Steady-state behavior of RLS adaptive algorithms

This paper treats analytically and experimentally the response of RLS {Recursive Least Squares} adaptive filters with exponential windows to stationary and nonstationary inputs. A new formula for the "estimation-noise" has been derived involving second- and fourth-order statistics of the filter input as well as the exponential windowing factor and filter length. Under general time-varying conditions it is shown that the time constant associated with "lag effects" depends solely on the exponential weighting parameter λ. In addition the calculation of the excess mean square error due to the lag for an assumed Markov channel provides the necessary information about tradeoffs between speed of adaptation and steady-state error. In the simple case of channel identification it is shown that the LMS and RLS adaptive filters have the same tracking behavior.