In the decision-theoritic literatur, there are few if any results of the generality required for a substantial portion of the information gathering problems described in the previous two chapters. However, there are well-known results for minimum mean-square error parameter estimation (MMSE) for known linear systems corrupted by Gaussian noise. When there is an accompanying linear dynamic system, the optimal solution to the estimation problem is known as the Kalman filter [Gelb, 1974].1 In the case of nonlinear systems, the most common alternative is to approximate the nonlinear system by a linear one and apply MMSE procedures. These methods have been used in countless applications and are a standard technique in nearly every book on control, decision theory or estimation. The appeal of these methods is their mathematical and computational simplicity, particularly when dealing with dynamic systems—systems whose state evolves over time.
Unable to display preview. Download preview PDF.