This chapter presents a sound insight into the theory of unscented Kalman filtering for continuous–discrete stochastic systems. In particular, it gives precise definitions of the unscented transform and explores its expectation and covariance approximation properties, which create a solid theoretical background for designing advanced state estimation tools in the realm of nonlinear Gaussian systems of such sort. A special emphasis is placed on two unscented Kalman filtering design approaches and on their practical implementation aspects since these can expose instabilities in solving real-world state estimation tasks because of the mean and covariance approximation, discretization and rounding operations implemented in computer-based simulations. Under some circumstances, such numerical integration and round-off errors committed may affect severely the calculation and result in non-symmetric and/or indefinite covariance matrices yielded, which demolish the theoretical rigor of unscented Kalman filtering and can even fail this state estimation method itself. This chapter pays its particular attention to the issue of numerical stability and presents a remedy for treating such a covariance-matrix-symmetry-and-positivity-loss in the manner of square-root filtering. Two specific square-rooting techniques grounded on the Cholesky factorization and SVD are considered and justified, here. The theoretical analysis of unscented Kalman filters under exploration, which are summarized in the fashion of pseudo-codes situated in appendix of this chapter, is supported with illustrative calculations performed in MATLAB.
Unscented Kalman Filtering for Nonlinear Continuous–Discrete Stochastic Systems
Studies in Systems, Decision and Control
State Estimation for Nonlinear Continuous–Discrete Stochastic Systems ; Kapitel : 5 ; 411-577
07.09.2024
167 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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