This chapter presents a sound insight into the theory of Kalman filtering with deterministically sampled mean and covariance for continuous–discrete stochastic systems. In particular, it introduces the notion of universal expectation and covariance calculation principle inspired by the quadrature and cubature rule approximations of Gaussian-weighted integrals arisen as well as by the UT elaborated in Chap. 5. It creates a solid theoretical background for designing advanced state estimation tools in the realm of all existing or future Gaussian filters of such sort. A special emphasis is placed on two Kalman-filtering-with-deterministically-sampled-mean-and-covariance-design-approaches and on their practical implementation and use aspects since these can expose instabilities in solving real-world state estimation tasks because of the expectation and covariance approximation, discretization and rounding operations involved 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 covariances yielded, which demolish the theoretical rigor of Kalman filtering with deterministically sampled mean and covariance and can even fail such state estimation methods. This chapter pays its particular attention to the issue of numerical stability and presents a remedy for treating this covariance-matrix-symmetry-and-positivity-loss in the form of square-root filtering. Two specific square-rooting schemes grounded on the Cholesky factorization and SVD are explored and justified, here. The theoretical analysis of Kalman filtering methods with deterministically sampled mean and covariance, which are summarized in the kind of pseudo-codes placed in appendix of this chapter, is supported with illustrative calculations performed in MATLAB.
Gaussian Filtering with Deterministically Sampled Expectation and Covariance
Studies in Systems, Decision and Control
State Estimation for Nonlinear Continuous–Discrete Stochastic Systems ; Kapitel : 6 ; 579-737
07.09.2024
159 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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