Delay Estimation Methods to Support Per-Channel Analysis and Explore More Robust Metrics

[patrk]

Current situation

Delay estimation is a heuristic method suggested by Hillebrand, which computes an overall delay estimate across all channels in a measurement. This method calculates a single scalar value representing the delay based on the phase of the signals.

Goals

• Enhance the granularity and accuracy of delay estimation
• Ensure the PTE calculation is more reflective of the complex dynamics
• Investigate and potentially implement more robust and versatile delay estimation metrics
• Method is more or less deterministic and has profound mathematical foundations that ensure reliability and accuracy in its estimations (nice to have)

To improve delay estimation should explore additional metrics beyond the current heuristic.

Suggested metrics or concepts include:

• Cross-Correlation: Utilize cross-correlation to identify the time lag at which two signals are most similar
• Phase-Locking Value (PLV): Investigate the use of PLV for estimating delays by measuring the phase synchronization between signals.
• Mutual Information: Evaluate mutual information as a metric for delay estimation
• Dynamic Time Warping
• Wavelet Coherence
• Or even dive deeper into Hilbert Phase Analysis on which Hillebrand estimation is vaguely based

AC:

• method must be capable of calculating delay estimations on a per-channel-pair basis, resulting in a delay matrix that represents the time delays between each pair of channels in the dataset
• PTE calculation mechanism must be adapted to accept and effectively process a delay matrix as its input and use the correct delay estimate between channel pairs for the window sizing and shifting
• tests that underline the sanity and robustness of the overall algorithm with the integration of the new delay estimation method(s)