Minimax Sensor Location and Bayesian Estimation of the Probability of Detection

This grant provides funding for the development of mathematical techniques for the problem of locating a finite number of sensors to detect an event in a given region. The overall problem consists of two main tasks: the sensor location problem and the estimation of the probability of detection. In the sensor location problem, the objective is to minimize the maximum probability of non-detection and the underlying region consists of a line or curve in the plane. These results will then be extended to develop tractable mathematical models and solution algorithms for a continuous planar region or a 3-dimensional region. Optimization techniques such as simulated annealing, genetic algorithms, and differential evolution will be studied as possible solution strategies for this class of nonlinear programming problems. Estimation of the probability of detection involves testing for complete spatial randomness. If events exhibit this property, then a uniform distribution may be appropriate. Otherwise, historical event data will be modeled as a spatial non-homogeneous Poisson process defined on the region. The mean rate of event occurrences will be estimated using a Bayesian approach that incorporates prior beliefs about the likelihood of events in different subregions within the region to be monitored.

If successful, the results of this research will make available an integrated set of tools and solution methodologies for solving sensor location problems, including tools for the visualization of the resulting optimal sensor configurations. The sensor location problem has a multitude of applications. For example, the location of aircraft detection sensors, the placement of sentries along a border to detect enemy penetration, the detection of nuclear tests, the detection of natural and hazardous man-made events, as well as the monitoring of contaminants in streams and rivers. The proposed work will also contribute to the numerical tools available for nonlinear optimization and Bayesian estimation.