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 floatingpoint error and the computational cost of the MC‐RLS algorithm are analyzed. It is shown that both floatingpoint error and computational cost are smaller than those of conventional RLS algorithms that use real signals.