Convergence and error analysis of the fixed point RLS algorithm with correlated inputs

The steady state mean square prediction error is derived for the fixed-point RLS (recursive least squares) algorithm, both for the exponentially windowed RLS (forgetting factor, γ<1), and the prewindowed growing memory RLS (γ=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 divergence of the algorithm for γ=1