Performance Optimization of Angle-Based Network Localization

Recent advances in sensor network localization have enabled sensor nodes to localize themselves by using the measurements of inter-node angles. According to our earlier work, the proposed angle-based localization algorithms' performance, particularly, the convergence rate, is relatively poor, which, however, has not been adequately addressed in the existing literature. Motivated by this, this paper aims to improve the performance of angle-based localization algorithms, specifically, the stability margin, convergence rate and robustness against measurement noises. Firstly, we show that the stability margin, convergence rate and robustness of angle-based localization algorithms are commonly determined by one parameter, namely, the minimum eigenvalue of the network's localization matrix. Secondly, we formulate the performance optimization problem as an eigenvalue optimization problem, and show the non-differentiability of the eigenvalue optimization problem. By carefully choosing the decision variable, we utilize interior-point methods to obtain an optimal solution to the eigenvalue optimization problem. Finally, simulation examples validate the improvement of the algorithms' performance.