Separable Approximation for Solving the Sensor Subset Selection Problem FARHAD GHASSEMI VIKRAM KRISHNAMURTHY, Fellow, IEEE University of British Columbia 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. Manuscript received February 3, 2009; revised August 1, 2009; released for publication September 18, 2009. IEEE Log No. T-AES/47/1/940045. Refereeing of this contribution was handled by D. Salmond. Authors current addresses: F. Ghassemi, Sloan School of Management, Massachusetts Institute of Technology, 100 Main Street, Cambridge, MA 02140, E-mail: (farhad@mit.edu); V. Krishnamurthy, Dept. of Electrical Engineering, University of British Columbia, 2332 Main Mall, Vancouver, BC V6T 1Z4, Canada. 0018-9251/11/$26.00 c ° 2011 IEEE I. INTRODUCTION Recent widespread application of wireless sensor networks in pervasive surveillance and environment monitoring has stirred new efforts to develop efficient sensor management techniques [1]. In such applications, a large number of sensors equipped with microprocessors and wireless communication modules are often deployed in hostile environments to monitor a parameter. Sensors collect measurements and transmit them to their peers or a query node. Such operations can rapidly deplete sensors of their energy. It is, therefore, critical to have a balance between the amount of energy that can be consumed and the amount of information that can be gained. One approach for creating this balance is to maximize one quantity while holding the other one fixed. The sensor subset selection problem formalizes this approach, where a prespecified number of sensors are selected to estimate the value of the parameter such that a metric of estimation accuracy is maximized. The constraint on the number of sensors imposes a limit on the amount of energy that can be consumed. Commonly, metrics of estimation accuracy are defined based on scalar functions of the Fisher information matrix (FIM) or the Bayesian Fisher information matrix (B-FIM) [2]. The FIM is employed in the non-Bayesian framework when no prior knowledge is available about the value of the parameter. The B-FIM is employed in the Bayesian framework when some prior knowledge is available about the value of the parameter. An efficient non-Bayesian estimator attains the inverse of the FIM as the covariance matrix of its estimation error. Similarly, an efficient Bayesian estimator attains the inverse of the B-FIM as the covariance matrix of its estimation error. Hence, an appropriate scalar function of the (B-)FIM, which maps the chosen matrix to a real number, is a reasonable metric of estimation accuracy. The scalar functions that are often considered for this mapping are the determinant, trace, and largest eigenvalue of the (B-)FIM. Each of these scalar functions also quantifies a different aspect of the confidence ellipsoid [3] of the estimate. For instance, decreasing the trace of the inverse of (B-)FIM decreases the sum of the squares of each axis of the confidence ellipsoid, and decreasing the determinant of the inverse of (B-)FIM decreases the volume of the confidence ellipsoid. Regardless of the choice of the scalar function, the sensor selection problem is a combinatorial optimization problem, which quickly becomes intractable as the number of sensors increases. In [4], the authors mainly consider the sensor subset selection problem when only one sensor must be selected. This instance of the problem is not difficult to solve as one only needs to evaluate the metric N times, IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 1 JANUARY 2011 557