Research On Proximal Alternating Minimization Localization Algorithm For Asynchronous Source Localization

Location-based services are closely related to the daily life of human beings,but the problem of asynchronous is prevalent in all kinds of positioning systems.The current ranging technology cannot directly measure the exact distance between the receiver and the transmitter,instead,it only gets the noisy measurement value with environmental noise and other factors.Moreover,in practical engineering applications,the receiver and transmitter are often in an asynchronous state,and there is an initial clock offset between their local time.Because the traditional positioning algorithm does not consider the existence of clock offset,the estimated position error of the unknown node is large.Many experts and scholars have proposed the corresponding positioning algorithm for the asynchronous TOA-based source localization problem to obtain the more accurate coordinate position of the unknown node.At present,there are mainly two types of asynchronous source localization models.Most of the research work is to relax or approximate the asynchronous source localization problem which is difficult to be directly optimized,and to obtain the estimated position of unknown nodes by solving the processed objective function,which results in the loss of location performance.In this paper,the single signal of opportunity localization scheme is constructed as an asynchronous TOA-based source localization problem.This objective function contains two unknown variables and is highly non-convex and non-smooth.In order to obtain higher localization performance,the proximal alternating minimization positioning method is proposed to directly optimize the original objective function.This method utilizes the biconvex property of original asynchronous problem to decompose it into two subproblems: the clock offset subproblem and the synchronous source localization subproblem.The global optimal solution is derived for the clock offset subproblem and an efficient sub-gradient algorithm is proposed to quickly optimize the synchronous source localization subproblem.Based on the Fisher Information Matrix,the Cramér-Rao Lower Bound of the asynchronous TOA-based source localization model is derived,and it is theoretically proved that the proximal alternating minimization positioning method can guarantee the convergence to the Lyapunov stable point.The advantages and disadvantages of the existing asynchronous TOA-based source localization convex optimization algorithms are analyzed theoretically.The simulation results demonstrate that not only the performance of proximal alternating minimization positioning method is much better than the existing localization algorithm,but also the computational complexity is greatly reduced.