl Equino) nd tht of the Ascending Node in the Line of Nodes mesured positively from 0 0 to 80 0 in the forwrd direction. If the line eqution of the Line of Nodes is determined from the GEI/J000 coordintes of the Ascending Node nd the Descending Node, the Grdient of tht line will be equl to the Longitude of the Ascending Node ( ) s the reference X is direction is the direction of Vernl Equino. Z coordintes in tht line eqution will be equl to (or very close to) zero. This cn be illustrted by Figure

183 Also, the intercept of tht line should be going through the origin, which is the centre of the erth, if ll the clcultions, trnsformtions nd progrmming worked correctly. When the lgorithm is implemented, this verifiction is ttined s the intercept vlues re very close to zero. The intercept vlues of the Line of Nodes eqution re given below in Tble 7.5 for smpled dtes: No Dte Intercept vlues of the Line of Nodes eqution (s percentge of peripsis) 0/03/ /0/ /05/ /07/ /0/ /04/ /05/ /07/ /08/ /03/ Tble 7.5 Intercept vlues of the Line of Nodes eqution for smpled dtes 7.8. Verifiction : Z coordinte close to zero The lgorithm converts GEI/J000, which hve vrying, y, z coordintes to coordinte system with nd y es on the orbitl plne nd the z is perpendiculr to tht plne. 58

184 The step 6 of the lgorithm sttes tht from point 7 till point 35, the lgorithm determines the ellipse eqution of the orbit in the formt: b y 6.7 For tht, it is necessry to crry out is rottions to bring the GEI/J000 bsed coordintes to the orbitl is, then rotte the X is to the semi mjor is of the ellipse nd then move the origin to the centre of the ellipse from the centre of the erth which is focus of the ellipse. Therefore, if the lgorithm is working without errors, ll the z coordintes obtined fter the lst coordintes trnsformtion should be zero (or very smll vlues). It cn be seen tht the eqution 6.7 is D eqution nd there re no z vlues. This is verified by the following grphs of originl z coordintes in GEI/J000 coordintes vlues nd z coordintes vlues fter the coordinte trnsformtions ginst Time. 59

185 Z Coordinte (km) Z Coordinte (km) Time (Minutes) Legend Z coordintes vlues fter the coordinte trnsformtions GEI/J000 Z coordinte vlues Figure 7.0 Grph of GEI/J000 Z coordinte vlues nd z coordintes vlues fter the coordinte trnsformtions ginst Time strting t on 0/06/ Time (Minutes) Legend Z coordintes vlues fter the coordinte trnsformtions GEI/J000 Z coordinte vlues Figure 7. Grph of GEI/J000 Z coordinte vlues nd z coordintes vlues fter the coordinte trnsformtions ginst Time strting t on 30/0/004 60

186 Z Coordinte (km) Z Coordinte (km) Time (Minute Legend Z coordintes vlues fter the coordinte trnsformtions GEI/J000 Z coordinte vlues Figure 7. Grph of GEI/J000 Z coordinte vlues nd z coordintes vlues fter the coordinte trnsformtions ginst Time strting t on 08/08/ Time (Minutes) Legend Z coordintes vlues fter the coordinte trnsformtions GEI/J000 Z coordinte vlues Figure 7.3 Grph of GEI/J000 Z coordinte vlues nd z coordintes vlues fter the coordinte trnsformtions ginst Time strting t on /03/006 6

187 Z Coordinte (km) Time (Minutes) Legend Z coordintes vlues fter the coordinte trnsformtions GEI/J000 Z coordinte vlues Figure 7.4 Grph of GEI/J000 Z coordinte vlues nd z coordintes vlues fter the coordinte trnsformtions ginst Time strting t on /0/ Verifiction : Argument of Peripsis vlues re very close by vector nlysis method nd from the lgorithm The lgorithm clcultes the Argument of Peripsis ( ) t Step. The procedure ws detiled in section 6.4. nd detiled in Figure 6.6. The point 7 of the section 6.4. sttes tht The Argument of Peripsis should be clculted from the X nd Y coordinte vlues of the Peripsis nd Apopsis points in the orbitl plne. These vlues re clculted in the W nd Z columns in the TEC Builder. The Peripsis nd Apopsis points in the originl coordintes re mrked their respective trnsformed is coordintes in the orbitl plne re used for the clcultion of the Argument of the Peripsis. 6

188 For verifiction, the Argument of Peripsis ( ) cn lso be clculted from the GEI/J000 coordintes of the pogee / perigee points nd the Line of Nodes eqution, in vector nlysis. The verifiction is demonstrted for the orbit on 0/03/004 below: P ( , 356.9, ) p O(0,0) ( ) A(9548.4, 8573., 0) Figure 7.5 Vector digrm for the perigee nd the Ascending Node Perigee coordintes in GEI/J000 P( , 356.9, ) Therefore the vector p = i j k Ascending Node coordintes in GEI/J000 A(9548.4, 8573., 0) Therefore the vector = i j + 0 k Therefore the ngle between them = Cos - (.p /(. p ) Argument of Peripsis ( ) = From the TEC Builder the Argument of Peripsis ( ) = The vlues re very close. 63

189 Trnsformed Y Coordinte (km) Verifiction 4: The trnsformed coordintes produce perfect ellipticl orbits. The lgorithm produces perfect ellipticl orbits s illustrted by the plots obtined for smpled dtes below (Multiple orbits hve been plotted consequently for continuous verifiction): Trnsformed X Coordinte (km) (Repeting) Figure 7.6 Orbitl plot for 0/03/004 to 0/03/004 64

190 Trnsformed Y Coordinte (km) Trnsformed X Coordinte (km) (Repeting) Figure 7.7 Orbitl plot for 08/08/005 to 7/08/005 65

191 Trnsformed Y Coordinte (km) Trnsformed X Coordinte (km) (Repeting) Figure 7.8 Orbitl plot for /03/006 to 09/04/006 66

192 Trnsformed Y Coordinte (km) Trnsformed X Coordinte (km) (Repeting) Figure 7.7 Orbitl plot for /0/004 to 9/0/004 67

193 Trnsformed Y Coordinte (km) Trnsformed X Coordinte (km) (Repeting) Figure 7.8 Orbitl plot for 30/0/004 to 9// R 68

194 7.8.5 Verifiction 5: Consistent inclintion ngle over the orbitl period, which grdully chnges in conformity with ctul GEI/J000 coordinte plots The inclintion ngle clculted by the lgorithm is consistent throughout the orbitl period nd it grdully chnges over time s the stellite hs been mnoeuvred over the yers. This is in consistent with the orbitl plots in Figure 3.5, which demonstrtes the chnging orbitl elements over the yers 004, 005 & 006. The inclintion ngle vlues re given below in Tble 7.6 for smpled period: No Period The inclintion ngle vlues /0/004 to 9/0/ /03/004 to 0/03/ /06/004 to 30/06/ /0/004 to 9// /08/005 to 8/08/ /03/006 to 09/04/ Tble 7.9 Inclintion ngle for smpled periods 7.9 Notes on vector nlysis of this methodology The bove nlysis could be implemented using orbitl stte vectors of the stellite too. Compring Figures 7.8 nd 7.0, it is seen tht the Incident ngle α will be equl to the ngle between the position vector r nd velocity vector v. Therefore, if the two orbitl stte vectors the position vector nd the velocity vector could be worked out from the 69

195 vilble dt, the Incident ngle α could be worked out. Furthermore, the orbitl elements cn be worked out using stndrd conversion formule. Figure 7.0 Orbitl stte vectors the position vector nd the velocity vector From the NASA Stellite Sitution Centre dt, the position vector r cn be directly determined using the GEI/J000 coordintes. Nevertheless, the velocity vector cnnot be directly determined s the stellite velocity dt is not vilble. Therefore, the velocity vector needs to be worked out from the GEI/J000 coordintes dt nd the vilble time stmp dt. Tht process will involve interpolting nd pproimting stellite displcement over two or three consecutive dtsets, s the ect direction of the velocity vector cnnot be known from single set 70