Adaptive robust Kalman filter for relative navigation using global position system

An adaptive robust Kalman filter algorithm is derived to account for both process noise and measurement noise uncertainty. The adaptive algorithm estimates process noise covariance based on the recursive minimisation of the difference between residual covariance matrix given by the filter and that calculated from time-averaging of the residual sequence generated by the filter at each time step. A recursive algorithm is proposed based on both Massachusetts Institute of Technology (MIT) rule and typical non-linear extended Kalman filter equations for minimising the difference. The measurement update using a robust technique to minimise a criterion function originated from Huber filter. The proposed adaptive robust Kalman filter has been successfully implemented in relative navigation using global position system for spacecraft formation flying in low earth orbit, with real-orbit perturbations and non-Gaussian random measurement errors. The numerical simulation results indicate that the proposed adaptive robust filter can provide better relative navigation performance in terms of accuracy and robustness as compared with previous filter algorithms.