Vision-Based Spacecraft Relative Navigation Using Sparse-Grid Quadrature Filter

In this paper, vision-based relative navigation of two spacecraft is addressed using the sparse-grid quadrature filter. The relative navigation provides the estimates of the relative orbit and relative attitude as well as the gyro biases. It is a challenging problem because of its high nonlinearity and dimensionality. The extended Kalman filter (EKF) and the unscented Kalman filter (UKF) have been used in the past to solve this problem. However, these filters are not accurate enough in the presence of large initial uncertainties or high nonlinearities. Moreover, although other filters, such as the Gauss-Hermite quadrature filter and the particle filter, can be more accurate than the EKF and UKF, they are hard to use in this high-dimensional estimation problem since a large number of quadrature points or particles are required and therefore the computation complexity is prohibitive. It is shown in this paper that the new sparse-grid quadrature filter can achieve much higher estimation accuracy than EKF, UKF, and the cubature Kalman filter without excessive computation load.