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

2025-01-30

AI Summary

This work addresses the challenge of parameter estimation for multicomponent high-order polynomial chirp signals—such as musical vibrato—under strong noise conditions. We propose a curvature-guided Langevin Monte Carlo (CG-LMC) method, which explicitly incorporates the average curvature of the target function into the sampling dynamics—a novel departure from conventional MCMC or standard LMC approaches. This curvature-aware design enhances global exploration of multimodal and non-convex likelihood landscapes. Under extremely low signal-to-noise ratio (SNR) conditions, CG-LMC achieves significantly improved estimation accuracy, reducing parameter estimation error by over 40% compared to standard LMC and traditional MCMC methods. The framework combines theoretical rigor with practical implementability, offering a new paradigm for real-time non-stationary signal processing in applications including radar detection and biomedical signal analysis.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations
• Security and Privacy: Large-scale security measurements

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.

Problem

• Multi-pitch Estimation
• Noisy Environment
• Music Analysis

Innovation

• Improved Langevin Monte Carlo Method
• Complex Trill Estimation
• Noise Robustness