Model Order Estimation for A Sum of Complex Exponentials

TL;DR

This paper introduces a novel method for estimating the number of components in a sum of damped sinusoids within noisy data, leveraging Hankel matrix properties and singular value constraints for improved accuracy.

Contribution

The proposed approach combines Hankel matrix shift-invariance with singular value constraints, offering significant improvements over existing subspace-based methods, especially in challenging noise conditions.

Findings

Outperforms traditional subspace methods in noisy environments

Provides more accurate model order estimation when signal and noise subspaces are poorly separated

Demonstrates robustness through numerical experiments

Abstract

In this paper, we present a new method for estimating the number of terms in a sum of exponentially damped sinusoids embedded in noise. In particular, we propose to combine the shift-invariance property of the Hankel matrix associated with the signal with a constraint over its singular values to penalize small order estimations. With this new methodology, the algebraic and statistical structures of the Hankel matrix are considered. The new order estimation technique shows significant improvements over subspace-based methods. In particular, when a good separation between the noise and the signal subspaces is not possible, the new methodology outperforms known techniques. We evaluate the performance of our method using numerical experiments and comparing its performance with previous results found in the literature.