A New Algorithm for Calibration of Radar Biases Based on ADS-B

Transcription

1 A New Algorthm for Calbraton of Radar Bases Based on ADS-B 1 Wuzhenya, 2 Huangzhujan, 3 Hujun, 4 Yangchangq 1,4 College of Computer Scence, Schuan Unversty, Chengdu, , Chna, @qq.com 2 Chengdu Aeronautc Vocatonal and Techncal College,Chengdu,610065,Chna *3 Department of Computer, Chengdu Normal Unversty, Chengdu, , Chna, hujun@cdatc.com Abstract For the low precson of sngle radar survellance, a novel algorthm for calbraton of radar bases based on Kalman flter s proposed. The algorthm s manly based on the theory of radar bas model, and mxes the dfference between the ADS-B data wth hgh precson and radar data wth low precson, then uses the Kalman flter to estmate the radar dfference value and conduct real-tme calbraton on radar. Fnally, smulaton experment s done wth Actual data. Results show that the technology can effectvely estmate the measurement bas of sngle radar at real tme, and the measurng range precson of the radar can be tens of meters. Keywords: ADS-B, Radar Bases, Real Tme Calbraton, Kalman Flter 1. Introducton In Chna s modern ar traffc survellance and command system, the survellance nformaton, wth hgher precson and broader coverng area than sngle sensor, s ganed through mxed processng on mult-sensor survellance data [1-8]. In recent years, as the ADS-B, Automatc Dependent Survellance-Broadcast, has been gradually appled both n Chna and n foregn countres, precson of the survellance data n these areas has been greatly mproved. However, because of the expensve ADS-B arborne equpment, the dffculty to re-equp, and other reasons, the ADS-B arborne equpment hasn t been allocated on most Chna s cvl arplanes. Therefore, to effectvely use the hghly-precse ADS-B data n real-tme calbraton on the sngle radar bas on ground, can substantally mprove the sngle radar s survellance precson on some arplanes unable to provde ADS-B data. In the exstng mult-sensor survellance data processng theores, large numbers of studes ar e about the bas calbraton among sensors of the same type. Documents [20-21]ntrocuces mul t-sensor regstraton algorthm. Documents [13-14]ntroduce several novel real-tme optmzng methods on radar bases. They tell us how to conduct optmzed real-tme estmaton on bases among other radars by usng data from radars wth hgh precson and how to calbrate radars; Document[15]ntroduces how to calbrate the bases among dfferent knds of sensors on the g round of the arport; Document[16]ntroduces bas calbraton on non-synchronous radar data n the mult-radar network;document[17]ntroduces how to calbrate bases on radars wth GPS d ata, how to compare data from three sensors wth dfferent precson on the same target, and how to calbrate bases of radars; Document[18]ntroduces how to mx the ADS-B data wth th e radar data on the same target for algorthm; Document[19]ntroduces the mxed real-tme est maton on bases of dfferent knds of sensor systems on the same target. Ths estmaton meth od can make use of the advantages of dfferent knds of sensors. Internatonal Journal of Advancements n Computng Technology(IJACT) Volume4, Number20,November 2012 do: /jact.vol4.ssue

2 The paper, based on the radar bas analyss model, presents the algorthm to calbraton on bases of sngle radar n the ADS-B data group on dfferent targets, and analyses the bases an d reasons for these bases. Meanwhle, smulaton experments are done to test the effectvenes s of the algorthm. 2. Algorthm to calbraton on bases based on kalman flter The number of arcrafts wth ADS-B equpment that can be traced by ground radar A s L, and the L+1 arcraft sn t equpped wth ADS-B equpment. Assumng locaton of the radar s the orgn of coordnates, the radar system bas and random bas are consdered whle the responder bas s neglected, the radar bas model [20] can be descrbed as: m 1 0 n K (1) m n Here, ρ m and φ m represent the measured value of the arcraft at certan moment, ρ and φ represent the real value of the arcraft at the moment, K s the gan of range bas (Easy for algorthm, the coeffcent can be regarded as a constant value at certan moment.), Δρ and Δφ represent the radar system bas, n ρ and n φ respectvely represent the slope range and the angular measured nose. As the Kalman flter and other lnear estmaton methods requre lnear equaton, Equaton (1) s transformed nto the Cartesan coordnate as follows: x -H sn [(1 K) n] -H sn( n) y -H cos [(1 K) n ] -H cos( n ) (2) Take the transformng equaton as: Fxy, ((1 K) n, n ) (3) The transformng equaton can be lnearzed as: F ((1 K) RRn, n ) xy, R f f f f f Fxy, (, ) K n n x, y x, y x, y x, y x, y K n n (4) The ADS-B bas model [17] can be set up as: Where, X adsobs ads ads Then, Equaton (5) can be: X X H X (5) adsobs adstrue ads ads 267

3 cos sn adsb xads ( n) sn cos adsb yads ( n) The polar coordnate can be transformed nto Cartesan coordnate as: sn cos x ads =F( x ads+ cos x ads( n) sn yads( n), ads- x+ y) sn cos y ads =F( y ads+ cos x ads( n) sn yads( n), ads- x+ y) Based on Equaton (4) and Equaton (7), the bas observaton model at t s: x1 () t x1() t xads b1() t.. x () t x () t xads b () t () t Fx, y ( (), t ()) t fx, yadsb y 1() t y1() t y adsb1.. y () t y () t yadsb () t Where, { =1,, L}. If the ADS-B bas s neglected,.e., Δx ads =0, and Δy ads =0, the equaton can be smplfed as: () t fxy, fxy, fxy, fxy, f xy, Kt () () t () t n () t nr () t K() t () t () t n() t n() t HX Qn (6) (7) (8) (9) fx 1 fx 1 fx 1 K () t () t () t fxl fxl f xl Where, K () t () t () t H fy1 fy1 fy 1 K () t () t () t fyl fyl f yl K () t () t () t K and X Assumng 268

4 D = ((1+K) n ) -H fx D cos( n ) Xr fy D sn( n ) Yr 2 2 For Equaton (9), the followng equaton s approxmately establshed. f x f y f f x y f x = cos =sn D cos D sn D sn K K Assumng the observaton equaton as: f y D cos (10) ( k) H X( k) H n( k) (11) radar Wthout other pror nformaton, the state equaton of the system can be assumed as: X ( k+1) ( k) X( k) m( k) (12) Where Φ(k) s a 3 3 unt matrx. Based on the state equaton and the observaton equaton, we can get the lnear predcton recurson formula [21] : Xˆ( k+1 k) ( k) Xˆ( k k1) ( k) ( k) (13) The mean-square bas should be the mnmum n order to get the optmzed estmated value,.e., the mnmum value should be got n Equaton (14): ˆ 2 P ( k) E[( X( k) x( k)) ] (14) After solvng Equaton (14), the optmzed estmated value [22] can be deduced: X ( k) X ( k1) K( k)[ ( k) HX ( k 1)] (15) Where, the flter gan s: T T T 1 1 n K( k) PkH ( ) [ HPkH ( ) Rk ( )] (16) T Pk ( ) Pk ( 1) Qk ( 1) (17) 1 R and Q n Equaton (16) and (17) are the covarance matrx on the observed nose and the system nose respectvely. 3. Data smulaton The smulaton experment s conducted n order to test the performance of the equatons above. Assumng radar A s located n the orgn, L s the 10 arcrafts wth ADS-B arborne equpment, L arcrafts are flyng at a constant speed n dfferent tracks at the same heght (as seen n Fgure 1), the data refreshng cycle s 4s, the measurng nose s Gaussan nose, the already-known sngle radar range measurement system bas ΔR=2000m, and the angular measurng system bas Δθ=1. The Kalman flterng method s used for analog data smulaton, and the mean-square root bas of the radar range 269

5 and the angular measurement are respectvely calculated after 100 tmes of Monte Carlo smulaton. Fgure 1. Schematc dagram for smulated data flght trajectory (L=10,H=10000m) (a) Mean-square root bas of range 270

6 (b) Mean-square root bas of angle Fgure 2. Bas performance analyss (a) K 271

7 (b)δr (c)δθ Fgure 3. Bas calbraton value In Fgure 2, ADS-B data from L arcrafts (L=10) s calbrated, the range (a) and the angle (b) are the mean-square root bas. Fgure 3 shows the values of ΔR, Δθ and K n smulaton. From the fgures, t can be seen that real-tme bases n range measurement and angular measurement of sngle radar can be ganed by usng the algorthm, and the sngle radar bas can be calbrated at real tme. Through bas compensaton, the radar range measurement bas reduces from 2000 meters to 100 meters, and the angular measurement bas reduces from 1 degree to degree. What s more, as tme passes by, the mean-square root for range measurement ncreases from 90 meters to 40 meters, and the mean-square root for angular measurement ncreases from to Dfference between the estmated value 272

8 and the real value of the range bas and the angular bas by usng Kalman flterng method becomes smaller and smaller. At last, t comes to a stable optmzed estmated value. Based on the above smulated analyss, the presented algorthm s effectve to some extent, as t can conduct real-tme calbraton on sngle radar bas, rase the precson of range and angular measurement, and mprove the survellance precson of the sngle radar system. 4. Concluson In ths paper, a dynamc algorthm to calbraton of radar bases based on Kalman flter s provded by usng the avalable ADS-B survellance data, and real-tme calbraton s conducted on the system bases of sngle radar on ground, then survellance postonng precson of arcrafts wthout ADS-B arborne equpment n the ar route s mproved. Smulaton experment proves that the algorthm can effectvely estmate the system bases of the range and angular measurement on sngle radar, whch has great engneerng applcaton value n the ar traffc control and command practce. As the real-tme nature of the arcraft survellance postonng should be consdered n real ar traffc control and command, the effcency for the algorthm should be further mproved to ensure the real-tme nature of the calbrated result. 5. Acknowledgement Ths work s supported by Natonal Scence Foundaton of Chna (No ) and scence and technology research project of cvl avaton of Chna (MHRDZ200815). 6.References [1] Waltz, Eand Llnas J., Multsensor data fuson, Artech House,USA,1990 [2] BarShalom,Y., Multtarget-multsensor trackng:advanced applcatons, Artech House,USA,1990 [3] Yukun Chen, Xca S, Zhgang L," Research on Kalman-flter based multsensor data fuson", Systems Engneerng and Electroncs, vol.18, no. 3,pp , [4] Wu Lng,Lu Faxng,"Research on the algorthms for regstraton n sensor network for target trackng", Internatonal journal of dstrbuted sensor networks, vol.5,no.1,pp , [5] Farna, Studer F., Radar data processng, Reserch studes Press, USA,1989 [6] Pan JangHua, He JaZhou," On-lne absolute sensor regstraton n 3-D radars networkng", Cross Strat Quad-Regonal Rado Scence and Wreless Technology Conference, pp , [7] L Da, Zhang Fan,"Real-tme data compresson bas estmaton on netted radar", Internatonal Conferece on Sgnal Processng (ICSP), pp ,2010. [8] Song Qang, Xong We, He You,"A track algnment-correlaton algorthm wth systematc errors n radar network", Radar Conference,pp.1-4, [9] Valovage E.," Enhanced ADS-B research", Internatonal journal of Aerospace and Electronc Systems Magazne, vol.22,no.5,pp ,2007. [10] Ln X, Zhang Jun, Zhu Yanbo, Lu We,"Survellance accuracy analyss of ADS-B supportng the separaton servce n western Chna", Integrated Communcatons, Navgaton and Survellance 273

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