Dual Cutler-Vallisneri Corrections: Mitigating PSD Drift in Zero-Latency Gravitational-Wave Searches

Abstract

Maximizing pre-merger warning times in gravitational-wave searches requires minimizing algorithmic latency. While current pipelines typically rely on truncated linear-phase filters, minimum-phase whitening offers a zero-latency alternative that eliminates the acausal look-ahead buffer. However, this causal approach exposes the analysis to spectral drift, where the whitening operator applied to live data diverges from the static template bank, creating a functional perturbation of the matched-filter metric. We develop a perturbative framework generalizing the Cutler-Vallisneri formalism to address these metric errors, deriving analytic expressions for the resulting timing, phase, and SNR biases. Validated against exact stationary-phase models and numerical injections, these corrections achieve $<1\%$ error. Applying this framework to GWTC-4.0 events with realistic 1-week power spectral density (PSD) lags, we find that uncorrected drift induces severe systematics: detector-pair timing biases exceeding $200 μ$s, phase shifts up to 0.2 rad, and sky-localization errors of $5^{\circ}-10^{\circ}$. Additionally, we observe a median signal-to-noise ratio (SNR) loss of $3-5\%$, with outliers exceeding $8\%$. These results demonstrate that while minimum-phase whitening maximizes the early-warning window, analytic drift corrections are essential to maintain detection volume and pointing accuracy in future observing runs.

Figures (6)

• Figure 1: Analytic Validation (SPA Model). Verification of Dual CV corrections under a nonlinear whitening-phase perturbation $\Phi_a(f) = \alpha + \beta f + \gamma f^2$. Top: Normalized SNR$^2(t)$ slice for a representative perturbation $\epsilon=0.1$, showing the physical displacement of the peak relative to the baseline (blue). Bottom: Convergence of the analytic phase correction. The fractional error between the geometric prediction $\delta\phi^{(1)}$ and the exact numerical shift $\Delta\phi_{\mathrm{full}}$ scales linearly with $\epsilon$, confirming the validity of the first-order expansion.
• Figure 2: Numerical PSD-Drift Injection.Top: Baseline PSD $S_1(f)$ (solid) and perturbed PSD $S_2(f)$ at $\epsilon=0.1$ (dashed). An exaggerated curve at $\epsilon=0.5$ (green) illustrates the Gaussian drift morphology. Bottom: Matched-filter SNR surface $J(t)$ at fixed phase $\phi=\phi_0$. The spectral mismatch shifts the peak time (vertical lines) and reduces the maximum amplitude, in exact agreement with the analytic prediction (horizontal dotted line).
• Figure 3: Convergence of Corrections. Fractional error between the analytic Dual CV predictions and the full numerical shifts as a function of drift amplitude $\epsilon$. Orange squares: Phase bias convergence. Blue circles: Calibrated timing bias convergence. Both metrics exhibit the expected linear scaling ($\mathcal{O}(\epsilon)$ residuals), demonstrating the robustness of the first-order expansion for realistic drift magnitudes.
• Figure 4: GWTC-4.0 Bias Distribution (1-Week Lag). Histograms of analytic Dual CV corrections for $\sim 160$ event-detector pairs. Left: Timing biases $\delta t^{(1)}$ exhibit a heavy tail extending beyond $\pm 200\,\mu\mathrm{s}$, driven by spectral line drift. Right: Phase biases $\delta\phi^{(1)}$ are generally confined to $\pm 0.2\,\mathrm{rad}$.
• Figure 5: Sky Localization Impact. Systematic shifts in Right Ascension ($\Delta\alpha$) and Declination ($\Delta\delta$) induced by uncorrected PSD drift. While the median shift is $\lesssim 2.5^\circ$, outliers in the scatter plot (right) reveal shifts exceeding $5^\circ$--$10^\circ$, posing a critical risk for electromagnetic follow-up.

Theorems & Definitions (6)

• Lemma B.1: Shift of a nondegenerate maximizer
• proof
• Lemma B.2: Hessian--Fisher identity
• proof
• Theorem B.3: Geometric First-Order Bias
• proof