Design of FIR-Type Filtering Algorithms for Markov Jump Linear Systems

To design a finite impulse response (FIR) filter for Markov jump linear systems (MJLSs), a fundamental problem is to avoid constructing the extended state-space model without knowing the mode sequence. This article proposes a new FIR filtering algorithm for MJLSs to address this problem. Under each mode, the variational inference approximates the posterior distribution as a product of Gaussian distribution and inverse gamma distribution by minimizing the Kullback–Leibler divergence. A recursion is then derived over a predefined estimation horizon, where the influence of abandoning the measurements beyond the horizon is compensated. By setting the estimation horizon length as a fixed number, the recursion achieved becomes a new FIR filter for MJLSs, while a new suboptimal Bayesian estimator appears when the horizon length is determined as the full horizon. A Newtonian tracking example as well a three degree-of-freedom hover model is presented to demonstrate that the proposed FIR method has good immunity against unpredicted modeling uncertainties at the cost of extra computational resources and memories, and its full-horizon form does not show this feature and may lose to some exiting algorithms when the underlying model is accurate.