基于距离测量的凸松弛近似最大似然源定位
Approximate Maximum Likelihood Source Localization from Range Measurements Through Convex Relaxation
摘要：
这项工作考虑的问题，定位一个单一的来源，从嘈杂的距离测量的一组节点在无线传感器网络。我们提出了两个新的技术，我们指定为源定位与核范数（SLNN）和源定位与l1范数（SL-l1），扩展到任意实尺寸，包括3D，我们以前的工作制定的二维源定位在复平面。从广义上讲，我们的方法是基于制定一个最大似然（ML）估计问题的源位置，然后使用凸松弛技术，以获得一个半定的程序（SDP），可以在全球范围内有效地解决。SLNN直接逼近高斯ML解决方案，并且松弛比同类中的其他方法更紧。我们提出了一个分析的约束集的二维复杂版本的SLNN（SLCP），以证明所观察到的紧张的放松的凸性。在全局定位精度方面，SLNN优于最先进的基于迭代或封闭形式公式的优化方法。我们提出了SL-l1算法来解决拉普拉斯噪声的情况下，该模型的距离测量中的离群值的存在。我们克服了不可微的拉普拉斯似然函数重写ML问题的高斯情况下，一个精确的加权版本，并比较两种解决方案的战略。其中之一是迭代的，基于块坐标下降，并使用SLNN作为子处理块。另一个，只获得稍微差一点的性能，是noniterative和基于SDP放松的加权ML问题。
英文摘要：
This work considers the problem of locating a single source from noisy range measurements to a set of nodes in a wireless sensor network. We propose two new techniques that we designate as Source Localization with Nuclear Norm (SLNN) and Source Localization with l1-norm (SL-l1), which extend to arbitrary real dimensions, including 3D, our prior work on 2D source localization formulated in the complex plane. Broadly, our approach is based on formulating a Maximum-Likelihood (ML) estimation problem for the source position, and then using convex relaxation techniques to obtain a semidefinite program (SDP) that can be globally and efficiently solved. SLNN directly approximates the Gaussian ML solution, and the relaxation is shown to be tighter than in other methods in the same class. We present an analysis of the convexity properties of the constraint set for the 2D complex version of SLNN (SLCP) to justify the observed tightness of the relaxation. In terms of global accuracy of localization, SLNN outperforms state-of-the-art optimization-based methods with either iterative or closed-form formulations. We propose the SL-l1 algorithm to address the Laplacian noise case, which models the presence of outliers in range measurements. We overcome the nondifferentiability of the Laplacian likelihood function by rewriting the ML problem as an exact weighted version of the Gaussian case, and compare two solution strategies. One of them is iterative, based on block coordinate descent, and uses SLNN as a subprocessing block. The other, attaining only slightly worse performance, is noniterative and based on an SDP relaxation of the weighted ML problem.
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