Novel iterative cubature Kalman filters under maximum correntropy criterion for the robust state estimation

The cubature Kalman filter (CKF) based on maximum correntropy criterion (MCC) is robust under non-Gaussian noises, but it may encounter numerical problems when there are large outliers. First, based on the MCC and weighted least square (WLS) methods, a new cost function is introduced to calculate the state and covariance updates, which can better solve numerical problems caused by large outliers. Then, a nonlinear measurement function is used, and the measurement information is updated through the latest iterative values, which can obtain more accurate results under various non-Gaussian noises. In addition, the Gauss-Newton, Levenberg-Marquardt, and Quasi-Newton methods are used, and three iterative algorithms named GN-IMCC-CKF, LM-IMCC-CKF, and QN-IMCC-CKF are respectively derived for the updating steps. Compared with the existing algorithms, the simulation results of two classical models show that the proposed algorithms have better numerical stability and estimation accuracy under non-Gaussian systems.