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, filtering problem is presented using a new polynomial systems ap- proach. The polynomial matrix solution is closely related to the recent H, state-space-based Riccati equation results, and the links between the polynomial and state-equation methodologies are demonstrated. The H, 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 cal- culation of the H, 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, filters.