Third‑generation gravitational‑wave detectors will see binary‑neutron‑star inspirals for many hours, sometimes nearly a day. Over such long observations the Earth’s rotation changes a detector’s sensitivity to the sky. That time dependence breaks a common shortcut used in Bayesian parameter estimation and makes the calculations prohibitively slow. This paper shows a practical way to restore the shortcut and speed up inference for day‑long signals.

The author uses the Jaranowski–Królak–Schutz (JKS) decomposition, an exact five‑harmonic expansion of a ground interferometer’s antenna response. In plain terms, the rotating detector response is written as a fixed set of five known time functions multiplied by five coefficients that depend on the source sky position, orientation, and distance. That split isolates the slow, rotation‑driven part of the signal from the expensive intrinsic waveform calculations that describe the binary’s orbit.

To compress the costly frequency‑domain work, the method also uses a stationary‑time map, a frequency grid set by the waveform’s phase curvature, and error‑controlled relative binning. The stationary‑time map lets the slow antenna functions be evaluated using the waveform’s dominant time‑to‑frequency mapping. The curvature‑controlled grid reduces the number of frequency points needed to represent the intrinsic waveform accurately. Relative binning then turns each likelihood evaluation into a sparse update on top of reusable summaries.

Putting these pieces together, the paper reports an acceleration of order 10^4 for likelihood evaluations on a 21.3‑hour binary‑neutron‑star signal. The five‑function JKS basis has a fixed size that does not grow with signal duration. That means the expensive parts of the calculation can be reused while the sampler explores sky position and other “extrinsic” parameters. The result is that day‑long third‑generation (3G) signal inference becomes practical for the signal model studied here.