A GAME-THEORY APPROACH TO ROBUST DISCRETE-TIME H-INFINITY-ESTIMATION

The deterministic robust estimation problem is formulated in the discrete-time case as a zero-sum two person difference game, in which a statistician plays against nature. The statistician tries to estimate a linear combination of the states of an uncertain linear system, which is driven by nature. Saddle-point strategies for the statistician in the above game are difficult to find. A suboptimal strategy is, therefore, considered which guarantees an H(infinity) performance bound on the estimation error. Different patterns of the information that is available to the statistician are treated, and the corresponding fixed-point, fixed-lag, and fixed-interval smoothing strategies are derived.