Game optimal sensor management strategies for tracking elusive space objects

This paper presents a pursuit-evasion (PE) orbital game approach for space situational awareness (SSA), where imperfect measurements and/or informational uncertainties are addressed. Whether deliberate or unintentional, some of space objects may cause confusion to observers (satellites) by performing orbital maneuvers. Generally, the space-object tracking problem can be modeled as a one-sided optimization (optimal control) setup or a two-sided optimization (game) problem. In the optimal control setup, the states (positions and velocities) of space objects are computed (filtered) based on the sensor measurements. However, the optimal control approach does not consider the intelligence of the space objects that may change their orbits intentionally to make it difficult for the observer to track it. The proposed PE approach provides a method to solve the SSA problem, where the evader will exploit the sensing and tracking model to confuse the pursuer by corrupting their tracking estimates, while the pursuer wants to decrease the tracking uncertainties. The uncertainties are modeled based on the tracking entropy. For the applied consensus-based filters, the entropy is simplified as the product of eigenvalues of error covariance matrices. The fictitious play framework has been exploited to solve the non-linear PE games. Examples are presented for different maneuvering scenarios with optical tracking used space-based optical (SBO) sensors.