Filtering of Discrete-Time State-Space models with the p-Shift Kalman-like Unbiased FIR Algorithm

In this paper, we show a simple way to derive the p-shift finite impulse response (FIR) unbiased estimator (UE) recently proposed by Shmaliy for time-invariant discrete-time state-space models. We also examine its iterative Kalman-like form. We conclude that the Kalman-like algorithm can serve efficiently as an optimal estimator with large averaging horizons. It has better engineering features than the Kalman one, being independent on noise and initial conditions. Both algorithms produce similar errors, although the proposed one overperforms the Kalman filter if the noise covariance matrices are filled incorrectly. The full horizon Kalman-like and Kalman algorithms produce equal errors only within some range of averaging horizons. With smaller horizons, the Kalman filter is more accurate and, with larger ones, the proposed solution provides better denoising. Simulation results are obtained for the 3-state space polynomial model and quadratic noiseless signal measured with noise. Key–Words: Kalman-like filtering, FIR estimator, State-space