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 \BBR2. 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.

[1]  Kevin Murphy,et al.  Switching Kalman Filters , 1998 .

[2]  Sharon Gannot,et al.  Microphone Array Speaker Localizers Using Spatial-Temporal Information , 2006, EURASIP J. Adv. Signal Process..

[3]  C. J. Harris,et al.  Comparison of two measurement fusion methods for Kalman-filter-based multisensor data fusion , 2001 .

[4]  Jingdong Chen,et al.  Microphone Array Signal Processing , 2008 .

[5]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[6]  S. R. Jammalamadaka,et al.  Directional Statistics, I , 2011 .

[7]  Otmar Loffeld,et al.  Phase Unwrapping using 2D-Kalman Filter - Potential and Limitations , 2008, IGARSS 2008 - 2008 IEEE International Geoscience and Remote Sensing Symposium.

[8]  Johannes Traa.  Multichannel source separation and tracking with phase differences by random sample consensus , 2013 .

[9]  J. L. Roux.  An Introduction to the Kalman Filter , 2003 .

[10]  Nando de Freitas,et al.  Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks , 2000, UAI.

[11]  Yiming Pi,et al.  Phase noise filtering and phase unwrapping method based on unscented Kalman filter , 2011 .

[12]  Krishnaraj M. Varma,et al.  Time-Delay-Estimate Based Direction-of-Arrival Estimation for Speech in Reverberant Environments , 2002 .

[13]  P. Smaragdis,et al.  Learning source trajectories using wrapped-phase hidden Markov models , 2005, IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 2005..