Efficient and Accurate Frequency Estimation of Multiple Superimposed Exponentials in Noise

TL;DR

This paper introduces an efficient iterative algorithm for accurately estimating multiple superimposed exponential frequencies in noisy signals, outperforming existing methods with fewer iterations.

Contribution

The paper presents a novel iterative frequency estimation algorithm combining leakage subtraction, with theoretical analysis of bias, variance, and convergence behavior.

Findings

Algorithm converges to asymptotically unbiased estimates.

Estimates have variance slightly above the Cramer-Rao lower bound.

Simulation results show superior accuracy over state-of-the-art methods.

Abstract

The estimation of the frequencies of multiple superimposed exponentials in noise is an important research problem due to its various applications from engineering to chemistry. In this paper, we propose an efficient and accurate algorithm that estimates the frequency of each component iteratively and consecutively by combining an estimator with a leakage subtraction scheme. During the iterative process, the proposed method gradually reduces estimation error and improves the frequency estimation accuracy. We give theoretical analysis where we derive the theoretical bias and variance of the frequency estimates and discuss the convergence behaviour of the estimator. We show that the algorithm converges to the asymptotic fixed point where the estimation is asymptotically unbiased and the variance is just slightly above the Cramer-Rao lower bound. We then verify the theoretical results and estimation performance using extensive simulation. The simulation results show that the proposed algorithm is capable of obtaining more accurate estimates than state-of-art methods with only a few iterations.