Cubature Kalman Filters for Continuous-Time Dynamic Models Part II: A Solution Based on Moment Matching

High-order deterministic Runge-Kutta methods are often used to predict forward continuous-time nonlinear differential equations describing physical systems. However, the stochastic nature of dynamic models in practical systems necessitates other methods for propagating forward the uncertain probability density function of a target state over time. This paper presents a variant of the cubature Kalman filter for nonlinear continuous-time dynamic models that uses a moment matching technique to predict forward the target state and covariance matrix. In this formulation, deterministic Runge-Kutta algorithms can be used for state prediction. Unlike previous work, the formulation presented is derived to handle non-additive process noise.