SIAM Review
Wireless Location in CDMA Cellular Radio Systems
Wireless Location in CDMA Cellular Radio Systems
Semidefinite programming based algorithms for sensor network localization
ACM Transactions on Sensor Networks (TOSN)
A constrained least squares approach to mobile positioning: algorithms and optimality
EURASIP Journal on Applied Signal Processing
Closed-Form Formulae for Time-Difference-of-Arrival Estimation
IEEE Transactions on Signal Processing
Semidefinite programming-based localization algorithm in networks with inhomogeneous media
Proceedings of the 2012 ACM Research in Applied Computation Symposium
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A common technique for passive source localization is to utilize the range-difference (RD) measurements between the source and several spatially separated sensors. The RD information defines a set of hyperbolic equations from which the source position can be calculated with the knowledge of the sensor positions. Under the standard assumption of Gaussian distributed RD measurement errors, it is well known that the maximum-likelihood (ML) position estimation is achieved by minimizing a multimodal cost function which corresponds to a difficult task. In this correspondence, we propose to approximate the nonconvex ML optimization by relaxing it to a convex optimization problem using semidefinite programming. A semidefinite relaxation RD-based positioning algorithm, which makes use of the admissible source position information, is proposed and its estimation performance is contrasted with the two-step weighted least squares method and nonlinear least squares estimator as well as Cramér-Rao lower bound.