The dissertation considers three topics in the areas of estimation, tracking and optimization. The first topic focuses on near-optimal routing of assets, such as ships, submarines and UAVs, in uncertain and dynamic environments. 3D and 4D navigation in uncertain environments is challenging as it involves many contextual elements, such as different environmental conditions, multiple objectives, changes in mission goals while en route, and asset status. Several solution approaches, including the min-max game, bi-objective shortest path problem and a cone programming approach are investigated. We demonstrate their performance and utility via application to a real-world shipping tragedy using weather forecast realizations available prior to the event, and several score card routes used to evaluate the ship routing algorithms. The second topic involves dynamic scheduling of UAVs to maximize the reward associated with the detection of a set of targets in minimum time, subject to restricted operating zones, limited fuel capacity, deadlines, random processing times and multiple pop-up targets. Branch-and- bound, rollout-based approximate dynamic programming and tabu search-based algorithms are developed and evaluated as to their suitability as decision support systems to human operators. A two-step rollout algorithm generates solutions in the order of seconds, which can be useful as a decision support to alleviate the operator workload. The third topic focuses on adaptive estimation of the state of charge (SOC) and hardware-in- the-loop testing of a battery fuel gauge (BFG). A BFG helps to extend battery life by tracking the state of charge and many other diagnostic features. We elaborate on a BFG that adapts to battery chemistries and a robust reduced order filter to track the state of charge of batteries based on instantaneous terminal voltage, load current, and temperature measurements. Further, an approach to validate the SOC and time-to-shutdown estimates of a BFG with a hardware-in-the-loop testbed under realistic usage scenarios is detailed.
