To extend the proposed MCRP framework to handle uncertainties in target locations, observation rewards, and satellite capabilities, a stochastic optimization approach can be employed. This involves incorporating probabilistic models for uncertain parameters, such as target locations and observation rewards, into the MCRP formulation. This can be achieved by introducing scenario-based optimization, where multiple scenarios representing different possible realizations of uncertainties are considered. The objective would then be to optimize the decision variables under all scenarios to ensure robustness against uncertainty.
For uncertain target locations, a scenario generation method can be used to create a set of potential target location scenarios based on historical data, predictive models, or expert knowledge. Observation rewards can be modeled as random variables with known probability distributions, allowing for the consideration of uncertainty in reward outcomes. Satellite capabilities, such as propulsion constraints or sensor limitations, can also be modeled stochastically to account for variability in satellite performance.
By incorporating uncertainties into the MCRP framework, decision-makers can make more informed decisions that are robust to variations in target locations, observation rewards, and satellite capabilities. This enhanced framework would provide a more realistic representation of the dynamic and uncertain nature of Earth observation satellite constellation reconfiguration.