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. Note to Practitioners—In the field of industrial automation, accurate state estimation is crucial for optimal control. Traditional Gaussian-based filters struggle with non-Gaussian noise prevalent in real-world applications such as aerospace tracking and smart manufacturing. This noise degrades estimation accuracy and system performance. Our work addresses this challenge by proposing the CD-MCCKF. By adaptively adjusting the kernel width, CD-MCCKF maintains high estimation accuracy without the need for trial-and-error tuning. In practical applications, this filter can significantly improve the reliability of the system in non-Gaussian environments by providing more accurate state estimation. Key insights include the proposal of an adaptive kernel width adjustment strategy and the theoretical proof of stochastic stability. However, the boundedness assumption and non-Gaussian noise in our work do not hold in all practical scenarios. Future research could explore the filter’s robustness in more complex environments and extend its applicability to high-dimensional systems, while also investigating its potential applications in various domains such as robotics, navigation systems, and intelligent manufacturing systems.