Localization and ambiguity resolution algorithm for time-difference fusion of three satellites based on observation filtering.

To address the issues of low accuracy and time-difference ambiguity in the localization and tracking of multiple satellites, we have conducted a thorough study of the localization algorithm and the ambiguity resolution algorithm for the time-difference fusion of multiple satellites. The localization algorithm based on Gaussian-Newton iteration for time-difference fusion of three satellites is proposed. The time-difference equation observed during the satellite overhead is combined with the elevation observation equation to construct the cost function for the overdetermined case, and the nonlinear least squares problem is solved based on Gaussian-Newton iteration. For localization and tracking for time-difference fusion, the Kalman filtering combined with Gaussian mixture model (KFGMM) is proposed as the ambiguity resolution algorithm of time-difference for stationary targets; the capacitive Kalman filtering combined with Gaussian mixture model (CKFGMM) is proposed for cruising targets. The mathematical model of time-difference ambiguity is established, the calculation method of time-difference window and number of ambiguous time-difference is given, and the measurements of ambiguous time-difference are approximated by Gaussian mixture model. Experiments show that localization algorithm for time-difference fusion of multiple satellites outperforms other advanced localization methods and achieves the Cramér-Rao Lower Bound (CRLB) of fusion localization; with the increase of filtering time, the ambiguity resolution algorithm for time-difference fusion of multiple satellites can reach the Bayesian Cramér-Rao Lower Bound (BCRLB) and outperforms the algorithm combining with the direction finding assistance for ambiguity resolution.