Square-root sigma-point Kalman filtering for spacecraft relative navigation

A variant of sigma-point Kalman filters family called square-root unscented Kalman filter is derived to estimate the relative attitude and position of two spacecrafts referred to as the leader and follower. The square-root forms of unscented Kalman filter have a consistently increased numerical stability because all resulting covariance matrices are guaranteed to stay semi-positive definite. The general six degrees of freedom relative equations of motion are developed based upon the tensors. All leader states are assumed known, whereas the relative states are estimated using available line-of-sight observations between the vehicles along with acceleration and angular velocity measurements of the follower. The quaternion is used to describe the spacecraft relative attitude kinematics, while a three-dimensional generalized Rodrigues parameter is used to maintain the quaternion normalization constraint in the filter formulation. The simulation results indicate that the proposed filter can provide lower relative attitude and position estimation errors with faster convergence rates than the standard extended Kalman filter.