A Wrapped Kalman Filter for Azimuthal Speaker Tracking

We present the wrapped Kalman filter (WKF) for tracking the azimuth of a speaker with a compact, 3-channel microphone array. Traditional extended and unscented filters assume that the observation is a rotating vector in ${\BBR^2}$. However, the azimuth inhabits a 1-D subspace: the unit circle. We model the state variable with a wrapped Gaussian distribution and show that this achieves a lower mean squared error than 2-D methods. We demonstrate the superior tracking performance of the WKF in simulated and real reverberant environments.