Modeling, Estimation and Optimal Filtration in Signal Processing

Chapter 4

Adaptive Filtering

4.1. Introduction

The classification of adaptive algorithms can follow various rules. Nonetheless, all recursive approaches can be written under the following generalized form:

where all the parameters combined in vector are updated using the function F(.). This function is specific for each particular algorithm and generally depends on a state vector (k). The parameter K (k) is a weighting coefficient. Its expression depends on the particular algorithm that is studied. In addition, K (k) may be used to respect a particular optimization criterion, to ensure the convergence of the algorithm, etc.

This chapter is dedicated to recursive algorithms which require no prior information. These algorithms are versatile: they adjust themselves according to the statistical analysis carried out on the observed signals.

For our purposes, an adaptive filter will be defined as a digital filter whose coefficients are updated over time according to the appropriate criteria. As shown in Figure 4.1, _N (k) is the vector which concatenates the last N values, up to the instant ...