A Generalized Kalman Filter for 2D Discrete Systems

Abstract

This paper studies the problem of state estimator design for stochastic twodimensional (2D) discrete systems described by the secondary 2D Fornasini-Marchesini odel subject to white noise in both the state and measurement equations. The aim is to design a 2D Kalman filter that minimizes the variance of the estimation error of the state vectors. An explicit formulation of the estimator is derived, based on which, an algorithm for the design of the desired Kalman filter is proposed. Finally, examples are provided to demonstrate the effectiveness of the proposed method.