Receding Horizon Trajectory Optimization in Opportunistic Navigation Environments

Receding horizon trajectory optimization for optimal information gathering in opportunistic navigation environments is considered. A receiver is assumed to be dropped in an environment consisting of multiple signals of opportunity (SOPs) transmitters. The receiver has minimal a priori knowledge about its own states and the SOPs' states. The receiver draws pseudorange observations from the SOPs. The receiver's objective is to build a high-fidelity signal landscape map while simultaneously localizing itself within this map in space and time. Assuming that the receiver can control its maneuvers, the following two problems are considered. First, the minimal conditions under which the environment is completely observable are established. It is shown that receiver-controlled maneuvers reduce the minimal a priori information about the environment required for complete observability. Second, the trajectories that the receiver should traverse are prescribed. To this end, a one-step look-ahead (greedy) strategy is compared with a multistep look-ahead (receding horizon) strategy. The limitations and achieved improvements in the map quality and space-time localization accuracy due to the receding horizon strategy are quantified. The computational burden associated with the receding horizon strategy is also discussed.