Robust twistor-based spacecraft relative pose estimation using unscented Kalman filter

This paper presents new methods for spacecraft relative pose estimation using the Unscented Kalman Filter (UKF), taking into account non-additive process and measurement noises. A twistor model is employed to represent the spacecraft's relative 6-DOF motion of the chaser with respect to the target, expressed in the chaser body frame. The twistor model utilizes Modified Rodrigues Parameters (MRPs) to represent attitude with a minimal number of parameters, eliminating the need for the normalization constraint that exists in the quaternion-based model. Additionally, it incorporates both relative position and attitude in a single model, addressing kinematic coupling of states and simplifying the estimator design. Despite numerous existing pose estimation algorithms, many rely on the simplification of additive noise assumptions. This work enhances the robustness and improves the convergence of non-additive noise algorithms by deriving two methods to accurately approximate process and measurement noise covariance matrices for systems with non-additive noises. The first method utilizes the Stirling Interpolation Formula (SIF) to obtain equivalent process and measurement noise covariance matrices. The second method employs State Noise Compensation (SNC) to derive the equivalent process noise covariance matrix and uses SIF to compute the equivalent measurement noise covariance matrix. These methods are integrated into the UKF framework for estimating the relative pose of spacecraft in proximity operations, demonstrated through two scenarios: one with a cooperative target using Position Sensing Diodes (PSDs) and another with an uncooperative target using LiDAR for 3-D imaging. The effectiveness of these methods is validated against others in the literature through Monte Carlo simulations, showcasing their faster convergence and robust performance.