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.