Sensor Scheduling for Space Object Tracking and Collision Alert

Given the increasingly dense environment in both low-earth orbit (LEO) and geostationary orbit (GEO), a sudden change in the trajectory of any existing resident space object (RSO) may cause potential collision damage to space assets. With a constellation of EO/IR sensor platforms and ground radar surveillance systems, it is important to design optimal estimation algorithm for updating nonlinear object states and allocating sensing resources to effectively avoid collisions among many RSOs. We consider N space objects being observed by M sensors whose task is to provide the minimum mean square estimation error of the overall system subject to the cost associated with each measurement. To simplify the analysis, we assume that sensors can switch between objects instantaneously subject to additional resource and sensing geometry constraints. We first formulate the sensor scheduling problem using the optimal control formalism and then derive a tractable relaxation of the original optimization problem, which provides a lower bound on the achievable performance. We propose an open-loop periodic switching policy whose performance can approach the theoretical lower bound closely. We also discuss a special case of identical sensors and derive an index policy that coincides with the general solution to restless multi-armed bandit problem by Whittle. Finally, we demonstrate the effectiveness of the resulting sensor management scheme for space situational awareness using a realistic space object tracking simulator with both unintentional and intentional maneuvers by RSOs that may lead to collision. Our sensor scheduling scheme outperforms the conventional information gain and covariance control based schemes in the overall tracking accuracy as well as making earlier declaration of collision events.