Efficient tracking of spatially correlated signals in wireless sensor fields: A weighted stochastic gradient approach

A weighted stochastic gradient algorithm is proposed for cost-efficient tracking of unknown, correlated spatial signals from randomly distributed sensor observations in localized wireless sensor field. The algorithm is implemented in spatial modelling and spatial tracking phases. In spatial modelling phase, the algorithm finds the model parameters, and in spatial tracking phase, it updates these parameters. The spatial signal is modelled with its M iso-contour lines at equally spaced levels ${\left\{\ell \right\}}_{k=1}^M$ and the sensors with sensor observations in Δ margin of these contour levels report to the fusion centre (FC) for spatial monitoring purpose. Based on progressive learning and in successive iterations, the algorithm improves its findings of the signal strength's range, and the spatial, temporal and spectral attributes of the signal. To reduce the cost, in each iteration, only a subset of wireless sensors transmits the observations to the FC, in response to its query. In this article, the percentage of the reporting sensors to the FC is defined as the algorithm's cost. With importance sampling perspective, the sample space is reduced to those sensors whose observations are within a Δ margin of atleast one of these M contour levels. The Δ margin is pruned or enhanced using the proposed weighted stochastic gradient algorithm, dynamically in order to reduce the spatial tracking cost. The evaluation results show that after spatial modelling, spatial tracking is drastically of low cost and its performance is better than that of the conventional stochastic gradient method. The modelling error, the cost and the convergence of the proposed algorithm are investigated extensively, in this article. Spatial correlation in signal distribution and the coordinates of the wireless sensors are the only initial assumptions in spatial monitoring of the unknown signal distribution. The main purpose of this algorithm is low-cost identification of unknown correlated spatial signals from sensor observations, over time. An example for application of the proposed algorithm is environmental monitoring using wireless sensor observations.