April 2008
Intermediate
832 pages
26h 2m
English
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CHAPTER 30 Recursive Least-Squares
Now that we have studied in some detail the least-squares problem, we proceed to derive an algorithm for updating its solution. The resulting recursion will be referred to as the Recursive Least-Squares (RLS) algorithm and it will form the basis for most of our discussions in the future chapters.
30.1 MOTIVATION
Given an N × 1 measurement vector y, an N × M data matrix H and an M × M positive-definite matrix Π, we saw in Sec. 29.7 that the M × l solution to the following regularized least-squares problem:
is given by
where, in comparison with (29.28), we are assuming 
for simplicity of presentation. The arguments would apply equally well to the case 
— see the remark after Lemma 30.1.
We denote the individual entries of y by {d(i)}, and the individual rows of H by {ui}, say,
so that the solution 
in (30.2) is determined by data {d(
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