Optimal Sequential Fusion Estimation With Stochastic Parameter Perturbations, Fading Measurements, and Correlated Noises

Abstract

This paper focuses on the linear optimal recursive sequential fusion filter design for multisensor systems subject to stochastic parameter perturbations, fading measurements, and correlated noises. The stochastic parameter perturbations existing in the state model are described by white multiplicative noises. The fading measurement phenomena for different sensors are described by independent random variables with known statistical properties. Moreover, the measurement noises of different sensors are correlated with each other and also correlated with the system noise at the same time step. First, a model equivalent to the original system is established by transferring the multiplicative noises into the additive noises. Then, based on the equivalent model and an innovation analysis method, a sequential fusion filter in the linear minimum variance sense is proposed to solve the linear optimal state estimation problem in real time according to the arriving order of measurements from different sensors. Finally, the equivalence on estimation accuracy of the proposed sequential fusion filter and the centralized fusion filter is strictly proven, which shows the optimality of the proposed sequential fusion algorithm. Moreover, the proposed sequential fusion filter has a reduced computational burden. Compared with the distributed matrix-weighted fusion filter, the computation of cross-covariance matrices is avoided and the estimation accuracy is improved. Finally, a simulation example verifies the effectiveness of the proposed sequential fusion filtering algorithm.