Iterative algorithms for unbiased FIR state estimation in discrete time

Various iterative unbiased finite impulse response (UFIR) algorithms are proposed for filtering, smoothing, and prediction of discrete-time state-space models in white Gaussian noise. The distinctive property of UFIR algorithms is that noise statistics are completely ignored. Instead, an optimal window size is required for optimal performance. Under real-world operating conditions with uncertainties, non-Gaussian noise, and unknown noise statistics, the UFIR estimator generally demonstrates better robustness than the Kalman filter, even with suboptimal window size.