A NOVEL-APPROACH FOR STABILIZING RECURSIVE LEAST-SQUARES FILTERS

One reason recursive least squares (RLS) filters are not widely used in adaptive signal processing applications is because of instability problems resulting from finite precision implementation. This paper presents a novel approach for stabilizing RLS filters, applying the approach to the conventional RLS filter (order N2 operations per iteration). The approach relies on a detailed fixed point analysis, which provides two important benefits. First, the analysis reveals a bias in the error propagation mechanism, providing an analytical basis for instability problems. Second, the analysis indicates which specific roundoff errors are causing instability. These roundoff errors are then biased in such a way that the overall filter is biased towards stable performance. Experimental results indicate that stability can be achieved with negligible loss in least squares performance.