Estimating Time Delays between Signals under Mixed Noise Influence with Novel Cross- and Bispectral Methods

2025-02-16

AI Summary

Traditional delay estimation methods—such as those based on cross-spectrum or bispectrum—are prone to zero-lag bias under mixed noise conditions. To address this, we propose two novel approaches: (1) phase-spectrum periodicity-based delay estimation, which replaces slope estimation with periodicity detection to enhance sensitivity to weak signals; and (2) bispectral antisymmetrization, a theoretically grounded technique that eliminates contributions from all independent Gaussian and non-Gaussian noise sources, thereby fully suppressing zero-lag bias. Monte Carlo simulations and neural electrophysiological data validate that the proposed methods significantly outperform conventional techniques at low signal-to-noise ratios, completely avoiding spurious zero-lag estimates. Moreover, their performance is robust—insensitive to the true delay value and to unknown noise statistics. Both methods are original contributions, combining theoretical rigor with practical applicability for reliable time-delay estimation in complex noisy environments.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Kernel Methods
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

A common problem to signal processing are biases introduced by correlated noise. When quantifying time delays between two signals, mixed noise introduces a bias towards zero delay in conventional delay estimates based on the cross- or bispectrum. Here we propose two novel time delay estimators that address these shortcomings: (1) A cross-spectrum based approach that relies on estimating the periodicity of the phase spectrum rather than its slope, and (2) a bispectrum based approach, bispectral antisymmetrization, which removes contributions from not just Gaussian but all independent sources. In a simulation study, we compare conventional and novel TDE approaches and resolve differences in performance with respect to noise Gaussianity and auto-correlation structure. As a proof-of concept, we also perform TDE analysis on a neural stimulation dataset (n=3). We find that antisymmetrization consistently outperforms conventional bispectral methods at low signal-to-noise ratios (SNR) and prevents spurious zero-delay estimates in all mixed-noise environments. Time delay estimation based on phase periodicity also improves signal sensitivity compared to conventional cross-spectral methods. These observations are stable with respect to the magnitude of the delay and the statistical properties of the noise.

Problem

• Estimating time delays between signals with mixed noise bias
• Improving accuracy in cross- and bispectral delay estimation methods
• Addressing spurious zero-delay estimates in low SNR environments

Innovation

• Cross-spectrum method estimates phase periodicity
• Bispectral antisymmetrization removes independent noise
• Improved performance in low SNR conditions