# 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} }

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… Expand

## 5,208 Citations

The square-root unscented Kalman filter for state and parameter-estimation

- Mathematics2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221)
- 2001

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

- Engineering
- 2011

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

- Engineering
- 2017

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

- MathematicsArXiv
- 2017

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

- Mathematics
- 2013

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

- Engineering
- 2009

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

- Engineering, Mathematics
- 2014

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

- Mathematics
- 2012

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

- MathematicsProceedings 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

- EngineeringSensors
- 2020

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.

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