Convergence analysis of an adaptive pseudolinear-regression notch filtering algorithm

This paper analyzes the convergence properties of an adaptive pseudolinear regression notch filtering algorithm recently proposed in the literature for estimating the frequencies of multiple sine waves from measurements corrupted by possibly colored additive noise. Simple necessary and sufficient conditions for the local convergence of this algorithm to the true frequency values are derived. It is shown that the algorithm has an interesting decoupling property in the sense that satisfaction of the convergence condition by a certain frequency implies local convergence to that frequency no matter whether the other frequencies satisfy or do not satisfy the convergence conditions. However, it is also shown that the algorithm is not generally convergent and, therefore, cannot be recommended for widespread use in applications. Numerical examples are used to illustrate the main points in the theoretical analysis.