Cubature Kalman filters for continuous-time dynamic models Part I: Solutions discretizing the Langevin equation

The dynamics of many physical systems (maneuvering aircraft, satellites, etc.) are most easily described using nonlinear continuous-time differential equations, to which a stochastic process noise is added to handle unknown perturbations. Often, the magnitude of the process noise in a system depends upon the state, rendering the noise non-additive. This paper presents a variant of the cubature Kalman filter that handles the nonlinear continuous-time dynamics through stochastic discretization of the Langevin equation. A solution based on the Euler-Maruyama expansion for general noise is given, as well as a solution using an order 1.5 stochastic Runge Kutta method for additive noise. Only derivative-free techniques are considered, simplifying the utilizing of the algorithms. Additionally, only square-root filtering techniques are considered to provide good numerical stability.