Estimation variance and H∞-error minimization of stationary process with perfect measurements

The singular estimation problem of linear continuous-time stationary processes is solved both in the minimum error variance and the minimum H_∞-norm sense. Simple explicit expressions for the resulting estimators and their corresponding minimum criteria are derived in terms of the system structure parameters. These expressions enable an easy comparison between the two minimization procedures. The theory is demonstrated by a simple example of fourth order which is solved by both minimization methods