Research On Trust Region Based Asynchronous Source Localization Algorithm

The problem of source localization in wireless sensor networks is a research hotspot in the field of communications.Source localization problems are mainly divided into range-based least squares(RLS)problems and squared-range-based least squares(SRLS)problems.The objective function of the SRLS problem is smooth,and the generalized trust region subproblems(GTRS)algorithm can obtain its global optimal solution,but the computational complexity is high.The objective function of the RLS problem is non-convex and non-smooth.The exact solution to this problem is still an open problem.The existing localization algorithms are mainly based on the convex optimization methods,first convert the original objective function into a convex function,and then obtain the global optimal solution of the convex function.However,these localization algorithms have high computational complexity and are difficult to meet the needs of practical applications.In this paper,since the existing localization algorithms have high computational complexity,the trust region algorithm is applied to the source localization problem.Based on the smoothness of the SRLS problem,the optimal solution is obtained by using the trust region algorithm,and the convergence analysis of the trust region algorithm in the source localization problem is done.The simulation results show that the computational complexity of trust region algorithm for solving SRLS problem is significantly lower than that of GTRS algorithm.The asynchronous source localization problem is essentially an RLS problem and there is a clock skew between the anchor nodes and the unknown node.In this paper,the least squares algorithm is used to obtain the estimated value of the clock bias,and the original objective function is smoothed.Then the trust region algorithm is used to solve the problem.Finally,the Cramer-Rao lower bound of the trust region algorithm in this problem is derived.The initial point is the least squares estimate.The simulation results show that the computational complexity of trust region algorithm for solving the asynchronous source localization problem is significantly lower than that of the existing localization algorithms.This paper applies the trust region algorithm to the RLS and SRLS problems,demonstrates the feasibility of applying the trust region algorithm to the source localization problem,and the trust region algorithm can greatly reduce the computational complexity while ensuring the localization accuracy.