State estimation in pairwise Markov models with improved robustness using unbiased FIR filtering

We propose a novel estimation procedure for linear time-varying pairwise Markov models (PMM), that is robust to system parameter uncertainties occurring in real-world applications. In order to cope with mismodeling errors and ignorance of noise/initial state statistics, we solve a finite-horizon state estimation problem. The resulting unbiased finite impulse response filter for PMMs (PMM-UFIR) is first derived in batch form and then converted to a recursive Kalman-like form for the sake of complexity reduction. Closed forms for the error covariance matrix of the state estimate are also provided for analytical performance assessment. Numerical results illustrate the effectiveness of the proposed estimation method over Gaussian processes, by showing that the PMM-UFIR is nearly as accurate as (resp. more robust than) optimal filtering under perfect (resp. uncertain) system parameters after tuning the horizon size.