New extension of the Kalman filter to nonlinear systems

@inproceedings{Julier1997NewEO,
  title={New extension of the Kalman filter to nonlinear systems},
  author={Simon J. Julier and Jeffrey K. Uhlmann},
  booktitle={Defense, Security, and Sensing},
  year={1997}
}
  • S. Julier, J. Uhlmann
  • Published in
    Defense, Security, and…
    28 July 1997
  • Mathematics, Engineering
The Kalman Filter (KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. [] Key Method Using the principle that a set of discretely sampled points can be used to parameterize mean and covariance, the estimator yields performance equivalent to the KF for linear systems yet generalizes elegantly to nonlinear systems without the linearization steps required by the EKF. We show analytically that the expected performance of the new…
The square-root unscented Kalman filter for state and parameter-estimation
  • Rudolph van der Merwe, E. Wan
  • Mathematics
    2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221)
  • 2001
TLDR
The square-root unscented Kalman filter (SR-UKF) is introduced which is also O(L/sup 3/) for general state estimation and O( L/sup 2/) for parameter estimation and has the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances.
Application of Sigma Point Kalman Filter in
The Extended Kalman Filter has been one of the most widely used methods for estimation of non-linear systems through the linearization of non-linear models. In recent several decades people have
Adaptive cubature Kalman filter based on the variance-covariance components estimation
Although the Kalman filter (KF) is widely used in practice, its estimated results are optimal only when the system model is linear and the noise characteristics of the system are already exactly
Kalman Filter and its Modern Extensions for the Continuous-time Nonlinear Filtering Problem
TLDR
The issue of non-uniqueness of the filter update formula is discussed, a novel approximation algorithm based on ideas from optimal transport and coupling of measures is formulates and performance of this and other algorithms is illustrated.
Application of the Unscented Kalman Filtering to Parameter Estimation
TLDR
This chapter illustrates the application of one approach to deal with nonlinear model dynamics, the so-called unscented Kalman filter, and shows how some of the tools for model validation discussed in other chapters of this volume can be used to improve the estimation process.
Adaptive Robust Extended Kalman Filter
The extended Kalman filter (EKF) is one of the most widely used methods for state estimation with communication and aerospace applications based on its apparent simplicity and tractability (Shi et
Use of Extended Kalman Filter in Estimation of Attitude of a NanoSatellite
State estimation theory is one of the best mathematical approaches to analyze the changes in the states of a system or a process. The state of the system is defined by a set of variables that provide
Nonlinear filtering methodologies for parameter estimation
TLDR
A comprehensive comparison study of five filtering methods in the estimation of the state of the system and its unknown model parameters to give recommendations as to which filter is best under the various conditions.
The unscented Kalman filter for nonlinear estimation
  • E. Wan, R. Van Der Merwe
  • Mathematics
    Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373)
  • 2000
This paper points out the flaws in using the extended Kalman filter (EKE) and introduces an improvement, the unscented Kalman filter (UKF), proposed by Julier and Uhlman (1997). A central and vital
Extended Kalman Filter with Reduced Computational Demands for Systems with Non-Linear Measurement Models
TLDR
The paper describes a practical simulation-based method of determining the threshold and the accuracy of the filter for various threshold values was tested for simplified models of radar systems.
...
...

References

SHOWING 1-10 OF 32 REFERENCES
A comparison of several nonlinear filters for reentry vehicle tracking
This paper compares the performance of several non-linear filters for the real-time estimation of the trajectory of a reentry vehicle from its radar observations. In particular, it examines the
A new approach for filtering nonlinear systems
TLDR
A new recursive linear estimator for filtering systems with nonlinear process and observation models which can be transformed directly by the system equations to give predictions of the transformed mean and covariance is described.
Novel approach to nonlinear/non-Gaussian Bayesian state estimation
TLDR
An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters, represented as a set of random samples, which are updated and propagated by the algorithm.
NONLINEAR FILTERING BY APPROXIMATION OF THE A POSTERIORI DENSITY
TLDR
The problem of estimating from noisy measurement data the state of a dynamical system described by non-linear difference equations is considered and a Bayesian approach is suggested in which the density function for the state conditioned upon the available measurement data is computed recursively.
Suboptimal state estimation for continuous-time nonlinear systems from discrete noisy measurements
This paper presents the derivation of the dynamical equations of a second-order filter which estimates the states of a non-linear plant on the basis of discrete noisy measurements. The filter
Approximations to optimal nonlinear filters
  • H. Kushner
  • Mathematics
    IEEE Transactions on Automatic Control
  • 1967
Let the signal and noise processes be given as solutions to nonlinear stochastic differential equations. The optimal filter for the problem, derived elsewhere, is usually infinite dimensional.
Statistically Linearized Estimation of Reentry Trajectories
TLDR
It is found that a filter based on the technique of statistical linearization performs better than the extended Kalman in this application, believed to be the first application of the statistically linearized filter to a practical dynamics problem.
Tracking with debiased consistent converted measurements versus EKF
TLDR
This method is compared with the mixed coordinates EKF approach as well as a previous converted measurement approach which is an acceptable approximation only for moderate cross-range errors and is shown to be more accurate in terms of position and velocity errors.
Adaptive model architecture and extended Kalman-Bucy filters
In radar systems, extended Kalman-Bucy filters (EKBFs) are used to estimate state vectors of objects in track. Filter models accounting for fundamental aerodynamic forces on reentry vehicles are well
A consistent, debiased method for converting between polar and Cartesian coordinate systems
TLDR
It is shown that the performance of the algorithm is comparable to that of fourth order filters, thus ensuring consistency even when the uncertainty is large, and the algorithm can be extended to incorporate higher order information.
...
...