Study Of The Nodes Localization Algorithms Based On Convex Optimization In WSNs

RSS based and AOA based localization methods are often used in the wireless sensor networks(WSNs).However,due to the non-linearity and non-convexity of the objective function,these two localization methods may converge on local optimum when applied to WSNs localization.To overcome this problem,a semidefinite programming(SDP)based localization algorithm is proposed based on the characteristics of these two node localization problems,and this algorithm is meaningful for research.The main research of this paper is as follows:Firstly,many WSNs node localization algorithms based on RSS measurement are analyzed in this paper,such as Maximum Likelihood Estimator(MLE),Second Order Cone Programming(SOCP),Semidefinite Programming(SDP)and so on.Meanwhile,the drawbacks of the existing methods are also pointed out.And then,an improved SDP based localization approach is proposed through combining the convex optimization theory with the existing localization methods.Simulation results demonstrate that the proposed algorithm can locate the objective node when the number of the sensors is small,has higher positioning accuracy and is more robust than existing algorithms.In addition,our algorithm has better localization performance no matter where the objective node is.Secondly,to overcome the problems of the high non-linearity and non-convexity of the arctangent function in the AOA based WSNs localization,we introduce the Taylor series approximation to linearize the arctangent function.Based on the linearization,Min-Max theory and semidefinite relaxation(SDR)technique are applied to transform original problem into SDP convex optimization problem.Through the comparison of simulation results,the proposed algorithm is demonstrated to have better localization performance to some extent.