Error accumulation effects for the a posteriori RLSL prediction filter

This paper presents a numerical analysis of the a posteriori recursive least-squares lattice filter with indirect updating. The important problem of finite precision effects in adaptive RLS lattice filters is addressed for this particular filter algorithm but the technique is applicable to many other versions. New recursions for the filter residuals and the filter powers (forward and backward) are derived which describe the effects of arithmetic errors that originate at one stage (m) and are passed to the next stage (m+1). These recursions permit an arithmetic error analysis at the zeroth filter stage to have meaning at all future filter stages. Effects from machine precision, η, are linked to the forgetting factor, λ, and time, n, to derive bounds for arithmetic error growth at the zeroth filter stage. These results provide an explicit upper bound on the forgetting factor that ensures acceptable error propagation. Additionally, we offer a computationally inexpensive way to monitor arithmetic error effects during the normal execution of the filter algorithm through a running error analysis