Sensor network design for the estimation of spatially distributed processes
International Journal of Applied Mathematics and Computer Science
Journal of Intelligent and Robotic Systems
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Statistical methods for detecting and estimating biochemical dispersion by a moving source using model-based integrated sensor array processing are developed. Two possible cases are considered: a homogeneous semi-infinite medium (corresponding to the environment such as air above the ground for an airborne source) or a two-layer semi-infinite medium (e.g., shallow water). The proposed methods can be extended to more complex scenarios. The goals are to detect and localize the biochemical source, determine the space-time concentration distribution of the dispersion, and predict its cloud evolution. Potential applications include security, environmental monitoring, pollution control, simulating hazardous accidents, and explosives detection. Diffusion models of the biochemical substance concentration distribution are derived under various boundary and environmental conditions. A maximum-likelihood algorithm is used to estimate the biochemical concentration distribution in space and time, and the Cramer-Rao bound is computed to analyze its performance. Two detectors (generalized-likelihood ratio test (GLRT) and a mean-difference detector) are derived and then their performances are determined in terms of the probabilities of detection and false alarm. The results can be used to design the sensor array for optimal performance. Numerical examples illustrate the results of the concentration distribution and the performances of the proposed methods.