On the roles of smoothing in planning of informative paths

This paper investigates the roles of smoothing in planning of information-gathering paths for mobile sensors, when the goal is to minimize the entropy of some variables of interest at the final time of generated plan. The main result is that smoothing simplifies the process of calculating the information gathered up to some arbitrary time on the fly. This enables quantification of the correct cost-to-go value when applied to a receding-horizon approximation of the optimal path planning problem. Numerical examples on simplified weather forecasting, sensor scheduling, and target localization validate the theoretical findings.