Statistical Signal Processing in Engineering

9MLE and CRB for Some Selected Cases

In this chapter, MLE and the CRB are evaluated for some of the most common models and applications introduced in Chapter 5. Furthermore, from the inspection of the CRB, some methods are revised such as the common usage of numerical histograms. The numerical analysis in Chapter 10 is the natural complement of this chapter, pairing theory with numerical validations. Examples here are introductory to consolidate knowledge of the basics of estimation theory and bounds; extensive usage of these concepts can be found in applications in later chapters (Chapters 16, 17, 19, and 20).

9.1 Linear Regressions

Considering the linear regression model (Section 5.1)

with ; it is possible to obtain the MLE in a closed form. For it is:

In the case of uniform sampling with (including Δt in the variable B, or considering ) it is¹

where

The covariance matrix is ...