Optimal Estimation

Abstract

The preceding chapters provide the background necessary to introduce the optimal estimation problem. An “optimal estimate” is a best guess. However, we may express the “goodness” of an estimate in different ways, depending upon the particular engineering problem. After presenting the basic optimal estimation problem and some desirable properties of an estimate, we introduce three commonly-used optimality criterion: the maximum-likelihood, maximum a posteriori, and minimum mean-square error criteria. Each leads to a different estimate and a different form for the estimator. The estimators we discuss are typically implemented in digital systems, so we restrict ourselves to discrete-time signals and systems. Finally, we compare and contrast the different approaches.