In-Orbit Assessment of a Physics-based Star Tracker Model using DART and PSP Flight Data
Authors:   Johns Hopkins University Applied Physics Laboratory (APL), Laurel, United States, Miller Scott , Pittelkau Mark , Superfin Emil , O'Shaughnessy Dan 
Published: January 2024

A high-fidelity star tracker model was developed in support of NASA’s recent Double Asteroid Redirection Test (DART) mission and is presented herein. The model, while functionally agnostic, was specifically intended to emulate the noise characteristics of a Leonardo AA-STR star tracker. Since the AA-STR flown on DART was from the same procurement lot as the two AA-STR trackers currently in use on NASA’s Parker Solar Probe (PSP) mission, the model was evaluated relative to flight data obtained from both programs in several different operational scenarios. Findings from in-flight testing shed light on the advantages gained by a more complex physics-based modeling scheme over a simpler heuristic approach. These results may help to inform the modeling trade space in future missions.
The model’s Matlab/Simulink implementation contains both empirical and physical modeling attributes. Random measurement errors are captured as additive white Gaussian temporal noise (TN). Low Spatial Frequency Errors (LSFE), which are dominated by optical distortion caused by imperfections in the focal plane, are modeled physically: quaternion measurements are generated through the batch processing (QUEST) of local star measurements that depend on randomly-seeded lens distortion characteristics and an initial star field. High Spatial Frequency Errors (HSFE) primarily arise from the discrete sampling of the point spread function (PSF) of individual stars. As a physical mechanism, HSFE is captured by emulating a triangular-wave cyclic sampling of each star’s PSF prior to QUEST batch processing. Since measurement noise generated by a physical model is dependent both on star locations and lens distortion characteristics, implementing a physical model would usually necessitate a Monte Carlo analysis to bound predictions in lieu of specific vendor-supplied lens distortion data and/or known star field information. The tracker model also provides for the physical HSFE representation to be entirely replaced by a heuristic First Order Gauss-Markov (FOGM) process.
Fight test results provide insight into the model’s applicability under different operational conditions. Several PSP flight data sets were obtained, both while the star fields were slowly moving across the FOVs of both AA-STR trackers (gyro calibration events) and while the star fields were dynamically quasi-static (inertial hold events). PSP’s wheel-based attitude control subsystem (0.05 Hz bandwidth) provided tight pointing control during the capture events. In contrast, the DART capture events occurred during inertial–hold capture windows in which a thruster-based phase plane controller was employed. Star fields would thus drift across short spatial distances (in its single AA-STR tracker) before being “pushed” in a counter direction due to thruster pulsing. The results obtained from both the PSP and DART testing show that a heuristic HSFE FOGM model is generally adequate when the star field traverses the FOV at a constant rate, and that quasi-static motion precludes the need for LSFE physical modeling. But for conditions where the star field’s rate and direction are not uniform (e.g. thruster control), a rigorous physical model measurably improves fidelity.