Abstract
The state estimation of a complex dynamic stochastic system is described by a discrete-time state-space model with large parameter (including the covariance matrices of system noises and measurement noises) uncertainties. A new scheme of weighted multiple-model adaptive estimation is presented, in which the classical weighting algorithm is replaced by a new weighting algorithm to reduce the calculation burden and to relax the convergence conditions. Finally, simulation results verified the effectiveness of the proposed MMAE scheme for each possibility of parameter uncertainties.
Highlights
Kalman filter (KF) [1] can be viewed as a sensor fusion or data fusion algorithm
The state estimates of multiple model adaptive estimation (MMAE) with a weighting algorithm (6), (7), (8), (9), and (10) will converge to the optimal estimates given by the jth KF corresponding to Mj, that is, xk → xj k
The state estimates of MMAE with the weighting algorithm (13), (14), (15), (16), (17), and (18) will converge to the optimal estimates given by the jth KF corresponding to Mj, that is, xk → xj k
Summary
Kalman filter (KF) [1] can be viewed as a sensor fusion or data fusion algorithm It has many applications in information technology and engineering, such as in the guidance, navigation, and control of vehicles, aircraft and spacecraft [2]. It should be noted that the preliminary version of this manuscript has been published on the proceedings of the 2018 International Conference on Artificial Life and Robotics [24] In this augmented version, the following changes have been made: (1) The weighting algorithm was further improved, that is, weighting Algorithm 2 was presented to get a faster convergence rate than weighting Algorithm 1; (2) the proof of the convergence of the MMAE system was further polished in details; and (3) simulation results were presented to support the theoretical analysis. It should be noted that all the limit operations are in the sense of probability one
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