Received Signal Strength-Based Wireless Localization via Semidefinite Programming

Wireless localization has drawn significant attention over the past decade and the received signal strength (RSS) based localization scheme provides a low-cost, low-complexity and easy-implementation solution. When the statistics of the RSS measurement error is known, the Maximum Likelihood (ML) estimator is asymptotically optimal. However, due to the nature of the localization problem itself, the formed ML estimator is nonconvex, causing the search for the global minimum very difficult. In addition, its performance highly depends on the initial point provided if a local optimization method is applied to find the solution. To circumvent this problem, we apply the Semidefinite Programming (SDP) relaxation technique to the RSS-based localization problem. After reformulation and relaxation, we finally form a convex SDP estimator. A superior property of a convex estimator is that the solution is not affected by the initial point provided since any local minimum is also its global minimum. The Cramer-Rao Lower Bound (CRLB) is then derived as a benchmark for the performance comparison. Simulation results show that the proposed SDP estimator exhibit excellent performance in the RSS-based localization system and it is very suitable for the case when there are only very limited base stations hearable.