POLYNOMIAL MATRIX SOLUTION OF THE H-INFINITY FILTERING PROBLEM AND THE RELATIONSHIP TO RICCATI EQUATION STATE-SPACE RESULTS

A solution to the standard suboptimal H(infinity) filtering problem is presented using a new polynomial systems approach. The polynomial matrix solution is closely related to the recent H(infinity) state-space-based Riccati equation results, and the links between the polynomial and state-equation methodologies are demonstrated. The H(infinity) filter is derived by solving a special type of minimum-variance filtering problem, using a technique based on game theory. The solution of this game problem in a stochastic setting, by polynomial methods, is novel. The calculation of the H(infinity) filter involves a J-spectral factorization and the solution of two coupled diophantine equations. There are several computational advantages over previous polynomial methods for calculating H(infinity) filters.