Discovering pulsars in compact binaries with a hidden Markov model

Discovering radio pulsars in compact binaries, whose orbital periods $P_{\rm b}$ satisfy $P_{\rm b} \lesssim 1 \, \rm{day}$, is computationally challenging, because the time-dependent pulse frequency $f_{\rm p}(t)$ is strongly Doppler modulated by the binary motion. Here we present a new, fast, semi-coherent detection scheme based on a hidden Markov model (HMM) combined with a maximum likelihood matched filter, the Schuster periodogram. The HMM scheme complements traditional acceleration searches by dividing $f_{\rm p}(t)$ into piecewise-constant blocks and tracking the block-to-block evolution efficiently using dynamic programming. Monte Carlo simulations show that the new method can detect compact binaries with flux densities $S \geq 0.50 \, \rm{mJy}$ and orbital periods $P_{\rm b} \geq 0.012 \, \rm{day}$ under observing conditions (e.g.\ cadence) typical of radio pulsar surveys, with and without impulsive, narrowband radio frequency interference. The new method is fast; it employs the classic Viterbi algorithm to solve the HMM recursively. The central processing unit run time scales nominally as $T_{\rm run} \approx 2.8 \, N_B (N_T/10^2) (N_Q \ln N_Q/10^4 \ln 10^4) \, {\rm s}$ for $N_B$ subbands, $N_T$ coherent segments, and $N_Q$ frequency bins.