Estimators using covariance information under relation to game theoretic approach

In H_∞ signal estimation, we propose a filtering algorithm using covariance information. As in the H∞ filter, the algorithm for γ²=∞ is reduced to the recursive least squares (RLS) filter using the covariance information, where γ is the parameter concerned with the performance criterion of the estimator. The algorithm for γ²<∞ is preferable to the RLS filter using the covariance information in terms of estimation accuracy. For calculating the fixed-point smoothing (FPS) estimate, the smoothing algorithm is contained. The calculated filtering estimate is used as an initial value of the FPS estimator at the fixed point. We then assume that the covariance information and the autovariance functions K_x(T,T) of the state variable x(T) are given. K_x(T,T) is calculated by the system matrix A and the input matrix B. Algorithms for the filtering estimates zˆ₁ (T,T) of z₁(t)[=Cx(t)] and zˆ(T,T) of z(T)[=Hx(T)] are proposed. In the autovariance function p(T,T) of the filtering estimate of the state variable x(T), we use K_x(T,T). The FPS estimates zˆ₁(T,T) of z₁(t) and Z(t) are calculated in terms of the smoothing algorithm. We also present a new algorithm for the filtering estimate of z₁(t), particularly when z₁(t)=az(t) (a is a real constant). It is advantageous to calculate the filtering and FPS estimates using a, A, H and K_xy (t,t), where the latter three quantities can be obtained from the autocovariance function K_z(t,s) of the signal z(t). A numerical simulation shows that the filtering and FPS estimates by the RLS smoother using the filtering estimate as its initial value are more accurate than those by the RLS filtering and FPS algorithms of the earlier theorem