Computational aspects of continuous-discrete extended Kalman-filtering
This paper elaborates how the time update of the continuous-discrete extended Kalman-Filter (EKF) can be computed in the most efficient way. The specific structure of the EKF-moment differential equations leads to a new Taylor-Heun-approximation of the nonlinear vector field. Furthermore, the order of consistency and stability behavior of the outlined procedure is investigated. The results are incorporated into an algorithm with adaptive controlled step size, assuring a fixed numerical precision with minimal computational effort. Additionally, the upper bound of the step size is monitored continuously in order to guarantee positive semidefiniteness of the state error covariance matrix.
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