The Theater Positioning System (TPS), which can perform in GPS-denied environments and can work with, or independently of, GPS systems, is used as a backup to GPS in military. The principal difficulty in optimally combining this new system and GPS is caused by the somewhat unpredictable signal propagation of the TPS groundwave signal and thus results in less accurate performance when TPS works unaided in the environment while GPS is unavailable. A new navigation scheme that can provide an accurate position estimation for the GPS-denied user is developed. The scheme adopts a state-space model which is represented by stochastic differential equations (SDEs) and is used to predict the those propagation disturbances. We also propose a stochastic approximation method to solve the pseudorange equations which does not require prior knowledge of the noise covariance matrices. A numerical example is provided and compared to illustrate the performance of the methods proposed in this paper.
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