Estimating Multi-chirp Parameters using Curvature-guided Langevin Monte Carlo

TL;DR

This paper introduces a curvature-guided Langevin Monte Carlo method for estimating parameters of higher-order chirps in noisy signals, demonstrating robustness and effectiveness in low SNR conditions.

Contribution

It proposes a novel CG-LMC algorithm that leverages curvature information to reliably optimize non-convex chirp parameter estimation problems.

Findings

CG-LMC outperforms traditional methods in low SNR scenarios

The algorithm reliably finds the global minimizer in complex non-convex landscapes

Results demonstrate robustness across various noise levels

Abstract

This paper considers the problem of estimating chirp parameters from a noisy mixture of chirps. While a rich body of work exists in this area, challenges remain when extending these techniques to chirps of higher order polynomials. We formulate this as a non-convex optimization problem and propose a modified Langevin Monte Carlo (LMC) sampler that exploits the average curvature of the objective function to reliably find the minimizer. Results show that our Curvature-guided LMC (CG-LMC) algorithm is robust and succeeds even in low SNR regimes, making it viable for practical applications.