基于TDOA和FDOA多星联合定位技术研究
摘要
随着科技的发展,卫星定位技术在军事和民用领域具有越来越重要的地位和作用。由于无源定位系统本身不发射电磁波,完全是被动工作的,所以具有隐蔽性好、抗干扰能力强等优点。近年来,无源定位更是在航空、航海、航天和电子战等领域表现异常突出,发挥了无可替代的作用。因此,也越来越受到各国广泛的关注与重视。
本文主要研究被动辐射源的多星定位,研究工作覆盖卫星定位精度分析、多星构型和TDOA/FDOA联合定位算法。主要工作如下:
(一)为了设计好的卫星构型,本文介绍了克拉美罗界(CRLB)与几何稀度(GDOP)的推导过程,然后分析了一种典型的五星构型-五面体。通过仿真与分析,获得如下结论:主星与副星连线之间夹角在45°到60°时,能够获得较好定位性能。
(二)为了提高单独TDOA或FDOA定位的精度,提出了基于最大比合并的TDOA/FDOA联合算法。仿真结果表明,有地球约束情况下的最大比合并算法已经可以达到克拉美罗界,比单独定位算法和Ho最小二乘联合算法具有更好定位性能。
(三)深入研究了霍夫变换在卫星定位中应用,重点讨论了如何利用霍夫变换来实现数据的加权融合。最后的仿真结果表明,加权融合后的霍夫变换同单独TDOA或FDOA霍夫变换相比,具有更好的定位功能。
With the development of science and technology, multi-satellite passive location plays a more and more important role in the military and the civil applications. Because passive location system does not emit electromagnetic wave, it has a high concealing and anti-jamming ability. In recent years, passive location shows an irreplaceable role in aviation and navigation, aerospace and electronic warfare, etc. Thus, it obtains more and more widespread concerning from many countries.
This paper focuses on passive location and consists of the following parts: satellite locating accuracy analysis, joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) location algorithm. The main content is as follows:
a) To design a good satellite array shape, we describe the derivation process of Cramer-Rao lower bound (CRLB) and Geometric dilution of Precision (GDOP). Then, a typical five-satellite array shape is discussed. Simulation results and discussions show: if the angle between the lines connecting the main satellite and aiding ones is between 45°and 60°, then a better GDOP is achieved.
b) To improve the location precision of TDOA or FDOA, we propose a joint location algorithm based on maximum ratio combing (MRC). Simulation results show that this MRC algorithm under earth constraint (EC) can achieves CRLB and perform better than TDOA, FDOA and Ho algorithm regardless of EC.
c) Application of Hough Transform (HT) to passive location is deeply studied, and data fusion based on HT is discussed. The simulation results show that the weighted HT has a better location performance than TDOA or FDOA location based on HT.
本文主要研究被动辐射源的多星定位,研究工作覆盖卫星定位精度分析、多星构型和TDOA/FDOA联合定位算法。主要工作如下:
(一)为了设计好的卫星构型,本文介绍了克拉美罗界(CRLB)与几何稀度(GDOP)的推导过程,然后分析了一种典型的五星构型-五面体。通过仿真与分析,获得如下结论:主星与副星连线之间夹角在45°到60°时,能够获得较好定位性能。
(二)为了提高单独TDOA或FDOA定位的精度,提出了基于最大比合并的TDOA/FDOA联合算法。仿真结果表明,有地球约束情况下的最大比合并算法已经可以达到克拉美罗界,比单独定位算法和Ho最小二乘联合算法具有更好定位性能。
(三)深入研究了霍夫变换在卫星定位中应用,重点讨论了如何利用霍夫变换来实现数据的加权融合。最后的仿真结果表明,加权融合后的霍夫变换同单独TDOA或FDOA霍夫变换相比,具有更好的定位功能。
With the development of science and technology, multi-satellite passive location plays a more and more important role in the military and the civil applications. Because passive location system does not emit electromagnetic wave, it has a high concealing and anti-jamming ability. In recent years, passive location shows an irreplaceable role in aviation and navigation, aerospace and electronic warfare, etc. Thus, it obtains more and more widespread concerning from many countries.
This paper focuses on passive location and consists of the following parts: satellite locating accuracy analysis, joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) location algorithm. The main content is as follows:
a) To design a good satellite array shape, we describe the derivation process of Cramer-Rao lower bound (CRLB) and Geometric dilution of Precision (GDOP). Then, a typical five-satellite array shape is discussed. Simulation results and discussions show: if the angle between the lines connecting the main satellite and aiding ones is between 45°and 60°, then a better GDOP is achieved.
b) To improve the location precision of TDOA or FDOA, we propose a joint location algorithm based on maximum ratio combing (MRC). Simulation results show that this MRC algorithm under earth constraint (EC) can achieves CRLB and perform better than TDOA, FDOA and Ho algorithm regardless of EC.
c) Application of Hough Transform (HT) to passive location is deeply studied, and data fusion based on HT is discussed. The simulation results show that the weighted HT has a better location performance than TDOA or FDOA location based on HT.
引文
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[2]胡来招.无源定位.北京,国防工业出版社,2004
[3]Niezgoda,G.H.,and Ho,K.C.Geolocalization by combined range difference and rangerate difference measurements.In Proceedings of the IEEE International Conferenceon Acoustics,Speech and Signal Processing,Apr.1994,II357-360
[4]Jefe Mason.Algebraic Two-Satellite TOA/FOA Position Solution on an Ellipsoidal Earth IEEE Transactions on aerospace and electronic systems Vol.40,No.3 July 20041087-1092
[5]K.C.HO,Y.T.CHAN.Solution and Performance Analysis of Geolocation by TDOA.IEEE Transactions on aerospace and electronic systems.Vol.29,No.4 1993,1311-1322
[6]E.Weinstein and D.Kletter,Delay and Doppler estimation by time space partition of the array data,IEEE Trans Aerosp Elect Syst,vol.ASSP-31,pp:1523-1535,Dec.1983.
[7]毛永毅,TDOA/AOA数据融合定位算法.计算机工程与应用,2007,43(35),183-186
[8]刘继斌,刘培国,李高升,李文化,周蔚红.三维AOA/TDOA被动定位及其迭代融合算法.全球定位系统.2006.4.5-9
[9]Kaminer,I.,Kang,W.,Yakimenko,O.,and Pascoal.A Motion Detection Using TDOA and FDOA Measurements.IEEE Transactions on aerospace and electronic systems.2001.pp:759-763
[10]Ping Zou,Zhen Huang,Jianhua Lu.Passive Stationary Target Positioning Using Adaptive Particle Filter with TDOA and FDOA Measurements.10th Asia-Pacific Conference on Communications and 5th International Symposium on Multi-Dimensional Hobile Communications.Vol.1.29.2004.453-456
[11]Alex Mikhalev,Richard Ormondroyd.Passive Emitter Geolocation using Agent-based Data Fusion of AOA,TDOA and FDOA Measurements.
[12]R.Schmidt,A new approach to geometry of range difference location.IEEE Trans Aerospace Electron,vol.AES-8.pp:821-835,Nov.1972.
[13]R.Schmidt.Least squares range difference location.IEEE Trans on Aerospace and Electronic Systems.vol.32,no.1.pp:234-242.Jan.1996
[14]W.H.Foy.Position-location solutions by Taylor-series estimation.IEEE Trans on Aerospace and Electronic Systems.vol.12,no.2.pp:187-194.Mar.1976
[15]H.C.Shau and A.Z.Robinson, "Passive source localization employing intersecting spherical surfaces from time-of-arrival differences," IEEE Trans on ASSP, Vol.ASSP-35,No.8, Aug 1987
[16]J.O.Smith, J.S.Abel.Closed-Form Least-Squares Source Location Estimation from Range-Difference Measurements.IEEE Trans on ASSP, Vol.ASSP-35, No.12.Dec 1987
[17]Abel, J.S.A divide and conquer approach to least-squares estimation.IEEE Transactions on Aerospace and Electronic Systems.26,2.Mar.1990.pp: 423-427
[18]Y.T.Chan, K.C.Ho.A simple and efficient estimator for hyperbolic location.IEEE Trans Signal Processing, vol.42.pp: 1905-1915.1994
[19]F.Gustafsson.Positioning using time-difference of arrival measurements.Proc.ICASSP.2003, 6.Ⅵ5-553 -556
[20]Fredrik Gustafsson, Fredrik Gunnarsson, Niclas Bergman, Urban Forssell, Jonas Jansson, Rickard Karlsson, Per-Johan Nordlund.Particle Filters for Positioning, Navigation, and Tracking.IEEE Transactions on signal processing, vol.50, no.2.pp: 425-437.Feb.2002
[21]K.F.McDonald and W.S.Kuklinski, Track maintenance and positional estimation via ground moving target indicator and geolocation data fusion.Proc of the IEEE Radar Conference, pp: 239-245,2001.
[22]A.Mikhalev, R.F.Ormondroyd.Comparison of Hough Transform and Particle Filter Methods of Emitter Geolocation using Fusion of TDOA Data.4th Workshop on Positioning, Navigation and Communication 2007 (WPNC'07), Hannover, Germany,2007.
[23]K.C.Ho, and Wenwei Xu, Accurate Algebraic solution for Moving Source Location Using TDOA and FDOA Measurements.IEEE Trans Signal Processing, vol.52, no.9, pp:2453-2463.Sep.2004
[24]X.Sheng, Y.H.Hu.Maximum likelihood multiple-source localization using acoustic energy measurements with wireless sensor networks.IEEE Trans Signal Process, vol.53,no.l.pp: 44-53.Jan.2005
[25]D.Blatt, A.D.Hero.Energy-based sensor network source localization via projection onto convex sets.IEEE Trans Signal Process, vol.54, no.9.pp: 3614-3619.Sep.2006
[26]S.T.Birchfield, R.Gangishetty.Acoustic localization by interaural level difference in Proc.IEEE Int Conf.Acoust., Speech Signal Process.Mar.2005.pp: iv/1109-iv/1112.13
[27]W.Cui, Z.Cao, J.Wei.Dual-microphone source location method in 2-D space.In Proc. IEEE Int.Conf.Acoust,Speech,Signal Process.vol.4,pp:845-848.May 2006
[28]王文贯,唐诗华.GPS卫星定位误差概论.测绘与空间地理信息.Vol.29,No.5.2006.10.pp:39-42
[29]罗巧云,高勇强.无源雷达技术的发展.现代军事.2006.04.pp:58-60
[30]K.C.Ho,and Ming Sun,Passive Source Localization Using Time Differences of Arrival and Gain Ratios of Arrival.IEEE Trans Signal Processing.vol.56,no.2.pp:464-477.Feb.2008.
[31]Hua YB.A Peneil-MUSIC algorithm for finding two-dimensions angles and polarizations using crossed-diploes.IEEE Trans AP.1993.pp:370-375.
[32]Pauiraj A,Roy,R,Kailath T.A subspace rotational approach to signal Parameter estimation.Proc.IEEE.1986.7:1044-1045
[33]Gorman,J.D.,Hero,A.O.Lower bounds on parametric estimators with constraints.In Proceedings of the 4th ASSP Workshop Spectrum Estimation Modeling,Minneapolis,MN,Aug.1988,223-228.
[34]谢恺,钟丹星,邓新蒲,周一宇.一种空间时差定位的新算法.信号处理.Vol.22No.2.Apr 2006 pp:129-135
[35]王海丽,任萱,陈磊.三星时差定位星座的定位精度分析.中国空间科学技术.2000年10月
[36]刘庆富,卢艳娥,李晓明,袁火平.三星无源定位的精度分析及定位算法.航空学报.Vol129 No12,Mar.2008 456-461
[37]钟丹星,邓新蒲,周一宇.一种基于WGS_84地球面模型的卫星测时差定位算法.宇航学报.Vol.24,No.6,2003
[38]Steven M.Kay(罗鹏飞,张文明,刘忠,赵艳丽 等译).统计信号处理基础--估计与检测理论.北京:电子工业出版社.2003
[39]王海丽,陈磊,任萱.三星时差定位卫星簇的分析与设计.国防科技大学报.Vol.23,No.4,2001
[40]高虎,俞志强.基于四站时差定位原理的星型布站分析.空军雷达学院学报.Vol.18No.3,Sep.2004.22-24
[41]K.C.Ho,Y.T.Chan.Geolocation of a known altitude objects from TDOA and FDOA measurements.IEEE Trans on Aerospace and Electronic Systems.vol.33,no.3,pp:770-783,JULY 1997.
[42]FL Yarlagadda,Ali,N.Al-Dhahir,J.Hershey.GPS GDOP metric.IEE Proc.-Radal Sonar Nuvig.Vol.147,No.5.October 2000 259-264
[43]N.Levanon.Lowest GDOP in 2-D scenarios.IEE Pruc.-Rodar Sonar Navig Vol 147,No. 3.June 2000
[44]常新亚,张立华,陶成华.三星时差定位系统的目标定位精度分析.航天器工程.Vol.16,No.4.2007.7.121-126
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