Recursive Least-Squares Using the QR Decomposition

Abstract

In Chap. 3, we treated the nonrecursive solution of the Normal Equations as a batch processing least-squares problem. In many applications, like recursive identification and adaptive filtering, we are interested in a recursive solution of the Normal Equations such that given the solution at time t−1, we may compute the updated version of this solution at time t upon the arrival of new data. Algorithms of this type are known as recursive least-squares (RLS) algorithms. As mentioned in Chap. 2, we can exploit the recursive properties of the Normal Equations, which we have discussed, to derive recursive O(p²) or even fast recursive O(p) algorithms for calculating the updated solution of the Normal Equations at consecutive time steps of observation.