Gradient-based schemes of mobile sensor guidance for estimating spatially distributed systems in hazardous environments using value of information

In many situations, a mobile sensor must traverse in hazardous environments to collect information about spatially distributed processes. Without any constraints, the sensor will be guided in spatial locations that tend to improve the performance of the state estimator. This translates to larger values of the state estimation error. Such a guidance is information-sensitive as the sensor seeks “more” useful information within the spatial region. However, when exposure to hazardous environments affect the reliability and life-expectancy of the sensor, then a modification to the guidance must be considered in order to increase the life-expectancy of the sensor. Assuming that the cumulative exposure to the spatial field has a limit, beyond of which the sensor is rendered inoperable, then a modification to the information-sensitive guidance is warranted in order to prolong the life of the sensor. This of course compromises the value of information as an information-averse guidance will certainly prolong the life of a sensor, but the sensor will provide measurements with reduced value for the estimator. These concerns are considered here and a sensor guidance scheme is proposed that provides information-sensitive guidance when the accumulated exposure is below a user-defined limit and then switches to an information-averse guidance in order to prolong the life-expectancy of the sensor. Numerical studies for a diffusion partial differential equation with a single mobile sensor are provided to provide some insights on the modified sensor guidance policy and its increased life expectancy.