Performance analysis of a simplified RLS algorithm for the estimation of sinusoidal signals in additive noise

Adaptive estimation of nonstationary sinusoidal signals or quasi-periodic signals in additive noise is of essential importance in many diverse engineering fields, such as communications, biomedical engineering, power systems, pitch detection in transcription and so forth. So far, Kalman filtering based techniques, recursive least square (RLS), simplified RLS (SRLS) and LMS algorithms, for examples, have been developed for this purpose. This work presents in detail a performance analysis for the SRLS algorithm proposed recently in the literature; which is used to estimate an enhanced sinusoid. Its dynamic and tracking properties, noise and lag misadjustments are developed and discussed. It is found that the SRLS estimator is biased, and its misadjustments are functions of not only the noise variance but also, unpleasantly, of the signal parameters. Simulations demonstrate the validity of the analysis. Application of the SRLS to a real-life piano sound is also given to peek at its effectiveness.