Optimal minmax estimation and the development of minmax estimation error bounds

Abstract

It is often desired to create an optimal estimator of some parameter 6' given the observation 2. However, the relationship between 6' and z may depend on another parameter 4 which is unknown to the processor and not of direct interest. In this case, an estimator which performs well for one value of 4 may perform poorly for another value of 4. One approach to dealing with this problem is to develop an estimator whose worst case performance evaluated over some range of 4 is as good as possible. Such an optimal minmax estimator is derived. The derivation of this estimator also motivates an approach to developing lower bounds on the minmax estimation error achievable by any estimator.

Multi-sensor target tracking in the presence of clutter using game theory

“…In Ghazal and Doustmohammadi, 22 the target tracking problem is formulated as zero-sum game and a minimax algorithm is developed to estimate target position in radar/IR target tracking systems. In Preisig, 23 an optimal minimax filter is proposed for tracking a target based on the relationship between the measurements and states. In Yaesh and Shaked, 24 the problem of H 1 optimal state estimation filter of linear continuous-time system is evaluated when target tracking problem is formulated as a stochastic game.…”