Window optimization issues in recursive least-squares adaptive filtering and tracking

In this paper we consider tracking of an optimal filter modeled as a statinary vector. We interpret the Recursive Least-squares (RLS) adaptive filrering algorithm as a filtering operation on the optimal filter process and the intantaneous gradient noise (induced by the measurement noise). the filtering operation carried out by RLS algorithm depends on the window used in the least-squares criterion. To arrive at a recursive LS algorithm requires that the window impulse response can be expressed recursively (output of an IIR filter). In practice, only two popular window bchoices exist (with each one tuning parameter): the exponential window and the rectangular window. Since the complexity of RLS with a rectangular window essentially believed that this increase in complexity allows for some improvement in tracking performance. we show that for an ideal lowpass optimal filter evolution spectrum (Doppler spectrum), the exponential window always outperforms the rectangular window. however, the rectangular window can be generalized at a small cost for the resulting RLS algorithm to a window with nthree parameters (instead of just one), encompassing both rectangular and exponential windows as special cases. The tuning of these three parameters leads to improved performance.