A GBAS Testbed to Support New Montorng Algorthms Development for CAT III Precson Approach B. Belabbas, T. Dautermann, M. Felux, M. Rppl, S. Schlüter, V. Wlken, A. Hornbostel, M. Meurer German Aerospace Center (DLR. e.v.) Insttute of Communcatons and Navgaton Abstract The development of new montorng algorthms needs to have access to a platform that offers flexblty, operatonal evaluaton facltes, test and valdaton capactes. DLR s GBAS test bed offers all these features wth addtonal smulaton capablty. Ths paper llustrates these propertes by showng an applcaton of the recently developed absolute onosphere gradent montor by takng advantage of a network of three reference recevers located n the DLR s research arport at Braunschweg. Ths paper presents a frst draft of an absolute onosphere gradent montor capable of detectng gradents from 300 mm/km to 000 mm/km n order to fulfll the GAST-D requrements n terms of onospherc gradent montorng for the ground subsystem. The three recevers gve the possblty to buld two ndependent Absolute Slant Ionosphere Gradent Montors (ASIGM). The performances acheved depend on the performances of the recevers, ther relatve locaton and the orentaton of ther baselnes wth respect to the runway drecton. ASIGM wth baselne n the drecton of the runway provde the best observablty of an onsphere gradent that a GBAS user can experence durng the approach phase (for straght-n approaches). The smaller the angle between the runway and the consdered montor baselne s, the lower the uncertanty of the gradent n the drecton of the runway. Dstrbuton of recevers parallel to the runway provdes the best observablty condtons. Ths paper gves the optmal relatve locaton of recevers n order to acheve 00% detectablty n the 300 to 000 mm/km range of the absolute slant onosphere gradent. Two confguratons were nvestgated: one wth 3 and another one wth 4 recevers lnearly dstrbuted. The results obtaned are extremely promsng for the GAST-D requrements fulfllment and the correspondng archtectures can easly be mplemented. Introducton The Ground Based Augmentaton System Testbed developed by DLR uses three recevers wth separatons of 740, 760 and 770 m from each other (see Fgure 3). In ths paper we explore the capabltes of the absolute onosphere gradent montor as proposed n [] and adapt t for the mult recever (>) case. Intally, we present the dual baselne onosphere gradent montor and we defne the varables and parameters of the problem. Then we nvestgate the performance acheved wth the exstng archtecture of 3 recevers. Thrd, we adapt the montor for the exstng confguraton of the GBAS test bed and analyze the smulaton results of ths confguraton. Fnally, n the last part of ths manuscrpt, we nvestgate the specal case of co-lnearly dstrbuted recevers and propose optmal separaton strateges when usng 3 or 4 algned recevers. A concluson summarzes the results obtaned and gves drectons of future work.
Dual baselne absolute slant onosphere gradent montor The absolute slant onosphere gradent montor proposed n [] s based on sngle frequency double dfference carrer phase observatons. Assumng a precse knowledge of the recevers postons (and thus ther baselne separaton vector), t s possble to determne double dfference resdual bases lke the onospherc decorrelaton between recevers. These bases can be estmated as long as they are not wthn the measurement uncertanty to an nteger multple of a wavelength. In the followng, we keep the same notatons as n [] and descrbe the dual baselne absolute slant onosphere gradent montor. Fgure : Confguraton scheme and notatons. b j s the baselne vector defned by the reference recever RR and RR j. s the angle between b and the runway drecton, s the angle between the two baselnes Let s denote as the standard devaton of the overbound carrer phase resdual error (nose and multpath) of recever. In order to study the senstvty of the montor performances to recever carrer phase error, we keep the standard devaton of each recever ndependent and we defne rj j / the standard devaton rato between recever j and recever. Let s call j the standard devaton of the double dfference phase error when consderng recever j and recever as reference. Then j j r () Furthermore, we assume that the phase resdual errors are ndependent from satellte to satellte wth respect to one recever and ndependent from recever to recever wth respect to one satellte. We also assume that the errors or, more precsely, the error overbounds are Gaussan dstrbuted. Snce our nterest s to montor the onosphere gradent component n the drecton of the runway, t s necessary to adapt the ndvdual test statstcs by projectng the baselnes. The double dfference carrer phase observaton equaton can be wrtten as follow (see []): e b n b () T j j j j j j The left hand sde can be measured at each epoch and s composed of j the double dfference carrer phase measurement between recever and recever j, the dfferental recever T to satellte unt vector e (whch can be determned usng the navgaton message of the consdered satelltes) and the baselne vector between the recevers b j. The rght hand sde of the equaton s unknown and correspond to the sum of double dfference carrer phase cycle ambguty nj, the onosphere gradent j between recever and j tmes baselne b j, and the double dfference carrer phase resdual error j whose dstrbuton s overbounded by the Gaussan dstrbuton wth standard devaton j mentoned prevously. The ASIGMs measure the gradent n the baselne drectons whch are not necessarly algned wth the runway. Fgure descrbes ths schematcally: Fgure : Ionosphere gradent projectons from both montors. j s the gradent estmated usng RR and RR j and s the projecton of j n the o j drecton of the runway. and are the same angles as n Fgure.
From Fgure, we can see that o o 3, 3. (3) cos cos For each baselne, an absolute onosphere gradent montor usng the test statstc as defned n [] can be mplemented. We assume that these montors are ndependent and that each onosphere gradent detected by one of them s projected nto the runway drecton. One needs to be careful wth the fact that the montor can t observe drectly the gradent n the runway drecton but only the component n the drecton of the baselne. An extreme case s a baselne perpendcular to the runway. Ths would drve to an nfnte gradent when projected n the drecton of the runway. Therefore the angles and should be kept as close as possble to zero. The detectable onosphere gradents are those fulfllng the followng nequaltes: ffd md ( ) ffd md n k k n k k o (3) b cos b cos n' kffd kmd 3 ( n' ) o kffd kmd 3 3 (4) b cos b cos 3 3 wth n and n beng ndependent ntegers, s the wavelength of the consdered sgnal, k ffd s the nflaton factor for fulfllng the requred probablty of false alarm and k md s the nflaton factor for fulfllng the requred probablty of mssed detecton. Detals can be found n [].These expressons are symmetrc wth respect to n and n respectvely. Applcaton to DLR s GBAS Testbed For our smulatons, we used the actual recever locatons of the DLR s GBAS Testbed as shown n Fgure 3. Ths GBAS Test bed s composed of 3 recevers wth a plan to nstall a 4 th one. Fgure 3: GBAS reference recever locaton at Braunschweg arport The locatons of the recevers n ECEF coordnate system are gven n Table : Rx X n m Y n m Z n m RR 384069.039 75604.8 504909.863 RR 3840835.3 7486.969 504848.587 RR3 3840.939 7549.959 504488.675 Table : Recevers locatons n ECEF coordnates From these locatons we can determne the lengths of the baselnes as well as the angles between baselnes and runway drecton. We consder as a varable and for each value of the scalng factors r and r 3 are varyng from 0. to 0 (carrer phase nose of RR or RR 3 ranges from 0 tmes better to 0 tmes worse than carrer phase nose of RR ). There are dfferent approaches for takng beneft of both montors: BR 34 760m BR 50 770m 740m BR 98 A slant onosphere gradent s consdered detected f at least one montor can detect t (mnmze the mssed detecton probablty) A slant onosphere gradent s consdered detected only f both montors smultaneously detect t (mnmze the false alarm probablty) These two dfferent approaches represent exptreme cases for a commbned dual baselne montor.e ther applcaton gves upper and lower performance bounds. Smulaton and Analyss of Results The senstvty of the montor performance wth respect to the recever accuracy s plotted n Fgure 4a:
both montors can detect (represented by ) and Fgure 4d demonstrates the detectablty when at least one montor can detect (represented by ) Fgure 4a: Absolute slant ono gradent montor avalablty functon of standard devaton of phase error for baselne b. Red marks areas of slant gradent that the montor cannot detect for a gved The largest baselne b provdes the largest avalablty at the GBAS testbed. As only the regon 300-000 mm/km s relevant for GAST-D [], we decded to show only ths area n all our results. As geometry screenng [3] and [4] would nduce an unacceptable level of unavalablty of the system, the extreme onosphere gradents must be montored n an effcent way. Studes have been conducted to analyse the mpact of an onosphere montor n GBAS applcatons [5] and drve to the fact that n certan crcumstances an absolute onosphere gradent s necessary. Fgure 4c: ASIGM ASIGM3 detecton functonalty dependent on slant gradent and the level of double dfference carrer phase resdual error. Whte areas are detectable gradents. Mnmum Fgure 4d: ASIGM ASIGM3 detecton functonalty dependent on slant gradent and the level of double dfference carrer phase resdual error. Whte areas are detectable gradents. Fgure 4b: Absolute slant ono gradent montor avalablty functon of standard devaton of phase error for baselne b 3. Both Fgure 4c and 4d show a loss of perodcty at least for the range of nterest. The avalablty area s better n Fgure 4d than n Fgure 4c, as expected. The mpact of an addtonal montor wth a dfferent baselne reduces the area of undetectablty. An mportant aspect s the Fgures 4c and 4d show the montor results wth the logc as defned n the prevous paragraph. Fgure 4c shows results of detectablty when
Fgure 5: Percentage of detectablty area (color scale from 0 to 00%) functon of / (x axs) and 3/ (y axs) for ASIGM ASIGM3 combnaton ( st raw) and for ASIGM ASIGM3 combnaton ( nd raw) and for =0.5,, and 3 mm ( st, nd, 3 rd and 4 th column) mnmum for whch 00% of the gradents n the range 300-000 mm/km are detectable. Ths mnmum ~ mm s shown n Fgure 4d for the DLR GBAS Testbed. Ths s an mportant parameter as ths wll provde requrements for the antennas, recevers and level of multpath n the neghborhood of the antennas. The baselne for the addtonal antenna should be chosen n a way that the mnmum that provdes 00% detectablty s as large as possble. From Fgure 4d, an addtonal montor wth a maxmum detectablty around 500 mm/km wll mprove sgnfcantly the mnmum allowed carrer phase double dfference resdual error to acheve 00% detectablty. Fgure 5 shows the mpact of the level of the double dfference carrer phase error n the performance of a dual baselne montor. We have on x axs the carrer phase error standard devaton rato varaton / and on the y axs 3/. The colorbar represents the percentage of detectablty area covered by the gven confguraton. As expected the senstvty to the reference recever carrer phase error s very hgh (colomn to 4) for both confguratons. We used the same axs for all plots. We can see that the curves are symmetrc wth respect to the lne. 3 Optmal lnear dstrbuton of montors We consder n ths chapter that the recevers are all algned and parallel to the runway (co-lnear). Let m be the total number of recevers wth m. Let s fx the largest baselne b m B and consder one of the recevers at the edge to be the reference recever. Fgure 7 shows a schematc descrpton of ths confguraton. Fgure 6: Schematc descrpton of the lnear dstrbuton of recevers and notatons Suppose that the recevers have all the same performances: j {, j},,..., m where we have nserted the factor ½ for easer algebrac manpulaton. We defne b to be the baselne from recever to recever. Let s defne the baselne rato b / b m. There are m- ratos to be consdered wth 0 m.
We would lke to fnd the optmal that allows 00% detectablty n the range 300-000 mm/km usng the recevers wth the hghest values. The avalablty areas of the montor ASIGM (Absolute Slant Ionospherc Gradent Montor between recever RR and recever RR ) are defned usng the followng nequalty: ffd md ffd md n k k n k k (5) B B s the slant onosphere gradent detectable by the montor. Ths nequalty defnes the area where s detectable. It s defned for all ntegers n. We can observe that f 0, for any there exst an nteger n for whch n n and such an deal B B montor wth no carrer phase error would have 00% detectablty. The mnmum of for whch we have 00% of detectablty s obtaned n for n. The mnmum of for B whch we have 0% detectablty s obtaned for. It s nterestng to notce kffd kmd that ths s a constant. Ths s obtaned for n / n. The functon B g delmtng the area of avalablty of the montor ASIGM s a perodcally pecewse lnear functon that can be wrtten n the followng form: n f n (6) n n n n f n n (7) n n For m=3, we keep B and as varable. We search the optmal B of B and of that maxmze the level of double dfference carrer phase error and mantanng a 00% detectablty of an absolute slant onosphere gradent n the range 300-000 mm/km. A gradent must be at least detected by one montor to be consdered wthn the detecton range by the whole system. The second possble combnaton (detectablty when all montors detect) s not consdered n ths chapter. The optmal problem, defned through the objectve functon that we want to maxmze s taken as the carrer phase error that provdes 00 % of detectablty n the range 300-000 mm/km. The am s to fnd the baselnes that drve to ths maxmum and the value of the objectve funcon at ths optmum. The determnaton of ths optmum s done numercally by consderng dscrete values for each baselne. The functons defned by equatons 6 and 7 are calculated for each dscretzed baselne and for each nteger values correspondng to the 300-000 mm/km range. The monotors are then fused by takng the maxmum values of the functons correspondng to each montor for each slant onosphere gradent. For each dscrete value of the baselnes we fnd the mnmum of for whch 00% of detectablty s guaranted. The results are plotted n Fgure 7. Fgure 7: Maxmum standard devaton carrer phase error (color scale from 0 to 7 mm) that provdes 00 % detectablty n the range 300-000 mm/km functon of the largest baselne n meter n the x axs and b /B n the y axs We can notce n Fgure 7 a superposton of symmetrc trend wth respect to b /B and a dssymmetrc trend probably due to the dssymmetry of the range of slant onopshere gradents. For B below 8 meter, there s an ndependancy wth respect to. For B 90 m and 0.5 (recever n the mddle of the nterval), takes very low values and ths
archtecture although symmetrcal should be avoded. The values fund for the optmum are: 6.97 mm, B 77 m, 0.387. Ths confguraton provdes the followng detectablty area: Fgure 0a: Mnmum carrer phase error for 00% B, gradent detecton 3 Fgure 9: Slant onosphere gradent detecton area for m=3 recevers optmally lnearly dstrbuted. The hgh level of double dfference carrer phase nose allowed ( ) can be acheved wth a well calbrated antenna. The stng crtera should take nto consderaton the multpath envronment as usual. Attenton should be pad to the possble multpath correlaton between RR and RR due to the shorter baselne. If we apply these results to propose a possble locaton of a 4 th recever at Braunschweg research arport to acheve GAST-D requrements and consder the recevers RR and RR for the largest baselne ( B 770 m ), the optmal locaton for RR4 would be 77 m from RR and the maxmum allowed double dfference carrer phase error standard devaton would be 4.5 mm to acheve 00% of onosphere gradent detectablty. Fgure 0a: Mnmum carrer phase error for 00% B, gradent detecton 3 For m=4 and supposng all 4 recevers are algned. We fnd the followng optmal surfaces: Fgure 0c: Mnmum carrer phase error for 00%, gradent detecton B 3
The optmum s obtaned for 0.8, 3 0.53 m B, The result s a maxmum tolerable carrer phase error of 8.65 mm and t provdes the followng detectablty area: range as baselnes are necessary to estmate the front tself. A lnear dstrbuton of recevers n the drecton of the runway shows very promsng results. The optmal dstrbuton can be mplemented n a majorty of arports. Future work conssts of defnng an optmal combnaton of ndvdual montors to meet overall CAT III ntegrty and contnuty requrements valdated through measurements and hardware smulatons. Dependng on the combnaton strategy, ntegrty and contnuty allocatons can be derved at each recever level and therefore by balancng the weghtng decson, t wll be possble to exactly ft the overall performance requrements of the combned montor. Fgure : Slant onosphere gradent detecton area for m=4 recevers optmally dstrbuted As expected the addton of one recever provdes hgher maxmum allowable double dfference carrer phase error and the maxmum baselne remans acceptable for a majorty of arports. Concluson and future work A frst analyss gves us an estmate for the maxmum level of allowable carrer phase error at each recever and an onosphere based stng crtera for the fourth recever n Braunschweg. The thrd recever defnes a baselne that s not n the drecton of the runway. Therefore ts test statstc can t be drectly lnked to a gradent that could be experenced by a ground system or an Arcraft durng a CAT III precson approach. It s n that case necessary to adopt a conservatve approach consderng the gradent observed as the projecton of a gradent n the drecton of the runway. Ths would drve to a large number of false alarms and therefore can t fulfl the contnuty requrements. A possblty to use the non co lnearty of the baselnes could be n a complementary way for detectng addtonal characterstcs of the onosphere front lke ts drecton. In that case addtonal baselnes are necessary to ensure the 00% of detectablty n the 300-000 mm/km References [] S. Khanafseh and F. Yang and B. Pervan, Carrer Phase Ionosphere Gradent Ground Montor for GBAS wth Expermental Valdaton, ION GNSS 00, September 00 [] Internatonal Standards and Recommended Practces Aeronautcal Telecommuncatons Annex 0, Chapter 3, Appendx B + Attachment D. [3] Jyun Lee and Mng Luo and Sam Pullen and Young Shn Park and Per Enge and Mats Brenner, Poston-Doman Geometry Screenng to Maxmze LAAS Avalablty n the Presence of Ionosphere Anomales, ION GNSS, 006 [4] M. Harrs and T. Murphy, Geometry Screenng for GBAS to Meet CAT III Integrty and Contnuty Requrements, ION NTM, January 007 [5] M. Harrs and T. Murphy, Puttng the Standardzed GBAS Ionospherc Anomaly Montors to the Test, n Proceedngs of the ION GNSS 009, Savannah, GA, Sep 009.