A Fuzzy Adaptive Kalman Filter for Spacecraft Formation Navigation

Over the past two decades, advances in spacecraft technologies have prompted the development of autonomous onboard navigation systems. This paper presents the design of a novel Fuzzy Adaptive Extended Kalman Filter (FAEKF) suitable for estimating the relative position and velocity between two spacecraft flying in formation. A fuzzy adaptation architecture is embedded within a standard Extended Kalman Filter (EKF), thereby allowing the filter to adapt internal noise characteristics that would otherwise remain constant after the initial filter design. Inaccurate tuning of the process and measurement noise covariance matrices within an EKF are commonly a limiting factor in the estimation performance, especially in situations where the behaviour of the noise processes are poorly defined or subject to change. In this context, the proposed approach provides a method to update the process and measurement noise covariances online based on a covariance-matching analysis of the filter residuals. A demonstration of the technique is given through numerical simulations of a spacecraft formation in low-Earth orbit, which are used to compare state estimates from the FAEKF with those from measurement-only and non-adaptive EKF solutions.