A Generalized Multiple Model Adaptive Estimator for Parameter and State Estimation

C.D. Ormsby, J.F. Raquet, P.S. Maybeck

Abstract:	Precise differential positioning obtained using GPS requires accurately fixing carrier-phase integer ambigu-ities. Henderson [3] demonstrated a multiple Kalman filter approach to solving the carrier-phase ambiguity problem. Henderson's approach involved modifying the Multiple Model Adaptive Estimator (MMAE), using residuals calculated after measurement update to determine which hypothesized ambiguity set was correct. These residuals were termed "post-fit" residuals to distinguish them from traditional residuals. Henderson's research showed that this modified MMAE could be used for GPS carrier-phase ambiguity resolution in both static and kinematic scenarios. This research generalizes and provides a theoretical basis for Henderson's modified MMAE. It presents a generalized MMAE derivation with a user-defined design parameter. By varying the parameter, the designer can build a traditional MMAE or Henderson's modified MMAE, as well as many other generalized MMAE's, all from the same basic design. The generalized MMAE uses the same overall structure as the traditional MMAE with multiple elemental Kalman filters built based on each hypothesized parameter vector value. The generalization defines a new conditional probability calculation for the elemental filters based on traditional residuals, post-fit residuals, or any linear combination of the two. A derivation is given for selecting the optimal design parameter for two cases: 1) estimating GPS carrier-phase integer ambiguities 2) estimating unknown state propagation noise covariance. Both these cases are demonstrated using examples. The goal of the generalized MMAE is to decrease the time the MMAE takes to converge to the correct hypothesis.
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:	166 - 175
Cite this article:	Ormsby, C.D., Raquet, J.F., Maybeck, P.S., "A Generalized Multiple Model Adaptive Estimator for Parameter and State Estimation," Proceedings of the 59th Annual Meeting of The Institute of Navigation and CIGTF 22nd Guidance Test Symposium (2003), Albuquerque, NM, June 2003, pp. 166-175.
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