Separable Approximation for Solving the Sensor Subset Selection Problem

Abstract

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.