Performance optimization for continuous network localization

Recent advances in linear localization of sensor networks allow sensors to localize themselves by using inter-sensor measurements, such as distances, bearings and interior angles. According to earlier works, linear localization algorithms’ performance is relatively poor, which, however, has not been adequately addressed in the existing literature. The aim of this paper is to improve the performance of linear and continuous localization algorithms. More specifically, we focus on improving three key aspects of linear localization algorithms’ performance, i.e., the stability margin, convergence rate and robustness against measurement noises. Firstly, we propose a unified description for networks’ linear localization algorithms, given different types of measurements, and show that the stability margin, convergence rate and robustness of linear localization algorithms are commonly determined by one parameter, namely, the minimum eigenvalue of the network's localization matrix. Secondly, by carefully choosing the decision variable, we formulate the performance optimization problem as an eigenvalue optimization problem, and show the non-differentiability of the eigenvalue optimization problem. Thirdly, we propose a distributed optimization algorithm, which guarantees the convergence to an optimal solution of the eigenvalue optimization problem. Finally, simulation examples validate the effectiveness of the proposed distributed optimization algorithm.