Adaptive ODE solvers in extended Kalman filtering algorithms

Extended Kalman Filtering by

Dynamical Systems and Adaptive Timestepping Ode Solvers

Initial value problems for ODEs are often solved numerically using adap-tive timestepping algorithms. We formulate a large class of such algorithms as discrete dynamical systems which are discontinuous and of higher dimension than the underlying ODE. By assuming suuciently strong nite-time convergence results on some neighbourhood of an attractor of the ODE we prove existence and upper semicont...

Distributed Adaptive High-Gain Extended Kalman Filtering for Nonlinear systems

In this work, we propose a distributed adaptive high-gain extended Kalman filtering approach for nonlinear systems. Specifically, we consider a class of nonlinear systems that are composed of several subsystems interacting with each other via their states. In the proposed approach, an adaptive high-gain extended Kalman filter is designed for each subsystem. The distributed Kalman filters commun...

Adaptive Kalman Filtering

The increased power of small computers makes the use of parameter estimation methods attractive. Such methods have a number of uses in analytical chemistry. When valid models are available, many methods work well, but when models used in the estimation are in error, most methods fail. Methods based on the Kalman filter, a linear recursive estimator, may be modified to perform parameter estimati...

Synchronization through Extended Kalman Filtering

We study the synchronization problem in discrete-time via an extended Kalman filter (EKF). That is, synchronization is obtained of transmitter and receiver dynamics in case the receiver is given via an extended Kalman filter that is driven by a noisy drive signal from the transmitter. Extensive computer simulations show that the filter is indeed suitable for synchronization of (noisy) chaotic t...