Error Analysis of the Fixed Point RLS Algorithm

In this report, the steady state mea.n square prediction error is derived for the fixed point RLS (Recursive Least Squares) algorithm, both for the exponentially windowed RLS (forgetting factor, , < 1), and the prewindowed growing memory RLS (, == 1) for correlated inputs. It is shown that signal correlation enhances the excess error due to additive noise and roundoff noise in the desired signal prediction computation. However, correlation has no effect on the noise due to roundoff of the weight error update recursion, which is the error term leading to the di vergence of the algori thrn for , == 1. Also, it is shown that convergence rate of the algorithm depends on the filter order, choice of the forgetting factor and most important of all on the eigenvalue spread of the data. Convergence is slower if the data is highly correlated, i.e. has a large eigenvalue spread.