Reachability-Based Search for Tracking of Noncooperative Maneuvering Satellites in Data Sparse Environment

A generic Bayesian framework is presented to track lost-in-space noncooperative maneuvering satellites. The developed framework predicts the reachability set for a lost-in-space satellite given bounds on maneuver parameters such as maneuver time and maneuver magnitude. Reachability sets are represented as a desired order polynomial series as a function of maneuver parameters. Recent advances in non-product quadrature methods are utilized to compute coefficients of this polynomial series in a computationally efficient manner. A major contribution of this work is to develop quadrature methods to generate samples for spherically uniform distribution for bounded magnitude maneuvers. Samples generated from this polynomial series are used for direct particle propagation in a traditional Bayesian filter rather than solving governing equations of motion for each sample point. An important component of the developed framework is a search strategy which exploits the reachability set calculations to task the sensor to increase the detection probability of the satellite. The samples generated from initial reachability sets are updated to systematically reduce the target search region based on actual detection of the target in a Bayesian framework. Numerical simulations are performed to show the efficacy of the developed ideas for tracking a lost-in-space satellite with the help of space based sensor. Performance of the proposed method varies widely based on factors such as the reachability set polynomial order, maneuver uncertainty bounds, sensor parameters (Field of view, measurement frequency, and detection probability), and initial conditions. For numerical experiments performed, the observer gained the custody of the maneuvering target in 100 % and 96 % of Monte Carlo (MC) simulations for the single maneuver and two maneuver cases, respectively.