On the determination of optimal costly measurement strategies for linear stochastic systems

This paper presents the formulation of a class of optimization problems dealing with selecting, at each instant of time, one measurement provided by one out of many sensors. Each measurement has an associated measurement cost. The basic problem is then to select an optimal measurement policy, during a specified observation time interval, so that a weighted combination of “prediction accuracy” and accumulated “observation cost” is optimized. The current analysis is limited to the class of linear stochastic dynamic systems and measurement subsystems. The problem of selecting the optimal measurement strategy can be transformed into a deterministic optimal control problem. An iterative digital computer algorithm is suggested for obtaining numerical results. It is shown that the optimal measurement policy and the associated “matched” Kalman-type filter can be precomputed, i.e. specified before the measurements actually occur. Numerical results for a third-order system with two possible measurements are presented.