Abstract
The time delay of arrival- (TDOA-) based source localization using a wireless sensor network has been considered in this paper. The maximum likelihood estimate (MLE) is formulated by taking the correlated TDOA noise into account, which is caused by the difference with the TOA of the reference sensor. The global optimal solution is difficult to obtain due to the nonconvex nature of the ML function. We propose an alternative semidefinite programming method, which transforms the original ML problem into a convex one by relaxing nonconvex equalities into convex matrix inequalities. In addition, the source localization algorithm in the presence of sensor location errors and non-line-of-sight (NLOS) observations is developed. Our simulation results demonstrate the potential advantages of the proposed method. Furthermore, the proposed source localization algorithm by taking the NLOS TOA measurements as the constraints of the convex problem can provide a good estimate.
Highlights
Source localization using a number of distributed sensors has been extensively studied in the past few years for a wide range of applications such as radar, sonar, and microphone array [1,2,3]
The solution of time delay of arrival- (TDOA-)based maximum likelihood (ML) formulation (9) is included in the simulation, which is solved by the MATLAB routine fmincon
We investigate the problem of time difference of arrival (TDOA)-based source localization in sensor networks
Summary
Source localization using a number of distributed sensors has been extensively studied in the past few years for a wide range of applications such as radar, sonar, and microphone array [1,2,3]. Such an approximation will lead to performance degradation Note that these TOA- and TDOA-based source localization algorithms considered only line-of-sight (LOS) connections between the source and sensors. The discarding of the NLOS information leads to performance degradation which can be avoided by the third method, that is, “identify and employ” based approach Such an approach formulates the source localization problem as an optimization problem by taking the NLOS measurements as a constraint, for example, linear programming [31, 40] and SDP [41, 42], or by jointly considering LOS and NLOS measurements, for example, assigning different weights to LOS and NLOS measurements [43]. Throughout this paper, we shall use the following mathematical notations: (⋅)T denotes the transpose of a matrix or a vector; Tr(⋅) denote the trace of a square matrix; ‖ ⋅ ‖ denotes the Euclidean norm of a vector; Diag(⋅) denotes the diagonal matrix with the given vector on the main diagonal; 0m×n denotes the zero matrix with m rows and n columns; 1m denotes the m × 1 column vector with all entries being 1s; Im denotes the m × m identity matrix; A ⪰ B means A − B is positive semidefinite
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