The Use of Optimal Smoothing and Nonlinear Filtering in Pseudolite-Based Positioning Systems

T.J. Bouska, J.F. Raquet, P.S. Maybeck

Abstract:	Traditional optimal smoothing algorithms suffer from two limitations when applied to carrier-phase ambiguity states used in Kalman filtering. The first limitation is the inability to tolerate state and covariance dimension changes between measurement update cycles. The number of carrierphase ambiguities is dependent on the number of visible GPS transmitters (satellites or pseudolites). When a transmitter goes out of or comes into view, the number of ambiguity states change. Optimal smoothing algorithms, and particularly the Meditch algorithm, cannot handle the resulting state dimension changes. The second limitation of the Meditch optimal smoothing algorithm is the inability to accept changes in the meaning of the states that the filter is estimating. This occurs when the base in the double difference operation changes from one transmitter to another. This paper presents a modified Meditch optimal smoothing algorithm that allows state dimension changes and a double difference base transmitter change between measurement update cycles. This modification utilizes a transformation matrix that is applied to both the state vector and covariance matrix. In addition to optimal smoothing techniques this research investigated the application of nonlinear filtering to a simulated network of ground-based GPS pseudolites. Typically, an extended Kalman filter linearizes a nonlinear state dynamics model and/or measurement model with a first order Taylor series approximation. For GPS applications where the distance between receiver and satellite are on the order of 20,000 kilometers, this approximation is adequate. However when pseudolites are used, the ranges are significantly less, which can potentially cause severe measurement model nonlinearities. In this case, the first order Taylor series approximation is inadequate. This paper describes the evaluation of conditional moment estimators that perform a second order Taylor series approximation. A second order approximation provides higher accuracy in the linearization. Simulation results are included for three variations of second order Kalman filters.
Published in:	Proceedings of the 59th Annual Meeting of The Institute of Navigation and CIGTF 22nd Guidance Test Symposium (2003) June 23 - 25, 2003 Hyatt Regency Hotel Albuquerque, NM
Pages:	435 - 443
Cite this article:	Bouska, T.J., Raquet, J.F., Maybeck, P.S., "The Use of Optimal Smoothing and Nonlinear Filtering in Pseudolite-Based Positioning Systems," Proceedings of the 59th Annual Meeting of The Institute of Navigation and CIGTF 22nd Guidance Test Symposium (2003), Albuquerque, NM, June 2003, pp. 435-443.
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