Johannes Traa

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.

Multichannel source separation and tracking with RANSAC and directional statistics

We describe multichannel blind source separation and tracking algorithms based on clustering wrapped interchannel phase difference (IPD) features. We pose the clustering problem as one of multimodal circular-linear regression and present its probabilistic formulation. Phase wrapping due to spatial aliasing is explicitly incorporated by modeling the IPD features as circular variables. We present two methods based on Expectation-Maximization (EM) and a sequential variant of RANdom SAmple Consensus (RANSAC). We show that their strengths can be combined by using RANSAC to initialize EM. The IPD clustering algorithm is applied to separate stationary speakers from a multichannel mixture. We then extend it to the case of moving speakers by tracking their directions-of-arrival with the Factorial Wrapped Kalman Filter (FWKF) using RANSAC as a data preprocessor. Experimental results demonstrate that the proposed methods perform well in the presence of reverberant babble noise and spatial aliasing. The FWKF successfully tracks and separates moving speakers with separation quality comparable to that for stationary speakers.

Blind multi-channel source separation by circular-linear statistical modeling of phase differences

We address the problem of blind separation of speech signals with a microphone array. We demonstrate that a signal propagating towards the array at an angle corresponds to interchannel phase difference (IPD) data that lies on a wrapped line (i.e helix) in a circular-linear domain. Thus, the problem reduces to that of fitting helices to data that lies on a cylinder. However, outliers abound because of reverberation, noise, and signal overlap in the time-frequency domain, so we perform the clustering with a sequential variant of Random Sample Consensus (RANSAC). We show that this method can easily be applied to arrays with many microphones and that it is robust in reverberant experimental conditions.

MULTIPLE SPEAKER TRACKING WITH THE FACTORIAL VON MISES-FISHER FILTER

Multiple-target tracking with a microphone array is often addressed via the Bayesian filtering framework. For compact arrays, each source is represented by its direction-of-arrival (DOA), which evolves on the unit sphere. The unique topology of this space leads to analytical intractabilities that are often resolved via costly particle-based methods. In this paper, we derive a novel, deterministic inference algorithm called the von Mises-Fisher Filter (vMFF) for a dynamical system model defined on the sphere, and extend it to the multi-source scenario in the Factorial vMFF (FvMFF). We apply sensor fusion and probabilistic data association techniques to handle clutter and data association ambiguities in the observation set. We show that the vMFF combines the computational efficiency of a Kalman filter with the tracking accuracy of a particle filter to perform well across all noise levels. Finally, we apply the FvMFF to track multiple speakers in a reverberant environment.

Phase and level difference fusion for robust multichannel source separation

Inter-channel phase (IPD) and level (ILD) differences are common features in multichannel source separation algorithms like DUET and MENUET. However, their utility depends strongly on the configuration of the array and what microphone pairs are used to calculate them. IPDs are most useful when extracted from microphones that are close together as this avoids spatial aliasing. In contrast, ILD clusters are only well separated for widely spaced microphones. We investigate this trade-off between IPD and ILD features and propose a method to best combine them for multichannel source separation. Experimental results demonstrate the utility of this approach.

Robust interchannel phase difference modeling with wrapped regression splines

Inter-channel phase differences (IPD) are commonly used as features in microphone array-based source separation and localization algorithms. However, under real-world conditions, we may observe significant deviations from the assumed anechoic, linear model. Non-linearities arise from spatial aliasing, reverberation, and poor array calibration. In this work, we view the features as comprising a circular-linear dataset and model them with a wrapped regression spline. Experimental results demonstrate that this approach leads to more robust speech denoising than a linear model.

Method of moments learning for left-to-right Hidden Markov models

We propose a method-of-moments algorithm for parameter learning in Left-to-Right Hidden Markov Models. Compared to the conventional Expectation Maximization approach, the proposed algorithm is computationally more efficient, and hence more appropriate for large datasets. It is also asymptotically guaranteed to estimate the correct parameters. We show the validity of our approach with a synthetic data experiment and a word utterance onset detection experiment.