Windowing-based Adaptive Unscented Kalman Filter for Spacecraft Relative Navigation

In this paper, we study the problem of nonlinear filtering with unknown measurement noise covariance matrix. An adaptive filtering algorithm has been developed by integrating an estimate of the measurement noise covariance matrix into the unscented Kalman filter (UKF). The windowing approach is adopted to estimate the noise covariance matrix based on a set of innovation sequences in the window. Instead of predicting the noise covariance matrix by the historical innovation sequences, the innovation at the present time is utilized and a heuristic rule is suggested to extract the diagonal elements in the estimated matrix. An application to spacecraft relative navigation illustrates that the proposed filter performs better than the existing adaptive UKF. Simulation results show that the measurement noise variances can be estimated accurately with some penalty of time delay.