Research On Trust Region-Based Localization Algorithms For Wireless Sensor Networks

Since wireless sensor networks(WSNs) can provide accurate positions of sensor nodes, WSNs are widely applied to different areas. And localization algorithm is one of the research spots in the localization filed. Due to the limit of ranging techniques and the effect of environment, the ranges between anchor nodes and unknown nodes are always erroneous. As a result, the range-based algorithms are difficult to acquire exact positions of unknown nodes. Up to now, according to the ranging technique and environment, many researchers have proposed various techniques to obtain accurate positions in different situations.This thesis aims at solving the problem that the localization error of distributed range-based algorithms is large. To break up the whole into parts, this thesis increases the localization accuracy of the single unknown node, and then reduces the localization error of the entire network. Most researches transform localization problems into optimization ones, the optimal solutions of which can be considered as the unknown nodes' positions. As with the source localization problem which has only one single unknown node, the squared-range-based least squares(SRLS) problem has been solved well and its global solution can be obtained. On the contrary, due to the non-convexity and non-smoothness of the range-based least squares(RLS) function, how to solve the problem efficiently is still an open question. Unlike most of the researches transforming the RLS function into convex forms, the global optimal solution of which can be acquired, this thesis addresses the problem considering the non-smoothness property of the objective function and obtains the local optimal solution. This thesis transforms the original function into a smooth one by introducing a parameter, and proposes a trust region-based DTR algorithm to obtain the more accurate positions of the unknown nodes. Simulation results demonstrate that the proposed approach reduces the required iterations significantly and improves the accuracy simultaneously.As with the localization of sensor networks, this thesis considers the atomic multilateration as source localization problems, and then proposes a DTR-based algorithm for WSNs. This thesis analyzes the performance of the modified algorithm from two aspects, the average results of many simulation runs and the result of a single run. And simulation results demonstrate that the modified algorithm performs better than the original algorithm and the semi-definite relaxation based algorithm in terms of accuracy. This thesis also discusses the effect of two factors on localization errors: the introduced parameter and the change of the graph's structure formed by anchors and unknown nodes resulting from ranging errors.This thesis solves the non-convex and non-smooth localization problem from the perspective of local optimization. Although the obtained solution is local optimal, the positions of unknown nodes are more accurate.