9,170 research outputs found
A Geometric Approach to Sound Source Localization from Time-Delay Estimates
This paper addresses the problem of sound-source localization from time-delay
estimates using arbitrarily-shaped non-coplanar microphone arrays. A novel
geometric formulation is proposed, together with a thorough algebraic analysis
and a global optimization solver. The proposed model is thoroughly described
and evaluated. The geometric analysis, stemming from the direct acoustic
propagation model, leads to necessary and sufficient conditions for a set of
time delays to correspond to a unique position in the source space. Such sets
of time delays are referred to as feasible sets. We formally prove that every
feasible set corresponds to exactly one position in the source space, whose
value can be recovered using a closed-form localization mapping. Therefore we
seek for the optimal feasible set of time delays given, as input, the received
microphone signals. This time delay estimation problem is naturally cast into a
programming task, constrained by the feasibility conditions derived from the
geometric analysis. A global branch-and-bound optimization technique is
proposed to solve the problem at hand, hence estimating the best set of
feasible time delays and, subsequently, localizing the sound source. Extensive
experiments with both simulated and real data are reported; we compare our
methodology to four state-of-the-art techniques. This comparison clearly shows
that the proposed method combined with the branch-and-bound algorithm
outperforms existing methods. These in-depth geometric understanding, practical
algorithms, and encouraging results, open several opportunities for future
work.Comment: 13 pages, 2 figures, 3 table, journa
Source localization and denoising: a perspective from the TDOA space
In this manuscript, we formulate the problem of denoising Time Differences of
Arrival (TDOAs) in the TDOA space, i.e. the Euclidean space spanned by TDOA
measurements. The method consists of pre-processing the TDOAs with the purpose
of reducing the measurement noise. The complete set of TDOAs (i.e., TDOAs
computed at all microphone pairs) is known to form a redundant set, which lies
on a linear subspace in the TDOA space. Noise, however, prevents TDOAs from
lying exactly on this subspace. We therefore show that TDOA denoising can be
seen as a projection operation that suppresses the component of the noise that
is orthogonal to that linear subspace. We then generalize the projection
operator also to the cases where the set of TDOAs is incomplete. We
analytically show that this operator improves the localization accuracy, and we
further confirm that via simulation.Comment: 25 pages, 9 figure
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