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无线传感网中的多类应用均需要准确的定位算法。为了降低定位成本,减少能量消耗,常采用基于接收信号强度RSS(Received Signal Strength)测距,再利用最大似然ML(Maximum likelihood)估计法求解节点的位置。然而,ML估计为非线性、非凸性,难以获取全局最优解。为此,提出凸半定规划SDP(Semidefinite Programming)的合作式定位方案,利用凸半定规划策略将ML估计转换成凸优问题。同时,该方案考虑两类场景:源节点发射功率已知、未知。针对第一类场景,利用半凸松驰策略,并结合最小化最小二乘法,建立凸优表达式,最后利用CVX求解;针对第二类场景,先建立联合ML估计函数,再利用SDP估计,并结合起来简单的三步骤方案进行位置估计。仿真结果表明,提出的SDP算法的定位精度比SD/SOCP-1、SDPRSS平均提高了近15%至20%。此外,提出的SDP算法在所有场景的误差小于3m的出现概率占0.8,而SD/SOCP-1、SDPRSS算法小于0.5。
Many types of applications in wireless sensor networks require accurate positioning algorithms. In order to reduce the positioning cost and reduce the energy consumption, a method based on the received signal strength (RSS) distance measurement is often used, and the maximum likelihood estimation method is used to solve the position of the node. However, ML is estimated to be non-linear and non-convex, making it difficult to obtain the global optimal solution. To solve this problem, a cooperative positioning scheme of semidefinite programming (SDP) is proposed. The convex semidefinite programming strategy is used to transform the ML estimation into a convex optimization problem. At the same time, the scenario considers two scenarios: the transmit power of the source node is known and unknown. For the first kind of scenario, a convex convex optimal expression is established by using the semi-convex slack strategy combined with the least-squares method and finally solved by CVX. For the second kind of scenario, a joint ML estimation function is established first, and then SDP estimation is used, And combined with a simple three-step program for position estimation. The simulation results show that the proposed positioning accuracy of SDP algorithm is improved by 15% to 20% compared with SD / SOCP-1 and SDPRSS. In addition, the proposed SDP algorithm has a 0.8 probability of occurrence of error less than 3m in all scenarios, while SD / SOCP-1 and SDPRSS algorithms are less than 0.5.