SOAP: A generalised application of the Viterbi algorithm to searches for continuous gravitational-wave signals

All-sky and wide parameter space searches for continuous gravitational waves are generally template-matching schemes which test a bank of signal waveforms against data from a gravitational wave detector. Such searches can offer optimal sensitivity for a given computing cost and signal model, but are highly-tuned to specific signal types and are computationally expensive, even for semi-coherent searches. We have developed a search method based on the well-known Viterbi algorithm which is model-agnostic and has a computational cost several orders of magnitude lower than template methods, with a modest reduction in sensitivity. In particular, this method can search for signals which have an unknown frequency evolution. We test the algorithm on three simulated and real data sets: gapless Gaussian noise, Gaussian noise with gaps and real data from the final run of initial LIGO (S6). We show that at 95% efficiency, with a 1% false alarm rate, the algorithm has a depth sensitivity of $\sim 33$, $10$ and $13$ ,Hz$^{-1/2}$ with corresponding SNRs of $\sim 60$, $72$ and $74$ in these datasets. we discuss the use of this algorithm for detecting a wide range of quasi-monochromatic gravitational wave signals and instrumental lines.