Vision-Based Relative State Estimation Using the Unscented Kalman Filter

This paper presents a new approach to spacecraft relative attitude estimation and navigation based on the unscented Kalman filter which was implemented and evaluated for rendezvous and proximity operations. The use of the unscented Kalman filter requires propagation of carefully selected sigma points from the nonlinear system to map probability distribution more accurately than is possible using the linearization of the standard ext ended Kalman filter. This approach leads to faster convergence when using inaccurate initial conditions in attitude estimation and navigation problems. This method uses observations from a vision sensor to provide multiple line of sight vectors from the chief spacecraft to the deputy spacecraft. Because the observation equations associated with the vision sensor are coupled with the attitude matrix and the relative position vector, the estimation is performed based on the initial attitude and the initial navigation information. A multiplicative quaternion error is derived from the local attitude error that guarantees that the quaternion unit constraint is maintained in the filter. One scenario chosen for the study was the simulation of bounded relative motion for 10 hours, and another scenario chosen was a 30-minute rendezvous maneuver. Simulation results show that, in these scenarios, the unscented Kalman filter is more robust than the extended Kalman filter under realistic initial attitude and navigation conditions. The relative navigation results are valtdated by compartng them with the relative orbit computed by the High Precision Orbit Propagator (HPOP) of Satellite Tool Kit (STK). Finally, the estimation of the rendezvous maneuver is shown by comparing with the reference trajectory, a linear impulse rendezvous based on a Cochran-Lee-Jo (CLJ) transition matrix for an elliptical orbit