Optimal Lp filtering for discrete‐time non‐Gaussian dynamic systems

Abstract

Abstract This paper investigates the Lp filtering problem for linear dynamic systems. The main objective is to discuss the optimal filter for non‐Gaussian systems. The filter structure is obtained by extension of the maximum a posteriori estimation problem for general norm exponential probability density functions. The obtained filter has a linear structure, and two different algorithms are proposed for 1≤p2, it is the best for the systems with platykurtic error distributions. In this regard, it is shown that the L1 and L∞ filters have the best MSE performance for the systems with Laplacian and uniform error probability distribution functions, respectively. Simulation results verify the superior performance of the proposed filtering approach for linear time‐invariant and time‐varying systems.