A novel approach for stabilizing recursive least squares (RLS) filters is presented. The approach relies on a detailed fixed point analysis, which provides two important benefits. The analysis reveals a bias in the error propagation mechanism, providing an analytical basis for instability problems. The analysis then 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. >