# A Rapid Introduction to Adaptive FilteringLeast Squares

A Rapid Introduction to Adaptive Filtering: Least Squares [In this chapter we will cover the basics of the celebrated method of Least Squares (LS). The approach to this method is different from the stochastic gradient approach from the previous chapter. As always, the idea will be to obtain an estimation of a given system using input-output measured pairs (and no statistical information), and assuming a model in which the input and output pairs are linearly related. We will also present the Recursive Least Squares (RLS) algorithm, which will be a recursive and a more computational efficient implementation of the LS method. One of its advantage is that it can be used in real time as the input-output pairs are received. In this sense, it will be very similar to the adaptive filters obtained in the previous chapter. Several important properties of LS and RLS will be discussed.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Rapid Introduction to Adaptive FilteringLeast Squares

23 pages

Publisher
Springer Berlin Heidelberg
ISBN
978-3-642-30298-5
Pages
89 –112
DOI
10.1007/978-3-642-30299-2_5
Publisher site
See Chapter on Publisher Site

### Abstract

[In this chapter we will cover the basics of the celebrated method of Least Squares (LS). The approach to this method is different from the stochastic gradient approach from the previous chapter. As always, the idea will be to obtain an estimation of a given system using input-output measured pairs (and no statistical information), and assuming a model in which the input and output pairs are linearly related. We will also present the Recursive Least Squares (RLS) algorithm, which will be a recursive and a more computational efficient implementation of the LS method. One of its advantage is that it can be used in real time as the input-output pairs are received. In this sense, it will be very similar to the adaptive filters obtained in the previous chapter. Several important properties of LS and RLS will be discussed.]

Published: Aug 4, 2012

Keywords: Singular Value Decomposition; Recursive Little Square; Full Column Rank; Little Square Estimator; Little Square Problem