Estimating and detecting random processes on the unit circle

The problem of detecting a sinusoidal signal with randomly varying frequency has a long history. It is one of the core problems in signal processing, arising in many applications including, for example, underwater acoustic frequency line tracking, demodulation of FM radio communications, laser phase drift in optical communications and, recently, continuous gravitational wave astronomy. In this paper we describe a Markov Chain Monte Carlo based procedure to compute a specific detection posterior density. We demonstrate via simulation that our approach results in an up to $25$ percent higher detection rate than Hidden Markov Model based solutions, which are generally considered to be the leading techniques for these problems.