Proceedings ArticleDOI
Modification of the extended Kalman filter with an additive term of instability
K. Reif,F. Sonnemann,Rolf Unbehauen +2 more
- Vol. 4, pp 4058-4059
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TLDR
The purpose of this modification is two-fold: first the degree of stability can be assigned in advance and secondly this modification allows an effective treatment of the nonlinearities.Abstract:
In this paper we propose an observer for nonlinear systems similar to the extended Kalman filter. The observer gain is computed by a Riccati differential equation assuming a more instable system. The purpose of this modification is two-fold: first the degree of stability can be assigned in advance and secondly this modification allows an effective treatment of the nonlinearities.read more
Citations
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Journal ArticleDOI
Stochastic stability of the discrete-time extended Kalman filter
TL;DR: It is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough.
Journal ArticleDOI
The extended Kalman filter as an exponential observer for nonlinear systems
K. Reif,Rolf Unbehauen +1 more
TL;DR: Using the direct method of Lyapunov, it is proved that under certain conditions, the extended Kalman filter is an exponential observer, i.e., the dynamics of the estimation error is exponentially stable.
Journal ArticleDOI
A strong tracking extended Kalman observer for nonlinear discrete-time systems
Mohamed Boutayeb,D. Aubry +1 more
TL;DR: It is shown that the decreasing Lyapunov function condition leads to a linear matrix inequality (LMI) problem, which points out the connection between a good convergence behavior of the EKO and the instrumental matrices R/ sub k/ and Q/sub k/.
Journal ArticleDOI
Nonlinear state observation using H/sub /spl infin//-filtering Riccati design
TL;DR: The authors propose an observer for continuous-time nonlinear systems and prove that under certain conditions the proposed observer is an exponential observer by choosing an appropriate Lyapunov function.
Proceedings ArticleDOI
The over-extended Kalman filter - don't use it!
D.F. Bizup,D.E. Brown +1 more
TL;DR: In this paper, an alternative linearization of range rate that is not a function of the position elements is derived, which can improve a tracking system's velocity estimates without risk to its position estimates.
References
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Book
Applied Optimal Estimation
TL;DR: This is the first book on the optimal estimation that places its major emphasis on practical applications, treating the subject more from an engineering than a mathematical orientation, and the theory and practice of optimal estimation is presented.
Journal ArticleDOI
Nonlinear Observers—A State-of-the-Art Survey
E. A. Misawa,J.K. Hedrick +1 more
TL;DR: In this article, the state-of-the-art of nonlinear state estimators or observers is reviewed and the use of these observers in real time nonlinear compensators is evaluated in terms of their on-line computational requirements.
Journal ArticleDOI
Exponential observers for nonlinear dynamic systems
TL;DR: An observer theory is presented for nonlinear dynamic systems and two theorems are presented to give conditions on the system structure such that there exists an exponential observer for the given system.
Journal ArticleDOI
Brief Paper: An EKF-Based Nonlinear Observer with a Prescribed Degree of Stability
TL;DR: It is proved that the proposed observer based on a slight modification of the extended Kalman filter is an exponential observer and is applied to the highly nonlinear flux and angular velocity estimation problem for induction machines.