Stochastic Stability of the Continuous-Discrete Maximum Correntropy Cubature Kalman Filter

This paper investigates the stochastic stability of the continuous-discrete maximum correntropy cubature Kalman filter (CD-MCCKF), which is developed by embedding the maximum correntropy criterion as an optimization strategy into the continuous-discrete filtering architecture. By assuming that the relevant functions satisfy certain properties, we first establish the convergence of the employed numerical method and fixed-point iteration technique. Subsequently, combined with the findings on the error covariance boundary, it is proved that the estimation error of CD-MCCKF keeps mean-square bounded under specific conditions. To validate this stability analysis finding and evaluate the filtering performance, we conduct a classical case study. Simulation results confirm that CD-MCCKF not only maintains bounded estimation errors, but also surpasses the conventional continuous-discrete filters in terms of accuracy and convergence.