This paper addresses the Sensor Network Localization (SNL) problem using received signal strength. The SNL is formulated as an Euclidean Distance Matrix Completion (EDMC) problem under the unit ball sample model. Using the Burer-Monteiro factorization type cost function, the EDMC is solved by Riemannian conjugate gradient with Hager-Zhang line search method on a quotient manifold. A “rank reduction” pre-process is proposed for proper initialization and to achieve global convergence with high probability. Simulations on a synthetic scene show that our approach attains better localization accuracy and is computationally efficient compared to several baseline methods. Characterization of a small local basin of attraction around the global optima of the s-stress function under Bernoulli sampling rule and incoherence matrix completion framework is conducted for the first time. Theoretical result conjectures that the Euclidean distance problem with a structure-less sample mask can be effectively handled using spectral initialization followed by vanilla first-order methods. This preliminary analysis, along with the aforementioned numerical accomplishments, provides insights into revealing the landscape of the s-stress function and may stimulate the design of simpler algorithms to tackle the non-convex formulation of general EDMC problems.

中文翻译：

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通过黎曼共轭梯度和降阶进行传感器网络定位

本文利用接收信号强度解决传感器网络定位 (SNL) 问题。 SNL 被表述为单位球样本模型下的欧几里得距离矩阵完成 (EDMC) 问题。使用Burer-Monteiro分解型成本函数，利用商流形上的Hager-Zhang线搜索方法通过黎曼共轭梯度求解EDMC。提出了“降级”预处理，以进行适当的初始化并以高概率实现全局收敛。对合成场景的模拟表明，与几种基线方法相比，我们的方法获得了更好的定位精度并且计算效率更高。首次在伯努利采样规则和不相干矩阵完成框架下对 s 应力函数全局最优值周围的小型局部吸引力盆地进行了表征。理论结果推测，使用谱初始化和普通一阶方法可以有效地处理无结构样本掩模的欧几里德距离问题。这一初步分析以及前面提到的数值成果，为揭示 s-应力函数的情况提供了见解，并可能刺激更简单的算法的设计，以解决一般 EDMC 问题的非凸公式。