Global Continuation for Distance Geometry Problems
SIAM Journal on Optimization
Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks
ATEC '02 Proceedings of the General Track of the annual conference on USENIX Annual Technical Conference
Geographic routing without location information
Proceedings of the 9th annual international conference on Mobile computing and networking
Semidefinite programming for ad hoc wireless sensor network localization
Proceedings of the 3rd international symposium on Information processing in sensor networks
Robust distributed node localization with error management
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
Semidefinite programming based algorithms for sensor network localization
ACM Transactions on Sensor Networks (TOSN)
Theory of semidefinite programming for Sensor Network Localization
Mathematical Programming: Series A and B
Second-Order Cone Programming Relaxation of Sensor Network Localization
SIAM Journal on Optimization
SpaseLoc: An Adaptive Subproblem Algorithm for Scalable Wireless Sensor Network Localization
SIAM Journal on Optimization
Further Relaxations of the Semidefinite Programming Approach to Sensor Network Localization
SIAM Journal on Optimization
Sum of squares method for sensor network localization
Computational Optimization and Applications
Exploiting Sparsity in SDP Relaxation for Sensor Network Localization
SIAM Journal on Optimization
Explicit Sensor Network Localization using Semidefinite Representations and Facial Reductions
SIAM Journal on Optimization
(Robust) Edge-based semidefinite programming relaxation of sensor network localization
Mathematical Programming: Series A and B
Particle filters for positioning, navigation, and tracking
IEEE Transactions on Signal Processing
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In this paper, we strengthen the edge-based semidefinite programming relaxation (ESDP) recently proposed by Wang, Zheng, Boyd, and Ye (SIAM J. Optim. 19:655---673, 2008) by adding lower bound constraints. We show that, when distances are exact, zero individual trace is necessary and sufficient for a sensor to be correctly positioned by an interior solution. To extend this characterization of accurately positioned sensors to the noisy case, we propose a noise-aware version of ESDPlb (驴-ESDPlb) and show that, for small noise, a small individual trace is equivalent to the sensor being accurately positioned by a certain analytic center solution. We then propose a postprocessing heuristic based on 驴-ESDPlb and a distributed algorithm to solve it. Our computational results show that, when applied to a solution obtained by solving 驴-ESDP proposed of Pong and Tseng (Math. Program. doi: 10.1007/s10107-009-0338-x ), this heuristics usually improves the RMSD by at least 10%. Furthermore, it provides a certificate for identifying accurately positioned sensors in the refined solution, which is not common for existing refinement heuristics.