Adaptive extended Kalman filtering strategies for spacecraft formation relative navigation

The relative navigation problem for spacecraft formation flying missions in near-Earth orbit is addressed here through the design of two unique adaptive extended Kalman filter algorithms. The adaptive filters are capable of updating the internal noise characteristics of the Kalman filter in real time, and are viable in all orbit scenarios, including elliptical orbits subjected to perturbations. The first adaptive Kalman filter approach uses maximum likelihood estimation techniques to derive analytical adaptations laws, which are then improved through the novel inclusion of an intrinsic smoothing routine. The second approach uses an embedded fuzzy logic system based on a covariance-matching analysis of the filter residuals, where the fuzzy system has been specifically designed for the spacecraft navigation problem at hand. Numerical simulations of two spacecraft formations demonstrate that the proposed adaptive navigation algorithms are appreciably more robust to filter initialization errors, dynamics modelling deficiencies, and measurement noises than the standard Kalman filter. •Precise relative navigation algorithms presented for formation flying spacecraft.•Extended Kalman filter allows fusion of sensor data with mathematical models.•Real-time adaptations to Kalman filter using two methods: Maximum Likelihood estimation and Fuzzy Logic Control.•Theory presented along with numerical simulations for a low-Earth orbit spacecraft formation.•Adaptive Kalman filter mitigates error from model nonlinearities and measurements, improving relative navigation accuracy.