GAME-THEORY APPROACH TO FINITE-TIME HORIZON OPTIMAL ESTIMATION

A game theory approach is introduced which provides a simple solution to the problem of finite-time optimal estimation. In this game a measu rement record is given and the first player looks for the best estimat e of a prespecified combination of the system states in the presence o f ''hostile'' noise signals and system initial condition that am appli ed by his adversary (say nature). It turns out that the game possesses a saddle-point solution which leads to an optimal smoothed estimate t hat is identical to the corresponding L2-optimal estimate. A similar g ame is formulated and solved where the estimate is restricted to be ca usal. This game provides a saddle-point equilibrium interpretation to the finite-time H(infinity)-optimal filtered estimation. The two games are very closely related. It is shown that in the first game the firs t player's strategy, which is the optimal smoothed estimate, is a line ar-fractional transformation of the H(infinity)-optimal filter which a pplies a nonzero free contracting V parameter. It, therefore, achieves a unity H(infinity)-norm bound for the operator that relates the exog enous signals to the estimation error.