A Robust Mutual Information Method for Time-Delay Estimation Based on Multiscale Feature Extraction

Accurate parameter estimation from noisy, nonlinear time-series is a fundamental challenge in signal processing. Time-delay estimation, a critical step in techniques like time-delay embedding, is particularly susceptible to noise when using standard methods like mutual information (MI). This paper introduces a novel signal processing framework to overcome this limitation. We propose a multi-stage feature extraction front-end, termed GFMIEME, that transforms the raw signal into a more informative and noise-resilient feature space. This is achieved through a fine-grained multiscale analysis combined with the extraction of local statistical features (mean, standard deviation, root-mean-square). By computing MI in this enhanced feature domain, our method significantly boosts estimation accuracy. We benchmark our approach using chaotic signals, a canonical example of complex nonlinear data. Results show that our method successfully estimates the optimal time-delay at SNRs as low as 25 dB, a regime where traditional MI fails, demonstrating its superior robustness for practical signal analysis.