A hidden Markov model (HMM) solved recursively by the Viterbi algorithm can be configured to search for persistent, quasimonochromatic gravitational radiation from an isolated or accreting neutron star, whose rotational frequency is unknown and wanders stochastically. Here an existing HMM analysis pipeline is generalized to track rotational phase and frequency simultaneously, by modeling the intrastep rotational evolution according to a phase-wrapped Ornstein-Uhlenbeck process, and by calculating the emission probability using a phase-sensitive version of the Bayesian matched filter known as the $\mathcal{B}$-statistic, which is more sensitive than its predecessors. The generalized algorithm tracks signals from isolated and binary sources with characteristic wave strain $h_0\ge 1.3\times {10}^{-26}$ in Gaussian noise with amplitude spectral density $4\times {10}^{-24}{\mathrm{Hz}}^{-1/2}$, for a simulated observation composed of $N_T=37$ data segments, each $T_{\text{drift}}=10\mathrm{days}$ long, the typical duration of a search for the low-mass x-ray binary (LMXB) Sco $\mathrm{X}-1$ with the Laser Interferometer Gravitational Wave Observatory (LIGO). It is equally sensitive to isolated and binary sources and $\approx 1.5$ times more sensitive than the previous pipeline, which achieves $h_0\ge 2.0\times {10}^{-26}$ for a comparable search. Receiver operating characteristic curves (to demonstrate a recipe for setting detection thresholds) and errors in the recovered parameters are presented for a range of practical $h_0$ and $N_T$ values. The generalized algorithm successfully detects every available synthetic signal in Stage I of the Sco $\mathrm{X}-1$ Mock Data Challenge convened by the LIGO Scientific Collaboration, recovering the frequency and orbital semimajor axis with accuracies of better than $9.5\times {10}^{-7}\mathrm{Hz}$ (one part in $\sim {10}^8$) and $1.6\times {10}^{-3}\text{lt}\mathrm{s}$ (one part in $\sim {10}^3$) respectively. The Viterbi solver runs in $\approx 2\times {10}^3$ CPU-hr for an isolated source and $\sim {10}^5$ CPU-hr for a LMXB source in a typical, broadband (0.5-kHz) search, i.e., $\lesssim 10$ times slower than the previous pipeline.

• Received 15 June 2020
• Accepted 22 July 2021

DOI:https://doi.org/10.1103/PhysRevD.104.042003