Estimating the number of superimposed sinusoids

TL;DR

This paper introduces a new theoretical framework for model order selection algorithms to accurately estimate the number of superimposed sinusoids in noisy signals, emphasizing performance and consistency analysis.

Contribution

It presents a novel approach based on minimum error probability, providing closed-form error expressions and optimizing MOS algorithms, including a quasilikelihood method.

Findings

Framework enables consistency analysis of MOS algorithms

Closed-form expressions for error probabilities derived

Optimized MOS algorithms demonstrate improved performance

Abstract

Estimation of the number of superimposed sinusoids in the presence of noise is an important model order selection (MOS) problem in statistical signal processing. In this paper, we propose a new approach to the design of MOS algorithms for estimating the number of superimposed sinusoids. Our proposed approach is partially based on the minimum error probability criterion. Also, we pay a lot of attention to the performance and consistency analysis of the MOS algorithms. In this study, an error probability is used as a universal performance measure of the MOS algorithms. We propose a theoretical framework that makes it possible to provide consistency analysis and to obtain closed-form expressions for the approximated error probabilities of a wide range of MOS algorithms. As an example, we applied this framework to the consistency and performance analysis of several MOS algorithms for estimating the number of superimposed sinusoids. Using the obtained results, we provide a parametric optimization of the presented MOS algorithms. Finally, we examine a quasilikelihood approach to the design and performance analysis of the MOS algorithms. The proposed theoretical framework is used to find the scope of the quasilikelihood approach.