Abstract
This paper considers the finite-horizon discrete-time minimax estimation problems related to the H∞ estimation cost. Based on the Lagrange multiplier technique, we show that the minimax estimators are identical to H∞ estimators in both filtering and onestep prediction cases. Moreover, necessary and sufficient conditions for the existence of the minimax estimators are given in terms of an H∞ type Riccati difference equation (RDE) satisfying the positive definiteness of certain matrices. Using the RDE, we compare the minimax estimators with Kalman filter, and investigate the some properties of the minimax estimators. A numerical example is also included to show the applicability of the present minimax estimators.
