In this note, stability of the projection-based constrained discrete time extended Kalman filter (EKF) when applied to deterministic nonlinear systems has been studied. It is proved that, like the unconstrained case, under certain assumptions, the EKF with state equality constraints is an exponential observer, i.e., it keeps the dynamics of its estimation error exponentially stable. Also, it has been shown that a simple modification to the general definition of the EKF with exponential weighting increases the filter's degree of stability and convergence speed with or without state constraints.Index Terms-Asymptotic stability, Kalman filtering, nonlinear systems, state equality constraints.

In this paper the ingestion and subsequent metabolism of a drug in a given individual, are investigated through the use of compartmental models. An adaptive formulation of the widely used extended Kalman filter (EKF) has been derived in order to solve the resulting nonlinear estimation problem at the output of the compartments. The adaptive EKF employs a forgetting factor to emphasize artificially the effect of current data by exponentially weighting the observations. The dependence of EKF's performance on the selection of appropriate values of the arbitrary matrices, the measurement covariance R and the process noise covariance Q has been demonstrated through simulations. With the appropriate choice of the matrices the EKF provides a very useful tool for online estimation of both the state and the parameters.

Cataloged from PDF version of article.The paper has two parts. In the first part, the output gap and potential output series for the Turkish economy are derived within the context of a non-linear state space model, where the extended Kalman filter emerges as the estimation methodology. Such a methodology allows for time-varying parameters to decompose output into trend and cyclical components. The results imply that both the parameters in the model and the derived series are fairly reasonable and consistent with the path that the Turkish economy followed in the last fifteen years. In the second part, the relation between inflation and the output gap is analyzed. It is found that inflation and the output gap are not positively associated, contradicting studies that view demand side forces as the primary determinants of inflation in Turkey. (c) 2004 Elsevier B.V. All rights reserved

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Abstract:In this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non-linear discrete-time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter's stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable. The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.