基于TDOA/FDOA多星联合定位误差与卫星构型分析

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.

TDOA/FDOA joint location errors and satellite configuration for passive multi-satellite localization systems

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 a good 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 a good 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.