Gauge Theoretic Signal Processing II: Zero-Latency Whitening for Early Warning Pipelines

TL;DR

This paper introduces a gauge theoretic framework for causal whitening filters in gravitational-wave detection, reducing latency by up to 91% while maintaining detection sensitivity and accuracy.

Contribution

It validates a geometrically exact, parallel-transport-based update rule for causal filters that preserves SNR and phase, enabling low-latency gravitational-wave alerts.

Findings

Reduces whitening latency by 33% in production pipelines.

Preserves detection sensitivity and inter-detector timing accuracy.

Up to 91% trigger latency reduction possible with sub-second noise estimation.

Abstract

Low-latency gravitational-wave search pipelines provide early-warning alerts for multimessenger astrophysical transients. Current pipelines whiten the data stream using acausal, linear-phase filters, which require a look-ahead buffer that introduces several seconds of algorithmic latency. Eliminating this latency requires causal, minimum-phase whitening filters using only past data. However, operating causal filters under non-stationary noise is non-trivial: the drifting power spectral density must be tracked without degrading the matched-filter signal-to-noise ratio (SNR), filter updates must preserve the minimum-phase condition, and the altered phase response must be compensated to maintain sky-localization accuracy. In Paper I we introduced a gauge theoretic signal processing framework and showed that the minimum-phase connection on the manifold of power spectra provides a geometrically exact update rule for causal filters. Here we validate that framework numerically and operationally, demonstrating that parallel transport along this connection strictly preserves the minimum-phase property while exactly conserving the matched-filter SNR. We numerically certify the flatness of this connection, showing that the optimal filter is a path-independent state function of the instantaneous noise. Through an injection campaign on O3 data with 15,347 binary black hole signals across the LIGO-Virgo network, we confirm that this architecture preserves the detection sensitivity and inter-detector timing and phase accuracy of the linear-phase baseline. Implementing the framework in the production sgnl pipeline reduces whitening latency by 1.0 s (33%) at a 4-second noise estimation cadence, confirmed in controlled tests and on live O3 replay data at production scale. Stride reduction experiments show that up to 91% of baseline trigger latency can be eliminated with sub-second pipeline cadence.