Lessons in Estimation Theory for Signal Processing, Communications, and Control, Second Edition

Lesson 13 Mean-squared Estimation of Random Parameters

Summary

There are two major types of estimators of random parameters: mean-squared (MS) and maximum a posteriori (MAP). The former does not use statistical information about the random parameters, whereas the latter does. MS estimators are the subject of this lesson; MAP estimators are the subject of Lesson 14.

The MSE is shown to equal a conditional expectation, i.e., . This result is referred to as the fundamental theorem of estimation theory. When θ and Z(k) are jointly Gaussian, then it is possible to compute this expectation, and, in fact, processes the data, Z(k), linearly. When θ ...