CHAPTER 1 INRODUCTION. Navigation is the process of directing a moving vehicle or a person

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1 CHAPTER INRODUCTION. INTRODUCTION Navigation is the process of directing a moving vehicle or a person from one known place to the other known place. The modern navigational aids ses the Electromagnetic (EM) waves in the VHF and UHF range for providing the accrate knowledge of ser position. The radio navigation receiver processes these EM signals and performs the necessar comptations sch as distance bearing and estimated time of arrival for the ser to navigate to the desired location. The conventional navigational aids that provide the corse distance and horiontal and vertical gidance dring precision approaches are VHF Omni Range (VOR) Distance Measring Eqipment (DME) and Instrment Landing Sstem (ILS) respectivel. The advent of Global Positioning Sstem (GPS) has revoltionied the field of navigation particlarl in the field of civil aviation sector. The GPS is a reliable all weather satellite based radio navigation sstem that provides accrate three dimensional (3D) position velocit and timing information p to -6 seconds anwhere on or above the earth s srface. The 3D position determination is based on the trilateration concept. In this concept the nknown position of the receiver is compted b estimating the satellite positions in the space and measring the psedoranges to each satellite from the receiver. Even thogh satellite based

2 navigation sstems offers mch better accracies than the conventional navigational aids (VOR DME and ILS) the position accrac is affected b several error sorces sch as ionospheric dela tropospheric dela satellite clock bias receiver noise mltipath and satellite geometr. Becase of these errors the standalone GPS does not meet the reqirements of critical navigation applications sch as Categor I (CAT I) Precision Approaches (PAs) where the reqired horiontal and vertical accracies are 6m and 4.5-7m respectivel. However the reqired accrac can be achieved b agmenting the GPS. The generic name given to the GPS agmentation sstem is known as Space Based Agmentation Sstem (SBAS). The first SBAS was developed b US and is known as Wide Area Agmentation Sstem (WAAS). The Eropean space agenc has developed their own SBAS known as Eropean Geostationar Navigation Overla Sstem (EGNOS). Similarl in India SBAS is implemented jointl b the Airport Athorit of India (AAI) and Indian Space Research Organiation (ISRO) and is known as GPS Aided Geo Agmented Navigation (GAGAN). At present all the SBASs inclding GAGAN are meeting the reqirements of enrote navigation (.nmi accrac mintes integrit) accrac and approaches with vertical gidance (m horiontal m vertical and sec integrit). The SBAS is not able to achieve the CAT I aircraft landing reqirements (6m horiontal 4.5-7m vertical ' decision height and 6 sec integrit) (ICAO manal 999). The varios reasons that contribte in not achieving this reqired accrac are selection of a proper

3 3 navigation soltion algorithm in the receiver modeling of GPS signal errors geographic location of the receiver and the satellite-receiver geometr. The satellite-receiver geometr is different in low latitde region (6 N-36 N) than at other latitdes. The metric sed to measre the satellite receiver geometr is known as Geometric Diltion of Precision (GDOP). The predominant factor that significantl inflences the navigation soltion accrac is the proper selection of a ser receiver position estimation algorithm. Even thogh several position estimation algorithms are developed world wide the are not available in the pblic domain becase of commercial and secrit reasons. Therefore it is necessar to develop a sitable navigation soltion for receiver position estimation de to varios satellite geometr configrations. In this thesis two new algorithms namel Jacobian determinant based mlti polnomial resltant (JMR) techniqe and the Minkowski fnction based absolte position (MAP) algorithm are developed. The first one redces the nonlinear GPS psedorange eqations into qadratic eqations. The nonlinear terms in the for GPS psedorange eqations are eliminated b sbtracting one eqation from the other three psedorange eqations. The other one is the Minkowski fnction based absolte position algorithm which is ver comptationall efficient. Unlike least sqares estimation this method takes onl the actal measrement into accont to estimate the object position. This method ses the Minkowski fnctional for for-space for obtaining the accrate navigation soltion. The reslts of the two algorithms are compared with the standard recrsive least sqares (RLS)

4 4 estimation and the proposed algorithms have been validated with the real time dal freqenc GPS receivers data. This thesis also highlights the satellite and receiver clock error impact on the proposed navigation soltions and the statistical error analsis of the position errors compted de to varios navigation soltions. The practical data reqired for the analsis and validation of these algorithms is collected from the dal freqenc GPS receivers located at Andhra Universit College of Engineering Visakhapatnam (7.73 N/83.39 E) Airports Athorit of India Visakhapatnam Airport (7.73 N/83.3 E) NGRI Hderabad (7.47 N / E) and IISc Bangalore (3. N/77.5 E).. OBJECTIVES OF THE THESIS The main aim of the thesis is to develop new satellite based navigation soltions sing Jacobian determinant based mltipolnomial resltant techniqe and the Minkowski fnction based absolte position algorithm and to find ot the GPS receiver clock satellite clock and relativistic error impact on the position accrac over the Indian sbcontinent for precise position applications. To achieve the above objectives the following tasks are carried ot. i) A new navigation soltion based on mltipolnomial resltant techniqe b finding Jacobian determinant that sits the Indian sbcontinent is developed.

5 5 ii) A new non iterative absolte position algorithm based on the Minkowski fnction is developed for the estimation of ser position for precise applications. iii) The performance of the two proposed algorithms (Jacobian determinant based mltipolnomial resltant techniqe and the Minkowski fnction based absolte position algorithm) are compared b implementing the standard recrsive least sqares algorithm and validated with the real time dal freqenc GPS receivers. iv) The satellite atomic clock behavior is predicted and analsis is carried ot in terms of bias drift and drift rate to find their impact on timing and positioning accrac. v) The satellite clock receiver clock and the relativistic error impact on the proposed navigation soltions are carried ot. The statistical error analsis of the position errors compted de to varios navigation soltions over the Indian sbcontinent is also carried ot. vi) Satellite-receiver geometr impact analsis over time and space is carried ot to investigate how the DOP can change the position accrac significantl nder Best-4 and All-in-view configrations sing the DOP algorithm..3 LITERATURE SURVEY To flfill the objective of the thesis the fndamental concepts of the GPS signal strctre GPS observables GPS errors and agmentation are

6 6 essential. The characteristics of L (575.4MH) L (7.6MH) signals and PRN codes transmitted b GPS satellites are dealt b several athors (Rao Parkinson and Spilker 996 Hoffman et. al. 7 Borre and Strang 997 Leick 4 and Pratap 6). All these aspects are nderstood. To develop the non iterative absolte position algorithm based on the Minkowski fnction concepts of the GPS navigation soltion are to be thoroghl nderstood. For this several books (Ananda 988 Nagaraja 98 Rabban Katon and Fried 997 and X 3) jornals (Milliken 978 Parkinson et. al. 995 Hoshen 996 Toshiaki et. al. Enge et. al. Van Dierendonck and Spilker David and John 3 Per Enge 3 Kibe 6 Sasibhshana Rao 7 Bakhom ) were referred. Several algorithms were developed to compte the Diltion of Precision (DOP) which is a measre of satellite-receiver geometr. Based on the concepts of satellites position in the space (Hoffman et. al. 7 Langle 999 Leick 4) DOP algorithm is sed to investigate the best satellite geometr configration for low latitde GPS applications. Presentl GPS is sed in varios applications becase of its confidence and seflness. Each GPS satellite generates a niqe code seqence of eroes and ones. B matching the time difference of the psedo random noise code generated b the satellite's atomic clock and the ser's clock the receiver is able to match the code and calclate a time difference between them (Rao ). Based on the calclated time difference which is known as travel time of the satellite signal and known vale of the speed of

7 7 light the distance between the satellite vehicle(sv) and the receiver can be determined (speed of light mltiplied b time)(dail and Bell 996). The satellite and receiver clock discrepancies and inaccrac of the transmitted ephemeris the electromagnetic wave propagation throgh the atmosphere slows down. Becase of these reasons the compted distance between each satellite and the receiver is known as psedorange (Ivan 993). Simltaneos observations of for psedoranges are necessar to determine the X Y and Z coordinates of GPS receiver antenna and clock bias. Literatre shows that different approaches have been developed to solve the sstem of nonlinear eqations some closed-form soltions and some throgh lineariation process. These position estimation algorithms have been stdied and analed (Seiji and Toshiki 6 Andrew 4 Farrell and Barth 999). The GPS position accrac relies on the precise knowledge of the satellite orbits and the time. The GPS is a ranging sstem and was designed as a one-wa sstem where signals are transmitted onl from the satellite to ser. In this sstem there is an offset between the independent satellite and receiver clocks which translates into a position error (becase the receiver position is calclated from the time dela between the signal transmission at the satellite and reception at the receiver). This timing offset mst be inclded as nknown parameter in the position soltion in addition to the three X Y and Z coordinates (Rao ). The behavior of satellite clock errors and their impact on timing and positioning accrac is stdied. Using

8 8 GPS for precise determination of ser position the clock ticks from the GPS satellites mst be known to an accrac of -3 nsec. However becase the GPS satellites are constantl orbiting relative to observers on the Earth the Special and General theories of relativit effects predicted mst be taken into accont to achieve the desired -3 nsec accrac. The relativistic error effect on the navigation soltion is eplored (X 3). The GPS range measrements contain several errors reslting from a variet of sorces. These biased time dela measrements are therefore referred to as psedoranges. Psedorange errors can be broadl groped into two major categories: biases which are sstematic and which can be modeled in an eqation describing the measrements thereb removing or significantl redcing their effect and noise or random error each vale of which cannot be modeled bt whose statistical properties can be sed to optimie the analsis reslts (Kaplan 6). The statistical analsis of the GPS position accrac can be made b considering different accrac measres like distance root mean sqare (DRMS) twice distance root mean sqare ( DRMS) the circlar error probable (CEP) and the horiontal 95% accrac (R95) for two dimensional (D). Similarl for three dimensional (3D) position accrac statistical analsis can be made b considering the Spherical Error Probable (SEP) Mean Radial Spherical Error (MRSE) the 9% spherical accrac standard and 99% spherical accrac standard (Frank 7 Langle ). All these aspects are nderstood for developing new navigation soltion algorithms to sit the Indian sbcontinent conditions.

9 9.4 TECHNICAL APPROACH Literatre srve reveals that thogh several navigation soltion algorithms were developed world wide (Nainesh et. al. Sirola and Srjarinne Xiao-Wen and Christopher 3 Klas et. al. 6 Konghe and Yong 6 Niilo 6 Liqiang et. al. 7 Christopher et. al. 8 Lbna et. al. 9 Pfeil et. al. 9) the are not available in the pblic domain becase of the commercial and secrit reasons. Hence accrate reliable and cost effective navigation soltion algorithms that sit the Indian geographic area and area of application are developed. The eisting navigation soltions are based on iterative algorithms and reqire an initial estimate of the receiver position for compting the navigation soltion which is not possible in all conditions. A non-iterative point soltion approach algorithm comptes the navigation soltion based on the available satellite positions and psedorange measrements. The non-iterative algorithm does not reqire an initial estimate of the receiver position ( ). The observation eqation of the psedorange measred between the nknown receiver ( ) and known i th satellite (i i i) is given b (Klobchar 99 Bran and Patrick 994 Klobchar Joachim 3 Norsila and Mardina 9 Rao ) d c( t dt) iono trop (.) i sv PR where

10 ρ = geometric (or tre) range dρ = orbit errors Δtsv = satellite clock error dt = receiver clock error iono = ionospheric error trop = tropospheric error c = velocit of light in vacm εpr represents the psedorange noise respectivel In order to determine ser position in three dimensions ( ) and the receiver clock offset (dt) psedorange measrements are made to for satellites reslting in the sstem of eqations ρi = S i - - c dt (.) where vector S i represents the position of i th satellite relative to coordinate origin and is located at coordinates s s and s within the earth centered earth fied (ECEF) coordinate sstem. This vector is compted sing the orbital parameters broadcasted b the satellite. Vector represents receiver position with respect to the ECEF coordinate sstem. i ranges from to 4 and is sed to reference the satellites. The Eq. (.) can be epanded into the following set of eqations. ( ) ( ) ( ) ( ) ( ) ( ) 3 ( 3 ) ( 3 ) ( 3 ) 4 ( 4 ) ( 4 ) ( 4 ) (.3)

11 In the above eqations and are the nknown ser position co-ordinates. The above nonlinear eqations can be solved for ser position b lineariation sing Talor series epansion abot the approimate ser position ( û = ). = + Δ = + Δ = + Δ (.4) where and are the receiver tre ECEF soltion and Δ Δ and Δ are the difference between the tre soltion and the initial gess ( ). To correct the initial gess we need to calclate Δ Δ and Δ in order to pdate. After epanding the above eqations abot the approimate ser position and considering the first order derivatives onl the following matri eqations can be obtained. Δρ = H Δ (.5) where PR PR PR3 PR4 a a a a a a H a3 a3 a3 a4 a4 a4 cdt Δρ and Δ are derivatives of the actal ser position from approimate position and ai ai and ai are the direction cosines of the nit vector pointing from approimate ser position to the i th satellite. So the ser position can be fond as given below

12 Δ = H - Δρ (.6) Matri H The pdated ser position is given b ˆ To calclate navigation errors the ranging errors mst be mapped to the navigation soltion. This process depends on the receiver-satellite geometr. The factor mapping the ranging soltion to the navigation soltion is called Diltion of Precision (DOP). The information abot DOP is encoded in the geometr matri H and DOP matri G is compted from H. The DOP is calclated from the design matri H containing constant nit vectors H. G = (H T H) - (.7) The G matri maps ranging covariance matri into the navigation covariance matri. In its simplest form it provides a scaling factor from the psedorange errors to navigation errors. Δ = (H T H) - H T (Δρ) (.8) The final receiver coordinates are ˆ = + Δ ŷ = + Δ and ẑ = + Δ. The GPS position accrac improves with best GDOP. In order to estimate the accrac of the navigation soltion compted the DOP

13 3 algorithm is sed. Using this algorithm the best GDOP is investigated for different satellite configrations. The satellite clock error is cased b satellite oscillator not snchronied to tre time (GPS time). The satellite clock corrections are sent mch more freqentl than an other component of the vector correction. These errors represent the difference between the time reported b the satellite and the GPS sstem time. The behavior of satellite clock errors and their impact on timing and positioning accrac is investigated sing the proposed navigation soltion b collecting data from varios dal freqenc GPS receivers sing standard formlae. The desired clock ticks from the GPS satellites mst be with an accrac of -3 nsec for precise ser position determination. However becase the satellites are constantl moving relative to observers on the Earth effects predicted b the Special and General theories of relativit mst be taken into accont to achieve the desired -3 nsec accrac. When the satellite is at perigee the satellite velocit is higher and the gravitational potential is lower becase of which the satellite clocks rn slower. When the satellite is at apogee the satellite velocit is lower and the gravitational potential is higher and so the satellite clocks rn faster. This effect can be compensated b standard relativistic error formla. De to rotation of the earth dring the time of signal transmission a relativistic error is introdced which is called the sagnac effect. Dring the propagation time of the SV signal transmission a clock on the srface of the earth will eperience a finite rotation with respect to the resting reference frame at the

14 4 geo-centre. If the receiver eperiences a net rotation awa from SV the propagation time will increase and vice-versa. The satellite clock receiver clock and the relativistic error effect on the three navigation soltions is carried ot. Two new algorithms vi. Jacobian determinant based mlti polnomial resltant techniqe and the Minkowski fnction based absolte position algorithm are proposed for the estimation of precise ser position. Since the GPS measrements are like man other signals in that with enogh samples the probabilit distribtion for each of the three components ( coordinates) is tpicall bell-shaped allowing s to se a particlarl powerfl error model (Langle ). The statistical error analsis for the estimated ser position is carried ot sing the poplar D accrac measres like DRMS DRMS CEP and R95; and 3D accrac measres like SEP MRSE 9% spherical accrac standard and 99% spherical accrac standard. The proposed models are accrate and faster for real time applications like GAGAN. The practical data reqired for calclating different parameters in this work are taken from the dal freqenc GPS receivers located at Andhra Universit College of Engineering Visakhapatnam; Airports Athorit of India Visakhapatnam Airport; NGRI Hderabad and IISc Bangalore..5. APPLICATIONS OF THE THESIS i) The proposed non-iterative Jacobian determinant based mlti polnomial resltant techniqe and the Minkowski fnction based absolte position

15 5 algorithm navigation soltions can be sed for precise srveing and GAGAN applications over the Indian sbcontinent. ii) The navigation soltion error analsis carried ot for single and dal freqenc GPS receivers is sefl for the civil aviation sector in India to implement the Global Navigation Satellite Sstem (GNSS) b as spplement to the eisting grond based navigation sstems as per the International Civil Aviation Organiation (ICAO) reglation. iii) B incorporating the proposed mlti polnomial resltant navigation soltion in the GNSS aircraft receiver the GNSS navigation shares the advantages of increased fel efficienc improved air space tiliation redced flight times and precision approach capabilit. iv) The onboard atomic clocks on the satellites are the basis for control of time and freqenc of navigation signals. The prediction of atomic clock behavior plas an important role in the GPS performance. The satellite clock and relativistic error analsis made in this thesis will be sefl for precise GPS positioning de to the increasing nmber of sers reqiring centimeters accrac particlarl in the mlti sstem and mlti environment scenario. v) The bilt-in qart clocks in the GPS receivers ields relative freqenc offsets that are 3-4 orders higher than atomic clocks. The freqenc stabilit of qart clock is two orders worse than the atomic clocks. Enhancement of receiver position accrac is the primar goal of all GPS sers. To achieve this statistical error analsis is made on the

16 6 relationship between GPS receiver clock and GPS positioning precision de to the proposed navigation soltion. This analsis is mainl carried ot becase all the aircraft receivers are eqipped with qart based clocks as the atomic clocks are ver costl and cannot be afforded..6. ORGANIZATION OF THE THESIS This thesis consists of seven Chapters inclding the Introdction and Conclsions. Chapter presents the principle of operation of the satellite navigation sstem GPS signal characteristics and the varios error sorces in the GPS observables/observations. Chapter 3 discsses the important steps followed in GPS receiver signal processing: signal conditioning acqisition tracking and navigation data recover. The navigation message and the observation data formats are also eplained in this chapter. In Chapter 4 the proposed navigation soltions Jacobian determinant based mlti polnomial resltant techniqe and the Minkowski fnction based absolte position algorithm and the recrsive least sqares approimation algorithm are presented for precise navigation soltion. The reslts of position error analsis made for these three methods are also presented in this chapter. Chapter 5 presents the satellite clock and relativistic error impact on the navigation soltion. The effect of satellite-receiver geometr on the position accrac of GPS sstem is presented in Chapter 6. The freqenc distribtion of receiver position D 3D position accrac measres de to the three navigation soltions statistical error analsis of

17 7 the receiver clock and satellite clock error and its impact on the proposed navigation soltion and the overall reslts are presented in Chapter 7. The overall conclsions along with the sggestions for frther work are presented in Chapter 8.