Kalman Filters for Time Delay of Arrival-Based Source Localization

EURASIP Journal on Advances in Signal Processing, Mar 2006

In this work, we propose an algorithm for acoustic source localization based on time delay of arrival (TDOA) estimation. In earlier work by other authors, an initial closed-form approximation was first used to estimate the true position of the speaker followed by a Kalman filtering stage to smooth the time series of estimates. In the proposed algorithm, this closed-form approximation is eliminated by employing a Kalman filter to directly update the speaker's position estimate based on the observed TDOAs. In particular, the TDOAs comprise the observation associated with an extended Kalman filter whose state corresponds to the speaker's position. We tested our algorithm on a data set consisting of seminars held by actual speakers. Our experiments revealed that the proposed algorithm provides source localization accuracy superior to the standard spherical and linear intersection techniques. Moreover, the proposed algorithm, although relying on an iterative optimization scheme, proved efficient enough for real-time operation.

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Kalman Filters for Time Delay of Arrival-Based Source Localization

Hindawi Publishing Corporation EURASIP Journal on Applied Signal Processing Volume 2006 Kalman Filters for Time Delay of Arrival-Based Source Localization Ulrich Klee 0 Tobias Gehrig 0 John McDonough 0 0 Institut fu ̈r Theoretische Informatik, Universita ̈t Karlsruhe , Am Fasanengarten 5, 76131 Karlsruhe , Germany In this work, we propose an algorithm for acoustic source localization based on time delay of arrival (TDOA) estimation. In earlier work by other authors, an initial closed-form approximation was first used to estimate the true position of the speaker followed by a Kalman filtering stage to smooth the time series of estimates. In the proposed algorithm, this closed-form approximation is eliminated by employing a Kalman filter to directly update the speaker's position estimate based on the observed TDOAs. In particular, the TDOAs comprise the observation associated with an extended Kalman filter whose state corresponds to the speaker's position. We tested our algorithm on a data set consisting of seminars held by actual speakers. Our experiments revealed that the proposed algorithm provides source localization accuracy superior to the standard spherical and linear intersection techniques. Moreover, the proposed algorithm, although relying on an iterative optimization scheme, proved efficient enough for real-time operation. 1. INTRODUCTION Most practical acoustic source localization schemes are based on time delay of arrival estimation (TDOA) for the following reasons: such systems are conceptually simple. They are reasonably effective in moderately reverberant environments. Moreover, their low computational complexity makes them well-suited to real-time implementation with several sensors. Time delay of arrival-based source localization is based on a two-step procedure. ( 1 ) The TDOA between all pairs of microphones is estimated, typically by finding the peak in a cross-correlation or generalized cross-correlation function [1]. ( 2 ) For a given source location, the squared error is calculated between the estimated TDOAs and those determined from the source location. The estimated source location then corresponds to that position which minimizes this squared error. If the TDOA estimates are assumed to have a Gaussiandistributed error term, it can be shown that the least-squares metric used in Step ( 2 ) provides the maximum likelihood (ML) estimate of the speaker location [2]. Unfortunately, this least-squares criterion results in a nonlinear optimization problem that can have several local minima. Several authors have proposed solving this optimization problem with standard gradient-based iterative techniques. While such techniques typically yield accurate location estimates, they are typically computationally intensive and thus ill-suited for real-time implementation [3, 4]. For any pair of microphones, the surface on which the TDOA is constant is a hyperboloid of two sheets. A second class of algorithms seeks to exploit this fact by grouping all microphones into pairs, estimating the TDOA of each pair, then finding the point where all associated hyperboloids most nearly intersect. Several closed-form position estimates based on this approach have appeared in the literature; see Chan and Ho [5] and the literature review found there. Unfortunately, the point of intersection of two hyperboloids can change significantly based on a slight change in the eccentricity of one of the hyperboloids. Hence, a third class of algorithms was developed wherein the position estimate is obtained from the intersection of several spheres. The first algorithm in this class was proposed by Schau and Robinson [6], and later came to be known as spherical intersection. Perhaps the best-known algorithm from this class is the spherical interpolation method of Smith and Abel [7]. Both methods provide closed-form estimates suitable for real-time implementation. Brandstein et al. [4] proposed yet another closed-form approximation known as linear intersection. Their algorithm proceeds by first calculating a bearing line to the source for each pair of sensors. Thereafter, the point of nearest approach is calculated for each pair of bearing lines, yielding a potential source location. The final position estimate is obtained from a weighted average of these potential source locations. In the algorithm proposed here, the closed-form approximation used in prior approaches is eliminated by employing an extended Kalman filter to directly update the speaker’s position estimate based on the observed TDOAs. In particular, the TDOAs comprise the observation associated with an extended Kalman filter whose state corresponds to the speaker’s position. Hence, the new position estimate comes directly from the update formulae of the Kalman filter. It is worth noting that similar approaches have been proposed by Dvorkind and Gannot [8] for an acoustic source localizer, as well as by Duraiswami et al. [9] for a combined audio-vi (...truncated)


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Ulrich Klee, Tobias Gehrig, John McDonough. Kalman Filters for Time Delay of Arrival-Based Source Localization, EURASIP Journal on Advances in Signal Processing, 2006, pp. 012378, Volume 2006, Issue 1, DOI: 10.1155/ASP/2006/12378