This chapter presents a brief insight into the theory of Kalman filtering for discrete-time linear stochastic models. In particular, it gives precise definitions and explains all basic issues and notions of state estimation in Gauss–Markov stochastic processes. A special emphasis is placed on implementation aspects of the Kalman filtering since it can expose instabilities in solving real-world state estimation tasks because of round-off operations implemented in computer-based simulations. Under some circumstances, such round-off may affect severely the calculation and result in non-symmetric and/or indefinite covariance matrices yielded, which compromise the theoretical rigor of the Kalman filtering and produce state estimates of poor accuracy. 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 fashion of square-root filtering methods. Two square-rooting schemes are explored and justified, here. The theoretical analysis of Kalman filters under consideration, which are summarized in the form of pseudo-codes situated in the appendix of this chapter, is accompanied with illustrative calculations performed in MATLAB.
Kalman Filtering for Linear Stochastic Modeling Tasks
Studies in Systems, Decision and Control
State Estimation for Nonlinear Continuous–Discrete Stochastic Systems ; Kapitel : 3 ; 229-301
07.09.2024
73 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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