Adaptive filtering for jump Markov systems with unknown noise covariance

Abstract

The paper proposed an adaptive filter for jump Markov systems with unknown measurement noise covariance. The filter is derived by treating covariance as a random matrix and an inverse-Wishart distribution is adopted as the conjugate prior. The variational Bayesian approximation method is employed to derive mode-conditioned estimates and mode-likelihood functions in the framework of interacting multiple model. A numerical example is provided to illustrate the performance of the proposed filter.

Kullback–Leibler divergence for interacting multiple model estimation with random matrices

“…Step 2: Mode-conditioned filtering As in [19], the mode-conditioned posterior density function at time step k can be obtained by using variational Bayesian approximation…”

“…In this section, the performance of the proposed filter is compared with the previous work via a two-dimensional manoeuvring target tracking example. To produce a fair comparison, the tracking parameters in [19] are adopted. The coordinate turn model is used to represent the target dynamics…”

“…For example, the random matrix approach has been used for state estimation of stochastic systems with unknown measurement noise covariance [16,17]. This method is extended to address jump Markov linear systems in [18,19]. For a diagonal covariance matrix, the inverse-gamma distribution is used as the conjugate prior for each diagonal element of the covariance matrix [18].…”

Power allocation scheme for distributed filtering over wireless sensor networks

“…Yu et al [13] proposed a distributed consensus filtering algorithm based on pinning control. Li and Jia [14] proposed an adaptive filter for jump Markov systems with unknown measurement noise covariance. Yang et al [15] proposed an optimal consensus-based estimation algorithm with packet dropping.…”

Improved diagonal interacting multiple model algorithm for manoeuvering target tracking based on H ∞ filter

“…State estimate problem of discrete‐time stochastic systems with Markov switching parameters is always the focus of interest in the community of manoeuvering target tracking [1–5]. Multiple‐model (MM) algorithms [such as generalised pseudo‐Bayesian, interacting MM (IMM) and variable‐structure MM] are generally considered as mainstream approaches to address this problem [3].…”