New approaches to robust minimum variance filter design

This paper is concerned with the design of robust filters that ensure minim um filtering error variance bounds for discrete-time systems with parametri c uncertainty residing in a polytope. Two efficient methods for robust Kalm an filter design are introduced. The first utilizes a recently introduced r elaxation of the quadratic stability requirement of the stationary filter d esign. The second applies the new method of recursively solving a semidefin ite program (SDP) subject to linear matrix inequalities (LMIs) constraints to obtain a robust finite horizon time-varying filter. The proposed design techniques are compared with other existing methods. It is shown, via two e xamples, that the results obtained by the new methods outperform all of the other designs.