基于TDOA/FDOA多星联合定位误差与卫星构型分析
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摘要
针对多星定位系统对地面静态目标的无源定位误差分析问题,运用Fisher信息矩阵、Taylor级数、矩阵理论和统计理论,综合考虑时差、频差、卫星位置误差以及卫星速度误差,推导了到达时间差(time difference of arrival,TDOA)/到达频率差(frequency difference of arrival,FDOA)联合定位误差克拉美·罗界(Cramer-Rao lower bound,CRLB)的简单表达式,以及三星单独TDOA定位误差的CRLB,进而给出了避免TDOA定位盲区的良好卫星构型设计的充分条件.理论分析与仿真结果表明:在单独TDOA定位场景下良好的构型能完全消除定位盲区,定位精度随主星-星下点连线与主星-副星连线的夹角逼近90°而逐渐提高;通过引入FDOA与TDOA联合定位也能有效避免定位盲区,提高定位精度.
The passive location error and satellite configuration analysis of a static target on the Earth surface for passive multi-satellite localization systems is investigated.By using Fisher information matrix,Taylor series,matrix theory and statistical theory,a concise Cramer-Rao lower bound(CRLB)expression of time difference of arrival(TDOA)and frequency difference of arrival(FDOA)joint localization is derived,in which the TDOA measurement error,FDOA measurement error,satellite position error and satellite velocity error are all considered.Then,we derive the CRLB for three satellites location system based on TDOA.Furthermore,the sufficient condition of designing agood satellite configuration to eliminate the blind zones of TDOA location is given and proved.Theoretical analysis and simulation results show that the blind zones of sole TDOA localization can be completely eliminated by employing agood satellite configuration,and the location precision is gradually improved with the intersection angle between the line of the primary satellite to the subastral point and the line of the primary satellite to the secondary satellite tending to 90 degree.Moreover,by introducing FDOA measurement,TDOA and FDOA joint localization can avoid the blind zones effectively and improve the positioning accuracy.
The passive location error and satellite configuration analysis of a static target on the Earth surface for passive multi-satellite localization systems is investigated.By using Fisher information matrix,Taylor series,matrix theory and statistical theory,a concise Cramer-Rao lower bound(CRLB)expression of time difference of arrival(TDOA)and frequency difference of arrival(FDOA)joint localization is derived,in which the TDOA measurement error,FDOA measurement error,satellite position error and satellite velocity error are all considered.Then,we derive the CRLB for three satellites location system based on TDOA.Furthermore,the sufficient condition of designing agood satellite configuration to eliminate the blind zones of TDOA location is given and proved.Theoretical analysis and simulation results show that the blind zones of sole TDOA localization can be completely eliminated by employing agood satellite configuration,and the location precision is gradually improved with the intersection angle between the line of the primary satellite to the subastral point and the line of the primary satellite to the secondary satellite tending to 90 degree.Moreover,by introducing FDOA measurement,TDOA and FDOA joint localization can avoid the blind zones effectively and improve the positioning accuracy.
引文
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[18]朱伟强,黄培康,束锋,等.多星TDOA和FDOA联合定位精度分析[J].系统工程与电子技术,2009,31(12):2797-2800.ZHU W Q,HUANG P K,SHU F,et al.Analysis of precision of multi-satellite joint location based on TDOA/FDOA[J].Systems engineering and electronics,2009,31(12):2797-2800.(in Chinese)
[19]常新亚,谢斌,张晓敏,等.双星TDOA/FDOA定位系统的目标定位精度分析[J].航天器工程,2013,22(4):35-42.CHANG X Y,XIE B,ZHANG X M,et al.Target location accuracy analysis of dual-satellites location system using TDOA and FDOA[J].Spacecraft engineering,2013,22(4):35-42.(in Chinese)
[2] HO K C,LU X,KOVAVISARUCH L.Source localization using TDOA and FDOA measurements in the presence of receiver location errors:analysis and solution[J].IEEE transactions on signal processing,2007,55(2):684-696.
[3]曲付勇,孟祥伟.基于约束总体最小二乘方法的到达时差到达频差无源定位算法[J].电子与信息学报,2014,36(5):1075-1081.QU F Y,MENG X W.Source localization using TDOA and FDOA measurements based on constrained total least squares algorithm[J].Journal of electronics&information technology,2014,36(5):1075-1081.(in Chinese)
[4]束锋,朱伟强,陆锦辉,等.基于最大比合并的最大似然TDOA/FDOA联合定位方法[J].宇航学报,2010,31(4):1143-1148.SHU F,ZHU W Q,LU J H,et al.Maximum ratio combing based maximum likelihood TDOA/FDOA joint localization[J].Journal of astronautics,2010,31(4):1143-1148.(in Chinese)
[5]童娟娟,陈晓慧,束锋,等.基于最大似然网格搜索的TDOA和FDOA加权代价函数定位算法[J].电子器件,2015,38(1):209-213.TONG J J,CHEN X H,SHU F,et al.Maximum likelihood grid search based weighted cost function localization of TDOA and FDOA[J].Chinese journal of electron devices,2015,38(1):209-213.(in Chinese)
[6] WANG G,LI Y,ANSARI N.A semidefinite relaxation method for source localization using TDOA and FDOA Measurements[J].IEEE transactions on vehicular technology,2013,62(2):853-862.
[7] BIN Y Z,YAN Q,NAN L A.PSO based passive satellite localization using TDOA and FDOA measurements[C]//IEEE/ACIS,international conference on computer and information science,2011:251-254.
[8] LIU Z,ZHAO Y,HU D,et al.A moving source localization method for distributed passive sensor using TDOA and FDOA measurements[J].International journal of antennas and propagation,2016(4):1-12.
[9] SHU F,YANG S,QIN Y,et al.Approximate analytic quadratic optimization solution for TDOA-based multi-satellite localization with Earth constraint[J].IEEE access,2016,4:9283-9292.
[10] KAY S M.Fundamentals of statistical signal processing[M].London:PTR Prentice Hall,1993.
[11] HO K C,CHAN Y T.Geolocation of a known altitude object from TDOA and FDOA measurements[J].IEEE transactions on aerospace and electronic systems,1997,33(3):770-783.
[12]孙仲康.单多基地有源无源定位技术[M].北京:国防工业出版社,1996.
[13] PATTISON T,CHOU S I.Sensitivity analysis of dual-satellite geolocation[J].IEEE transactions on aerospace and electronic systems,2000,36(1):56-71.
[14] XUE Y,LI X,XU L,et al.Research on position differential method of dual-satellites TDOA and FDOA in passive location system[C]//2012IEEE International Frequency Control Symposium(FCS).Baltimore,July 19,2012:1-5.
[15] AILIN H E,KAI X U,BAO K,et al.Location Method and error analysis for dual-satellite TDOA and FDOA based on tangent plane of WSG-84model[J].Journal of projectiles rockets missiles and guidance,2014.
[16]王海丽,任萱,陈磊.三星时差定位星座的定位精度分析[J].中国空间科学技术,2000,20(5):24-29.WANG H L,REN X,CHEN L.Localization precision analysis of three satellites cluster for time-difference localization[J].Chinese space science and technology,2000,20(5):24-29.(in Chinese)
[17]沈如松,张育林.海洋监视卫星无源被动定位精度分析[J].中国空间科学技术,2005,25(3):35-39.SHEN R S,ZHANG Y L.Analysis of passive location precision using ocean surveillance satellite[J].Chinese space science and technology,2005,25(3):35-39.(in Chinese)
[18]朱伟强,黄培康,束锋,等.多星TDOA和FDOA联合定位精度分析[J].系统工程与电子技术,2009,31(12):2797-2800.ZHU W Q,HUANG P K,SHU F,et al.Analysis of precision of multi-satellite joint location based on TDOA/FDOA[J].Systems engineering and electronics,2009,31(12):2797-2800.(in Chinese)
[19]常新亚,谢斌,张晓敏,等.双星TDOA/FDOA定位系统的目标定位精度分析[J].航天器工程,2013,22(4):35-42.CHANG X Y,XIE B,ZHANG X M,et al.Target location accuracy analysis of dual-satellites location system using TDOA and FDOA[J].Spacecraft engineering,2013,22(4):35-42.(in Chinese)