论文标题
传感器网络本地化的块坐标下降方法
A Block Coordinate Descent Method for Sensor Network Localization
论文作者
论文摘要
传感器网络本地化（SNL）的问题可以作为半标准编程问题提出，并具有等级约束。我们提出了一种解决此类SNL问题的新方法。我们通过burer-monteiro分解将半矩阵的半矩阵分解为两个矩阵的产物。然后，我们将两个矩阵的差异添加到目标函数中，从而将SNL重新定义为无约束的多元素优化问题，我们将其应用块坐标下降方法。在本文中，我们还提供了所提出方法的理论分析，并表明也可以通过分析求解每个通过块坐标下降方法依次求解的子问题，并通过我们所提出的算法收敛到目标功能的平稳点产生的顺序。我们还提供了一系列惩罚参数，在任何累积点中，分解中使用的两个矩阵都一致。数值实验证实，所提出的方法确实继承了等级约束，并且它在不牺牲估计精度的情况下估计传感器位置的速度快，尤其是当测量距离包含错误时。
The problem of sensor network localization (SNL) can be formulated as a semidefinite programming problem with a rank constraint. We propose a new method for solving such SNL problems. We factorize a semidefinite matrix with the rank constraint into a product of two matrices via the Burer--Monteiro factorization. Then, we add the difference of the two matrices, with a penalty parameter, to the objective function, thereby reformulating SNL as an unconstrained multiconvex optimization problem, to which we apply the block coordinate descent method. In this paper, we also provide theoretical analyses of the proposed method and show that each subproblem that is solved sequentially by the block coordinate descent method can also be solved analytically, with the sequence generated by our proposed algorithm converging to a stationary point of the objective function. We also give a range of the penalty parameter for which the two matrices used in the factorization agree at any accumulation point. Numerical experiments confirm that the proposed method does inherit the rank constraint and that it estimates sensor positions faster than other methods without sacrificing the estimation accuracy, especially when the measured distances contain errors.
