Abstract
We investigate the problem of sensor and source joint localization using time-difference of arrivals (TDOAs) of an ad-hoc array. A major challenge is that the TDOAs contain unknown time offsets between asynchronous sensors. To address this problem, we propose a low-rank approximation method that does not need any prior knowledge of sensor and source locations or timing information. At first, we construct a pseudo time of arrival (TOA) matrix by introducing two sets of unknown timing parameters (source onset times and device capture times) into the current TDOA matrix. Then we propose a Gauss-Newton low-rank approximation algorithm to jointly identify the two sets of unknown timing parameters, exploiting the low-rank property embedded in the pseudo TOA matrix. We derive the boundaries of the timing parameters to reduce the initialization space and employ a multi-initialization scheme. Finally, we use the estimated timing parameters to correct the pseudo TOA matrix, which is further applied to sensor and source localization. Experimental results show that the proposed approach outperforms state-of-the-art algorithms.
Highlights
A D-HOC sensor networks composed of randomly distributed and independent recording devices, such as smartphones, wireless microphones, and laptops, have been attracting increased interest due to their flexibility in sensor placement [1], [2]
In this paper we present a method that jointly estimates the sensor and source locations from the biased time-difference of arrivals (TDOAs) measurements
Since we only have the TDOA matrix available, one possible solution is to convert to a matrix containing the desired low-rank structure
Summary
A D-HOC sensor networks composed of randomly distributed and independent recording devices, such as smartphones, wireless microphones, and laptops, have been attracting increased interest due to their flexibility in sensor placement [1], [2]. The low-rank structure embedded in the TOA measurements can be exploited to estimate the unknown onset times and capture times [16]–[18] These approaches typically involve a gradient-based optimization procedure, which is sensitive to local minima. When estimating the timing information, the existing low-rank approximation techniques are not applicable to TDOA because the latter does not contain the desired low-rank structure as TOA does To address this challenge, we construct a pseudo TOA matrix by introducing two sets of unknown timing parameters (source onset times and device capture times) into the current TDOA matrix. We construct a pseudo TOA matrix by introducing two sets of unknown timing parameters (source onset times and device capture times) into the current TDOA matrix To estimate these two parameters from the pseudo TOA, we propose a Gauss-Newton low-rank approximation algorithm.
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