Tracking Capability and Floating-Point Error Analysis in Multirate Complex Recursive Weighted Least Squares Algorithm.

This paper presents an analysis of a multirate complex recursive weighted least squares (MC-RLS) algorithm based on an analytic signal. Conventional adaptive filters for multiple sinusoid extraction have been based on lattice filter structures or gradient methods because of their low computational cost and/or low sensitivity to quantization errors. On the other hand, the RLS algorithm is easy to introduce assuming time-variant quantities in the algorithm when sinusoid frequencies have the time-varying property. However, the relationship between the tracking capability and the quantization error of the least-squares (LS) algorithm in the transversal structure has not been reported. In addition, an improvement algorithm for these errors have not been reported. In this paper, we shall describe a new RLS algorithm in a transversal filter structure with a superior transient property, reduced sensitivity to quantization errors, and low computational cost. First, an analytic signal-based autoregressive model is introduced and the MC-RLS algorithm is shown. Then, using an excess mean-square error of the MC-RLS algorithm, the tracking capability shown to be unaffected by the analytic transform and the decimation. In addition, the floating-point error and the computational cost of the MC-RLS algorithm are analyzed. It is shown that both floating-point error and computational cost are smaller than those of conventional RLS algorithms that use real signals. [ABSTRACT FROM AUTHOR]