Bayesian phase tracking for multiple pulse signals

The problem of estimating the frequencies and phases of two superimposed pulse-like, repetitive signals is considered. A method of solving this problem based on Bayesian (i.e., sequential Monte-Carlo or particle) filtering is presented. The particular problem motivating the technique is estimation of the rate of maternal and foetal heartbeats, although the technique is applicable to other domains. Aspects of the problem leading to the solution are discussed, and the performance of the proposed technique is presented on both simulated signals and real heart signals. The resulting frequency estimator has very similar functionality to a phase-locked loop, and so the performance measure used is the time to lose phase lock. The estimator is also analysed in terms of the posterior Cramér–Rao bound on the phase estimation accuracy.