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Separable Approximation for Solving the Sensor Subset Selection Problem

机译：解决传感器子集选择问题的可分逼近

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摘要

An algorithm is proposed to solve the sensor subset selection problem. In this problem, a prespecified number of sensors are selected to estimate the value of a parameter such that a metric of estimation accuracy is maximized. The metric is defined as the determinant of the Bayesian Fisher information matrix (B-FIM). It is shown that the metric can be expanded as a homogenous polynomial of decision variables. In the algorithm, a separable approximation of the polynomial is derived based on a graph-theoretic clustering method. To this end, a graph is constructed where the vertices represent the sensors, and the weights on the edges represent the coefficients of the terms in the polynomial. A process known as natural selection in population genetics is utilized to find the dominant sets of the graph. Each dominant set is considered as one cluster. When the separable approximation is obtained, the sensor selection problem is solved by dynamic programming. Numerical results are provided in the context of localization via direction-of-arrival (DOA) measurements to evaluate the performance of the algorithm.
机译：提出了一种解决传感器子集选择问题的算法。在这个问题中，选择预定数量的传感器以估计参数的值，使得估计精度的度量最大化。该度量标准定义为贝叶斯费舍尔信息矩阵（B-FIM）的行列式。结果表明，度量可以扩展为决策变量的同质多项式。在该算法中，基于图论聚类方法得出多项式的可分离近似。为此，构造了一个图，其中顶点表示传感器，边缘上的权重表示多项式中项的系数。利用在种群遗传学中​​称为自然选择的过程来找到图的主要集。每个主导集被视为一个群集。当获得可分离的近似值时，通过动态编程解决了传感器选择问题。在本地化的情况下，通过到达方向（DOA）测量来提供数值结果，以评估算法的性能。

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