Augmented Lagrange geolocation algorithm using TDOA measurements and calibration sources in the presence of satellite position errors

Satellite position errors are known to deteriorate geolocation accuracy significantly. Based on a time difference of arrival (TDOA) satellite localization system, this paper investigates the use of calibration sources to reduce the loss of localization accuracy due to satellite position errors. First, we deduce pseudo-linear equations according to the available TDOA measurements from the target and calibration sources. Based on these equations, a total least squares optimization model with an equality constraint is formulated. To solve this constrained optimization problem, we propose an augmented Lagrange geolocation algorithm by which the target position and refined satellite positions can be obtained. Subsequently, the theoretical performance of the augmented Lagrange geolocation algorithm is derived, and it is proved that the mean square error of the proposed algorithm coincides with the corresponding Cramér–Rao lower bound under first-order perturbation analysis. Finally, simulation results corroborate the theoretical developments and demonstrate the superior performance of the proposed algorithm compared with existing algorithms.