FIR Filtering of State-Space Models in non-Gaussian Environment with Uncertainties Plenary Lecture

This paper examines the recently developed p-shift iterative unbiased Kalman-like algorithm intended for filtering (p = 0), prediction (p > 0), and smoothing (p < 0) of linear discrete time-varying state-space models in non Gaussian environment with uncertainties. The algorithm is designed to have no requirements for noise and initial conditions and becomes optimal on large averaging intervals. It has the following advantages against the Kalman filter: bounded input/bounded output (BIBO) stability, better robustness against temporary model uncertainties and round-off errors, and low sensitivity to noise and initial conditions. It is shown that the estimator proposed outperforms the Kalman one when the noise covariances and initial conditions are not known exactly. If that is the case, then the Kalman-like algorithm demonstrates lower sensitivity to outliers and better robustness against the model uncertainties. Otherwise, the Kalman-like and Kalman estimators produce similar errors. The trade-off with the Kalman filter is investigated based on the polynomial state space model. Key–Words: Kalman-like FIR estimator, Gaussian noise with outliers, temporary uncertainty, error bound