基于凸半定规划的RSS测距的合作式定位方案

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。

Convex semidefinite programming based RSS ranging cooperative localization scheme

In the wireless sensor networks, location based applications require an accurate localization algorithm. To locate sensors at a low cost, the received signal strength (RSS) based ML (Maximum likelihood) estimator is used to localization. However, the difficulties in the ML problem are overcome by transforming the original nonconvex and nonlinear problem into a convex one, which is difficult to solve the globally optimal solution. Therefore, the convex Semidefinite Programming (SDP) localization scheme is proposed in this paper for both cases of known and unknown source transmit power. For the first case, applying semidefinite relaxation address the nonconvex problem, following least squares (LS) minimization, and form the SDP problem, which can be readily solved by CVX. For the second case, propose a simple three-step procedure to Localization. For all the scenarios presented in this work, the new approach outperforms the state-of-the-art approaches with an increase in the accuracy between 15-20% on average. Furthermore, the simulation results show that our approach achieves ME less than 3 m in 80% of the cases, while the existing ones accomplish the same accuracy in less than 50% of the cases.