Distributed estimation of a parametric field with random sensor placements

This paper considers a problem of distributed function estimation in the case when sensor locations are modeled as Gaussian random variables. We consider a scenario where sensors are deployed in clusters with cluster centers known a priori (or estimated by a high performance GPS) and the average quadratic spread of sensors around the cluster center also known. Distributed sensors make noisy observations about an unknown parametric field generated by a physical object of interest (for example, magnetic field generated by a ferrous object and sensed by a network of magnetometers). Each sensor then performs local signal processing of its noisy observation and sends it to a central processor (called fusion center) in the wireless sensor network over parallel channels corrupted by fading and additive noise. The central processor combines the set of received signals to form an estimate of the unknown parametric field. In our numerical analysis, we involve a field shaped as a Gaussian bell. We experiment with the size of sensor clusters and with their number. A mean square error between the estimated parameters of the field and the true parameters used in simulations is involved as a performance measure. It can be shown that a relatively good estimate of the field can be obtained with only a small number of clusters. As the number of clusters increases, the estimation performance steadily improves. The results also indicate that, on the average, the number of clusters has more impact on the performance than the number of sensors per cluster, given the same size of the total network.