Polynomial-time approximation algorithms for anchor-free TDoA localization

We consider the problem of anchor-free self-calibration of receiver locations using only the reception time of signals produced at unknown locations and time points. In our settings the receivers are synchronized, so the time differences of arrival (TDoA) of the signals arriving at the receivers can...

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Vydáno v:Theoretical computer science Ročník 553; s. 27 - 36
Hlavní autoři: Wendeberg, Johannes, Schindelhauer, Christian
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 09.10.2014
Témata:
Algorithms
Approximation
FPTAS
Localization
Mathematical analysis
Position (location)
Position measurement
Receivers
Run time (computers)
Tasks
TDoA
Approximation
FPTAS
Localization
TDoA
ISSN:0304-3975, 1879-2294
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Shrnutí:We consider the problem of anchor-free self-calibration of receiver locations using only the reception time of signals produced at unknown locations and time points. In our settings the receivers are synchronized, so the time differences of arrival (TDoA) of the signals arriving at the receivers can be calculated. Given the set of distinguishable time points for all receivers the task is to determine the positions of the receivers as well as the signal sources. We present the first polynomial-time approximation algorithms for the minimum problem in the plane, in which the number of receivers is four, respectively the number of signals is three. For this, we first consider the problem that the time points of m signals are jittered by at most some ϵ>0. We provide an algorithm which tests whether n given receiver positions are valid for measurements from m unknown senders with a run-time of O(n2m), and we provide an algorithm with run-time O(nmlog⁡m) which tests the validity of m given sender positions for n unknown receiver positions. Using these tests, we can compute all possible receiver and signal source positions in time O((2/ϵ)2n−3n2m), respectively O((2/ϵ)2m−3nmlog⁡m).
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2014.04.007