| The problem we investigate deals with an Image Intelligence (IMINT) sensor allocation schedule for High Altitude Long Endurance UAVs in a dynamic and Anti-Access Area Denial (A2AD) environment. The objective is to maximize the Situational Awareness (SA) of decision makers. The value of SA can be improved in two different ways. First, if a sensor allocated to an Areas of Interest (AOI) detects target activity, then the SA value will be increased. Second, the SA value increases if an AOI is monitored for a certain period of time, regardless of target detections. These values are functions of the sensor allocation time, sensor type and mode. Relatively few studies in the archival literature have been devoted to an analytic, detailed explanation of the target detection process, and AOI monitoring value dynamics. These two values are the fundamental criteria used to choose the most judicious sensor allocation schedule. This research presents mathematical expressions for target detection processes, and shows the monitoring value dynamics. Furthermore, the dynamics of target detection is the result of combined processes between belligerent behavior (target activity) and friendly behavior (sensor allocation). We investigate these combined processes and derive mathematical expressions for simplified cases. These closed form mathematical models can be used for Measures of Effectiveness (MOEs), i.e., target activity detection to evaluate sensor allocation schedules. We also verify these models with discrete event simulations which can also be used to describe more complex systems. We introduce several methodologies to achieve a judicious sensor allocation schedule focusing on the AOI monitoring value. The first methodology is a discrete time integer programming model which provides an optimal solution but is impractical for real world scenarios due to its computation time. Thus, it is necessary to trade off the quality of solution with computation time. The Myopic Greedy Procedure (MGP) is a heuristic which chooses the largest immediate unit time return at each decision epoch. This reduces computation time significantly, but the quality of the solution may be only 95% of optimal (for small size problems). Another alternative is a multi-start random constructive Hybrid Myopic Greedy Procedure (H-MGP), which incorporates stochastic variation in choosing an action at each stage, and repeats it a predetermined number of times (roughly 99.3% of optimal with 1000 repetitions). Finally, the One Stage Look Ahead (OSLA) procedure considers all the 'top choices' at each stage for a temporary time horizon and chooses the best action (roughly 98.8% of optimal with no repetition). Using OSLA procedure, we can have ameliorated solutions within a reasonable computation time. Other important issues discussed in this research are methodologies for the development of input parameters for real world applications. |
