4,179 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
Quantum Time and Spatial Localization: An Analysis of the Hegerfeldt Paradox
Two related problems in relativistic quantum mechanics, the apparent
superluminal propagation of initially localized particles and dependence of
spatial localization on the motion of the observer, are analyzed in the context
of Dirac's theory of constraints. A parametrization invariant formulation is
obtained by introducing time and energy operators for the relativistic particle
and then treating the Klein-Gordon equation as a constraint. The standard,
physical Hilbert space is recovered, via integration over proper time, from an
augmented Hilbert space wherein time and energy are dynamical variables. It is
shown that the Newton-Wigner position operator, being in this description a
constant of motion, acts on states in the augmented space. States with strictly
positive energy are non-local in time; consequently, position measurements
receive contributions from states representing the particle's position at many
times. Apparent superluminal propagation is explained by noting that, as the
particle is potentially in the past (or future) of the assumed initial place
and time of localization, it has time to propagate to distant regions without
exceeding the speed of light. An inequality is proven showing the Hegerfeldt
paradox to be completely accounted for by the hypotheses of subluminal
propagation from a set of initial space-time points determined by the quantum
time distribution arising from the positivity of the system's energy. Spatial
localization can nevertheless occur through quantum interference between states
representing the particle at different times. The non-locality of the same
system to a moving observer is due to Lorentz rotation of spatial axes out of
the interference minimum.Comment: This paper is identical to the version appearing in J. Math. Phys.
41; 6093 (Sept. 2000). The published version will be found at
http://ojps.aip.org/jmp/. The paper (40 page PDF file) has been completely
revised since the last posting to this archiv
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