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We analyze the behavior of the extended Kalman filter as a state estimator for nonlinear deterministic systems. Using the direct method of Lyapunov, we prove that under certain conditions, the extended Kalman filter is an exponential observer, i.e., the dynamics of the estimation error is exponentially stable. Furthermore, we discuss a generalization of the Kalman filter with exponential data weighting to nonlinear systems.
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Рейф et al. (1999) studied this question.
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