Game theory approach to discrete H∞ filter design

In this correspondence, a finite-horizon discrete H1 filter design with a linear quadratic (LQ) game approach is presented. The exogenous inputs composed of the “hostile” noise signals and system initial condition are assumed to be finite energy signals with unknown statistics. The design criterion is to minimize the worst possible amplification of the estimation error signals in terms of the exogenous inputs, which is different from the classical minimum variance estimation error criterion for the modified Wiener or Kalman filter design. The approach can show how far the estimation error can be reduced under an existence condition on the solution to a corresponding Riccati equation. A numerical example is given to compare the performance of the H1 filter with that of the conventional Kalman filter.