Analysis of a stabilization technique for the fixed-pointprewindowed RLS algorithm

A stable finite precision recursive least squares (RLS) algorithm is derived for the prewindowed growing memory case (forgetting factor, λ=1). The prewindowed growing memory RLS algorithm diverges under fixed-point implementation. The random walk phenomenon due to roundoff errors in the weight update causes the divergence of the algorithm. To overcome this effect, these roundoff errors are modeled such that their effect is incorporated into the algorithm. The steady-state behavior of this new algorithm is analyzed, and it is shown that the divergence phenomenon is actually eliminated, and the new algorithm converges