Case Study: Feasibility Analysis of Close-in Proximity Operations Using Angles-only Navigation

Abstract

The feasibility of angles-only navigation (AON)-based close-in proximity operation is studied for application to upcoming small satellite-based uncooperative rendezvous missions. For the relative motion equations described by Yamanaka-Ankersen, the Square-Root Unscented Kalman Filter (SRUKF) is adapted for relative position estimations, considering low-volume/mass, lower-power, simple optical/infrared instruments together with Lidar measurements. Considering simplicity and achievements in engineering, the multi-pulse glideslope guidance law is utilized. Using a linear covariance technique, a complete set of analytical functions are deduced for closed-loop true dispersions and estimated dispersion analysis. Monte Carlo simulation proves the offset observation model proposed provides a good solution for the range-observability dilemma: the range estimation error decreases from an initial decameter-level to a final decimeter-level. Two proximity operation mission trajectories are designed: direct v-bar quasi-linear glide approach for robotic arm capture or net capture, and glide approach (i.e., circumnavigate-glide approach for capture with attitude requirement). Using a well-designed relative approaching guidance profile, the camera operational range can be extended. This enables the operation time of the Lidar to be shortened, or even replaced by an optimal/infrared camera. This is very helpful in saving mass and power for the chaser. The variable-structure SRUKF proposed leads to a more robust trajectory: true dispersion is improved by two orders in the 100 m range, and more accurate covariance prediction (i.e., all sampled trajectories are inside the ellipse) when compared to the standard SRUKF. The analysis method proposed, which could raise analytical closed-loop linear covariance, is applicable for onboard maneuver planning and real-time closed-loop control error estimation.