Efficient Calculation of Sensor Utility and Sensor Removal in Wireless Sensor Networks for Adaptive Signal Estimation and Beamforming

Abstract

Abstract-Wireless sensor networks are often deployed over a large area of interest and therefore the quality of the sensor signals may vary significantly across the different sensors. In this case, it is useful to have a measure for the importance or the so-called 'utility' of each sensor, e.g., for sensor subset selection, resource allocation or topology selection. In this paper, we consider the efficient calculation of sensor utility measures for four different signal estimation or beamforming algorithms in an adaptive context. We use the definition of sensor utility as the increase in cost (e.g., mean-squared error) when the sensor is removed from the estimation procedure. Since each possible sensor removal corresponds to a new estimation problem (involving less sensors), calculating the sensor utilities would require a continuous updating of K different signal estimators (where K is the number of sensors), increasing computational complexity and memory usage by a factor K. However, we derive formulas to efficiently calculate all sensor utilities with hardly any increase in memory usage and computational complexity compared to the signal estimation algorithm already in place.

Sensor Selection for Estimation with Correlated Measurement Noise

“…Such a phenomenon was also discovered in the calculation of sensor utility for adaptive signal estimation [29] and leader selection in stochastically forced consensus networks [12]. Since activating a new sensor does not degrade the estimation performance, the inequality (energy) constraint in (P0) can be reformulated as an equality constraint.…”

“…The greedy algorithm is attractive due to its simplicity, and has been employed in a variety of applications [12], [29], [30]. In particular, a greedy algorithm was proposed in [30] for sensor selection under the assumption of uncorrelated measurement noise.…”

Greedy distributed node selection for node-specific signal estimation in wireless sensor networks

“…The utility is defined similarly to (14) where the utility of node k's signals with respect to node s's estimation problem is given by…”

“…Therefore, (21) cannot be used, and we need the original definition of the utility in (14). This relies on the ability for a node to calculate its optimal fall-back estimator, e.g., k's fall-back estimator when removing itself from the network isŴ k −k .…”

“…In order to select nodes from a given set, we introduce the concept of utility, which is assigned to a node as a way to determine its importance to the signal estimation problem at hand [13,14,15]. It is defined as the increase or decrease of the MMSE after removing or adding the respective node and re-optimizing the estimators.…”