One of the greatest technical challenges facing the military community today is the generation of battlespace awareness within the space domain. The battlespace awareness functions as a foundation for planning appropriate courses of action (CoAs) to respond to any possible threats and safeguard our space assets. This work proposes the development of the Multiple Model Adaptive Estimator with Koopman Operator (MMAE-KO). It is concerned with the enabling of proactive battlespace awareness in the increasingly congested, contested, and competitive space domain to the warfighter or other satellite operators. In particular, MMAE-KO will aid in classifying and tracking space objects within the vicinity of our space assets, as well as anticipating adversary spacecraft CoAs with different possible maneuvering capabilities. This is accomplished by developing a Bayesian framework that automatically filters the measurement data of high-valued space objects to identify their probable maneuvering types and maneuvering capabilities, their associated control policies, and threat level to our space assets. The probability of threat associated with each single model is evaluated considering the reachable set of the adversary spacecraft, evaluated in the Koopman Operator (KO) framework. The KO solution of the system generates a polynomial transition map of the state, such that the time propagation of any state can be calculated through a computationally fast polynomial evaluation rather than going through numerical integration. That is, the Koopman analysis of the dynamics obtains the complete eigendecomposition of the system, where any given observable can be represented as a linear combination of the basis functions. This representation leads to numerous advantages in astrodynamics, as it can be applied for the propagation of uncertainties and for the evaluation of the reachable set of the system. One of the main benefits is the trivial propagation of a large number of space objects, especially over different propagation models. Thus, we propose a new representation of the reachable set of states of a controlled system as a linear combination of the eigenfunctions, evaluated via the KO, analytically. The proposed MMAE-KO filter leverages the advantages of the MMAE filter with the KO representation of the dynamics to achieve a rapid and robust probabilistic identification of possible adversary spacecraft, with a classification of their possible actions, and prediction of their subsequent trajectories, as well as evaluation of their threat level to our space assets. As such, thanks to the KO state transition polynomial maps, the MMAE-KO algorithm is able to obtain a rapid prediction of the reachable set for each model, where the adaptive filter technique best utilizes a Bayesian update and hypothesis testing to assess the probability of each possible scenario.
