Chen Yuanpeng, Yao Zhiqiang, Peng Zheng
Intelligent Navigation and Remote Sensing Research Center, Xiangtan University, Xiangtan 411105, China.
Changsha Technology Research Institute of Beidou Industry Safety, Changsha 410006, China.
Sensors (Basel). 2020 Jun 19;20(12):3466. doi: 10.3390/s20123466.
In time-of-arrival (TOA)-based source localization, accurate positioning can be achieved only when the correct signal propagation time between the source and the sensors is obtained. In practice, a clock error usually exists between the nodes causing the source and sensors to often be in an asynchronous state. This leads to the asynchronous source localization problem which is then formulated to a least square problem with nonconvex and nonsmooth objective function. The state-of-the-art algorithms need to relax the original problem to convex programming, such as semidefinite programming (SDP), which results in performance loss. In this paper, unlike the existing approaches, we propose a proximal alternating minimization positioning (PAMP) method, which minimizes the original function without relaxation. Utilizing the biconvex property of original asynchronous problem, the method divides it into two subproblems: the clock offset subproblem and the synchronous source localization subproblem. For the former we derive a global solution, whereas the later is solved by a proposed efficient subgradient algorithm extended from the simulated annealing-based Barzilai-Borwein algorithm. The proposed method obtains preferable localization performance with lower computational complexity. The convergence of our method in Lyapunov framework is also established. Simulation results demonstrate that the performance of PAMP method can be close to the optimality benchmark of Cramér-Rao Lower Bound.
在基于到达时间（TOA）的源定位中，只有当获得源与传感器之间正确的信号传播时间时，才能实现精确的定位。在实际中，源节点和传感器节点之间通常存在时钟误差，导致它们经常处于异步状态。这就产生了异步源定位问题，该问题进而被表述为一个具有非凸和非光滑目标函数的最小二乘问题。现有算法需要将原始问题松弛为凸规划，如半定规划（SDP），这会导致性能损失。在本文中，与现有方法不同，我们提出了一种近端交替最小化定位（PAMP）方法，该方法无需松弛即可最小化原始函数。利用原始异步问题的双凸性质，该方法将其分为两个子问题：时钟偏移子问题和同步源定位子问题。对于前者，我们推导出全局解，而后者则通过从基于模拟退火的Barzilai-Borwein算法扩展而来的一种高效次梯度算法来求解。所提出的方法以较低的计算复杂度获得了较好的定位性能。我们还在李雅普诺夫框架下建立了该方法的收敛性。仿真结果表明，PAMP方法的性能可以接近克拉美罗下界的最优基准。
