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Computational aspects of continuous–discrete extended Kalman-filtering

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Abstract

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 hybrid integration algorithm, featuring a new Taylor–Heun-approximation of the nonlinear vector field and a modified Gauss–Legendre-scheme, generating positive semidefinite solutions for the state error covariance. 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.

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  1. Department for Applied Statistics, FernUniversität in Hagen, Universitätsstraße 41, 58097, Hagen, Germany

    Thomas Mazzoni

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  1. Thomas Mazzoni
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Mazzoni, T. Computational aspects of continuous–discrete extended Kalman-filtering. Comput Stat 23, 519–539 (2008). https://doi.org/10.1007/s00180-007-0094-4

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  • DOI: https://doi.org/10.1007/s00180-007-0094-4

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