Estimation of Time-Varying Bias Terms in Linear Systems

A.K. Leros (Greece)

Keywords

Linear systems, state estimation, Kalman filtering

Abstract

This paper addresses the problem of state estimation in a linear system under the presence of a bias term which varies rapidly with time, or undergoes abrupt changes. Such a behaviour is the result of a major change in the system model, e.g. a sensor or actuator failure. A state estimator in this case has to detect possible changes in the bias term, and estimate their magnitude. In the general case of the problem, no optimal algorithm exists. The algorithm proposed herein is based on the two-stage Kalman filter, originally due to Friedland, which is an optimal estimator for the case of a constant bias. Additionally, a Multimodel Partitioning Filter (MMPF) is employed for combined detection and estimation of potential bias changes. Although the MMPF typically operates on a bank of Kalman filters, the algorithm proposed herein is computationally efficient, since only two model-conditional ļ¬lters need be implemented in full, while calculation of the a posteriori probabilities is simple. Simulation experiments indicate that the performance of the proposed algorithm is superior to that of previously reported ones and close to the optimal.

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