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

Lesson 5 Least-squares Estimation: Recursive Processing

Summary

Modern digital computers have caused us to take a second look at the classical batch formulas of (weighted) least squares. These formulas can be made recursive in time by using simple vector and matrix partitioning techniques. The purpose of this lesson is to derive two recursive (weighted) least-squares estimators, referred to as the information and covariance forms.

The information form is most readily derived directly from the batch formulas in Lessons 3, whereas the covariance form is derived from the information form using a very important identity from matrix algebra, known as the matrix inversion lemma.

The information form is often more useful than the covariance form in ...