Euclidean distance matrices, semidefinite programming and sensor network localization

Euclidean Distance Matrices, Semidefinite Programming, and Sensor Network Localization

The fundamental problem of distance geometry, F P DG , involves the characterization and study of sets of points based only on given values of (some of) the distances between pairs of points. This problem has a wide range of applications in various areas of mathematics, physics, chemistry, and engineering. Euclidean Distance Matrices, EDM , play an important role in F P DG . They use the square...

Semidefinite Programming and the Sensor Network Localization Problem, SNLP

Research on ad hoc wireless sensor networks has increased greatly in recent years [24]. Sensor networks usually consist of a large number of sensors which are deployed to collect data of interest. Such networks are versatile tools which provide a low-cost method of target tracking, as well as monitoring seismic activity, temperature, sound levels, and light [7]. Information gathered by the sens...

Coordinate Shadows of Semidefinite and Euclidean Distance Matrices

We consider the projected semi-definite and Euclidean distance cones onto a subset of the matrix entries. These two sets are precisely the input data defining feasible semi-definite and Euclidean distance completion problems. We classify when these sets are closed, and use the boundary structure of these two sets to elucidate the Krislock-Wolkowicz facial reduction algorithm. In particular, we ...

Robust Semidefinite Programming Approaches for Sensor Network Localization with Anchors

(Robust) Edge-based semidefinite programming relaxation of sensor network localization

Recently Wang, Zheng, Boyd, and Ye [36] proposed a further relaxation of the semidefinite programming (SDP) relaxation of the sensor network localization problem, named edge-based SDP (ESDP). In simulation, the ESDP is solved much faster by interior-point method than SDP relaxation, and the solutions found are comparable or better in approximation accuracy. We study some key properties of the E...