l1-ATSXKF-based state and bias estimation for non-linear systems with non-Gaussian process noise

To solve the problem of state and bias estimation for the non-linear system with non-Gaussian noise terms, a series of exogenous Kalman filters (XKF)-based state and bias estimation algorithms are proposed. First, a non-linear system model with bias and non-Gaussian process noise is established. Second, the l₁ norm is incorporated into the two-stage exogenous Kalman filter (TSXKF) algorithm, known as the l₁-TSXKF, to mitigate the effect of non-Gaussian process noise. Considering the uncertainty in the system transition model, adaptive factors are introduced into the Kalman filter, known as the adaptive Kalman filter algorithm, to enhance the estimation accuracy by modifying the predicted state covariance. Then, the l₁ norm adaptive two-stage exogenous Kalman filter (l₁-ATSXKF) algorithm is designed by combining the advantages of the l₁ norm, adaptive factors and XKF in dealing with non-Gaussian process noise, model uncertainty and state/bias simultaneous estimation, respectively. Finally, the simulation results show that the proposed algorithms can reduce the influence of the non-Gaussian characteristics of the system and obtain high-precision attitude and bias estimation results quickly in the process of satellite attitude manoeuvre, which is conducive to the application of satellite in orbit.