Adaptive sampling for spatial prediction in wireless sensor networks
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Networks of wireless sensors are increasingly exploited in crucial applications of monitoring spatially correlated environmental phenomena such as temperature, rainfall, soil ingredients, and air pollution. Such networks enable efficient monitoring and measurements can be included in developing models of the environmental fields even at unobserved locations. This requires determining the number of sensors and their sampling locations which minimize the uncertainty of predictions. Therefore, the aim of this thesis is to present novel, efficient and practically feasible approaches to sample the environments, so that the uncertainties at unobserved locations are minimized. Gaussian process (GP) is utilized to statistically model the spatial field. This thesis includes both stationary wireless sensor networks (SWSNs) and mobile robotic wireless sensor networks (MRWSNs), and thus the issues are correspondingly formulated into sensor selection and sensor placement problems, respectively. In the first part of the thesis, a novel performance metric for the sensor selection in the SWSNs, named average root mean square error, which reflects the average uncertainty of each predicted location, is proposed. In order to minimize this NP-hard and combinatorial optimization problem, a simulated annealing based algorithm is proposed; and the sensor selection problem is effectively addressed. Particularly, when considering the sensor selection in constrained environments, e.g. gas phase hydrogen sulphide in a sewage system, a modified GP with an improved covariance function is developed. An efficient mutual information maximization criterion suitable for this particular scenario is also presented to select the most informative gaseous sensor locations along the sewer system. The second part of this thesis introduces centralized and distributed methods for spatial prediction over time in the MRWSNs. For the purpose of finding the optimal sampling paths of the mobile wireless sensors to take the most informative observations at each time iteration, a sampling strategy is proposed based on minimizing the uncertainty at all unobserved locations. A novel and very efficient optimality criterion for the adaptive sampling problem is then presented so that the minimization can be addressed by a greedy algorithm in polynomial time. The solution is proven to be bounded; and computational time of the proposed algorithm is illustrated to be practically feasible for the resource-constrained MRWSNs. In order to enhance the issue of computational complexity, Gaussian Markov random field (GMRF) is utilized to model the spatial field exploiting sparsity of the precision matrix. A new GMRF optimality criterion for the adaptive navigation problem is also proposed such that computational complexity of a greedy algorithm to solve the resulting optimization is deterministic even with increasing number of measurements. Based on the realistic simulations conducted using the pre-published data sets, it has shown that the proposed algorithms are superior with appealing results.
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