Continuous trajectory planning of mobile sensors for informative forecasting

This paper addresses the planning of continuous paths for mobile sensors to reduce the uncertainty in some quantities of interest in the future. The mutual information between the measurement along the continuous path and the future verification variables defines the information reward. Two expressions for computing this mutual information are presented: the filter form extended from the state of the art and the smoother form inspired by the conditional independence structure. The key properties of the approach using the filter and smoother strategies are presented and compared. The smoother form is shown to be preferable because it provides better computational efficiency, facilitates easy integration with existing path synthesis tools, and, most importantly, enables correct quantification of the rate of information accumulation. A spatial interpolation technique is used to relate the motion of the sensor to the evolution of the measurement matrix, which leads to the formulation of the optimal path planning problem. A gradient-ascent steering law based on the concept of information potential field is also presented as a computationally efficient suboptimal strategy. A simplified weather forecasting example is used to compare several planning methodologies and to illustrate the potential performance benefits of using the proposed planning approach.