Improved robust Huber–Kalman filtering

In this study, an improved robust Huber–Kalman filter (IRHKF) is derived based on robustifying the modified iterated extended Kalman filter (MIEKF) for nonlinear problems with non-Gaussian measurement noise in the presence of large initial errors. In developed IRHKF, the iterated measurement update estimate is used in the nonlinear regression procedure and the Huber's M-estimation technique-based robust filtering problem is solved by making use of the Gauss–Newton methodology. Moreover, the maximum likelihood criterion is taken as the terminated condition for the Huber iterated updates to make the IRHKF filter achieve the optimal solution. The improved performance of the developed IRHKF filter is then validated by employing a ballistic target re-entry problem, which is to estimate the trajectory of a re-entry vehicle under the condition that the measurement noises are contaminated by thicker tails and/or outliers. The simulation results indicated that the presented IRHKF filter exhibits the best performance in terms of robustness and estimation accuracy as compared to the robust MIEKF (RMIEKF), linear regression Huber-based extended Kalman filtering (HEKF) and the non-robust extended Kalman filter (EKF). © 2022, Shanghai Jiao Tong University.