Time-Varying Kernel Density Deconvolution using Random Finite Set Theory for State Noise Identification

Abstract

This paper focuses on the noise density identification for state-space models of linear time-varying systems. The density knowledge is essential for the optimal design of any modern state estimator, fault detector, or controller. The proposed method builds on newly derived algorithms for (i) calculation of the measurement prediction residue being independent of the state and linear in state and measurement noises, and (ii) kernel density deconvolution for process with non-stationary statistical properties based on the random finite set theory. The proposed method provides consistent estimate of the state noise density without any prior knowledge on distribution family, which is a unique property in noise identification state-of-the-art. The method is further enhanced by an automatic selection of the user-defined parameters, and is evaluated in numerical examples. The examples demonstrate not only the superior performance of the proposed method in terms of accuracy and robustness among others in ultra-wide-band-inspired tracking scenario, but also the importance of the correct state noise density identification for optimal state estimation and fault detection. The paper is supplemented with a MATLAB implementation.