A Gradient Search Method to Round the Semideflnite Programming Relaxation Solution for Ad Hoc Wireless Sensor Network Localization

In this report we develop an e‐cient and efiective procedure to solve the distance geometry problem. This method is based on the semideflnite programming (SDP) relaxation proposed in [5, 6], and further improved by a gradient-based local search method. We flrst develop two alternative SDP relaxations for the distance geometry problem, which represent the (weighted) maximum-likelihood estimation (WMLE). Then, using the SDP relaxation solution as the initial point, we apply a gradient-based search method to further reducing the estimation error. We show that the gradient search method permits an exact line-search and it can always improve the SDP solution with or without distance measurement noises. A checkable bound of suboptimality can be used to ensure the solution quality. We demonstrate the efiectiveness of the method from solving the 2-dimensional ad hoc wireless sensor network localization problem. Even for large scale problems with thousands of sensors, a satisfactory localization can be found on a single PC in few minutes.

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