Learning Source Trajectories Using Wrapped-Phase Hidden Markov Models

In this paper we examine the problem of identifying trajectories of sound sources as captured from microphone arrays. Instead of employing traditional localization techniques we attach this problem with a statistical modeling approach of phase measurements. As in many signal processing applications that require the use of phase there is the issue of phase-wrapping. Even though there exists a significant amount of work on unwrapping wrapped phase estimates, when it comes to stochastic modeling this can introduce an additional level of undesirable complication. We address this issue by defining an appropriate statistical model to fit wrapped phase data, and employ it as a state model of an HMM in order to recognize sound trajectories. Using both synthetic and real data we highlight the accuracy of this model as opposed to generic HMM modeling.