An Adaptive Kalman Filter for Spacecraft Formation Navigation using Maximum Likelihood Estimation with Intrinsic Smoothing

In the interests of enhancing autonomous navigation capabilities for Low Earth Orbit formation flying, this work presents the development of an Adaptive Extended Kalman Filter (AEKF) that estimates relative position and velocity states between two spacecraft. A standard EKF based on the nonlinear dynamics of relative motion is used to provide preliminary state estimates of the formation, which are then corrected through a fixed-window smoothing routine. Since uncertainties in the process and measurement noise covariances within the filter inherently limit the final accuracy of the EKF, an online tuning mechanism is derived using Maximum Likelihood Estimation (MLE) to optimize the noise covariances given an available set of measurements. Inclusion of these adaptations improves filter robustness by allowing the filter to handle situations where noise characteristics of the system are unknown or subject to change, while simultaneously eliminating the need for the initial manual covariance tuning process that accompanies EKF design. Numerical validation of the proposed algorithm is completed by comparing navigation solutions from the AEKF with those obtained from the non-adaptive EKF, using a realistic in-plane elliptical spacecraft formation.