Parameter Estimation Using Kalman Filters with Constraints

@article{Walker2006ParameterEU,
  title={Parameter Estimation Using Kalman Filters with Constraints},
  author={David M. Walker},
  journal={Int. J. Bifurc. Chaos},
  year={2006},
  volume={16},
  pages={1067-1078}
}
  • D. Walker
  • Published 1 April 2006
  • Mathematics
  • Int. J. Bifurc. Chaos
We suggest incorporating dynamical information such as locations of unstable fixed points into parameter estimation algorithms in order to improve the method of reconstructing dynamics from time series data. We show how the process of reconstruction using nonlinear filters such as the extended Kalman filter can be easily modified to take advantage of the additional information. We demonstrate the methods using data from two systems exhibiting chaotic dynamics — the Chua circuit and Chen's… 

System Identification using Constrained Kalman Filters

TLDR
It is shown how the process of reconstruction using the extended or iterated Kalman filter can be easily modified to include the additional information, and the models reconstructed by using constraints can better approximate the unstable fixed point structure of the underlying systems.

Detecting Unstable Fixed Points Using Kalman Filters With Constraints

  • D. WalkerM. Small
  • Mathematics
    IEEE Transactions on Circuits and Systems I: Regular Papers
  • 2006
TLDR
A novel application of the extended Kalman filter for detecting unstable periodic orbits of dynamical systems from experimental time series using local polynomial functions and candidate fixed-point values are considered as parameters to be estimated.

Constrained kalman filtering for nonlinear dynamical systems with observation losses

In this paper, the constrained extended Kalman filter (EKF) is discussed for nonlinear dynamical systems when observations are available according to a Bernoulli process. First, by using EKF

Constrained State Estimation for Nonlinear Systems with Unknown Input

This paper extends the problem of state estimation for linear discrete-time systems with unknown input to the nonlinear systems. Based on physical consideration, the constraints of state are also

Robust two-stage Kalman filtering with state constraints

In this note, the problem of state estimation is solved for uncertain linear dynamical systems where prior knowledge about the systems' states is available in the form of equality constraints. Gain

Conservative Term Constrained Kalman Filter for Autonomous Orbit Determination

TLDR
Using Lagrangian multiplier techniques, the conserved terms of orbit motion are incorporated into the estimation routines to reconstruct the Kalman filter, and the orthogonal and multipartial-norm-constrained Kalman filters are developed for the satellite in circular orbit and eccentric ones, respectively.

Steady-state performance constraints for dynamical models based on RBF networks

Asymptotic Identification of Bifurcation Parameters in a Three-Dimensional Discrete System with Chaotic Behavior

TLDR
It is shown that the identification error converges locally asymptotically to zero and therefore the bifurcation parameters are asymPTotically identified.

Constrained two-stage Kalman filter for target tracking

TLDR
This note investigates the problem of state estimation for an uncertain linear system with a priori known information in the form of equality constraints and develops a robust two-stage Kalman filter satisfying state constraints.

References

SHOWING 1-10 OF 40 REFERENCES

Reconstructing nonlinear dynamics by extended Kalman filtering

We investigate the use of the extended Kalman filter as a tool for the parameter estimation of radial basis function models. We show that the method is best used as an add-on to other estimation

Kalman Filtering of Time Series Data

We introduce the method of Kalman filtering of time series data for linear systems and its nonlinear variant the extended Kalman filter. We demonstrate how the filter can be applied to nonlinear

Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks

TLDR
These simulations suggest that recurrent controller networks trained by Kalman filter methods can combine the traditional features of state-space controllers and observers in a homogeneous architecture for nonlinear dynamical systems, while simultaneously exhibiting less sensitivity than do purely feedforward controller networks to changes in plant parameters and measurement noise.

Extracting unstable periodic orbits from chaotic time series data

A general nonlinear method to extract unstable periodic orbits from chaotic time series is proposed. By utilizing the estimated local dynamics along a trajectory, we devise a transformation of the

On selecting models for nonlinear time series

Kalman Filtering and Neural Networks

TLDR
This book takes a nontraditional nonlinear approach and reflects the fact that most practical applications are nonlinear.

A fully Kalman-trained radial basis function network for nonlinear speech modeling

  • M. Birgmeier
  • Computer Science
    Proceedings of ICNN'95 - International Conference on Neural Networks
  • 1995
TLDR
The network is applied to the task of learning the dynamics of speech signals obtained from sustained vowels, and subsequently used to re-synthesize these vowels autonomously.

Minimum description length neural networks for time series prediction.

  • M. SmallC. Tse
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2002
TLDR
This work proposes an alternative scheme that has previously been described for radial basis functions (RBF) for artificial neural networks (ANN), and shows that fundamental differences between ANN and RBF make application of this scheme to ANN nontrivial.

A new look at the statistical model identification

The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as

Embedding as a modeling problem