Performance analysis and FTF version of the generalized sliding window recursive least-squares (GSWRLS) algorithm

We derive a new RLS algorithm: the generalized sliding window RLS (GSWRLS) algorithm and its fast numerically stabilized version: the GSW SFTF algorithm. The generalised window used consists of an exponential decay with base /spl lambda/ for the first L lags, a decrease by a factor 1-/spl alpha/ at lag L, and a further exponential decay with base /spl lambda/ beyond lag L. The exponential and rectangular windows are special cases of the generalized window. We analyze the steady-state excess mean squared error components due to the estimation noise and lag noise with different models for the time-varying optimal filter coefficients. This analysis shows that the exponential window performs better than the rectangular window, but also that the optimal generalized windows performs even better.