# Some Relations Between Extended and Unscented Kalman Filters

@article{Gustafsson2012SomeRB, title={Some Relations Between Extended and Unscented Kalman Filters}, author={Fredrik K. Gustafsson and Gustaf Hendeby}, journal={IEEE Transactions on Signal Processing}, year={2012}, volume={60}, pages={545-555} }

The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the…

## 271 Citations

On Iterative Unscented Kalman Filter using Optimization

- Engineering2019 22th International Conference on Information Fusion (FUSION)
- 2019

Six iterated UKF (IUKF) variations are deriving based on two cost functions and three optimization algorithms, which show that IUKF algorithms can be used as a derivative free alternative to IEKF, and provide insights about the different design choices available in IukF algorithms.

An efficient implementation of the second order extended Kalman filter

- Computer Science14th International Conference on Information Fusion
- 2011

A numerical algorithm which is based on an extended set of sigma points (compared to the UKF) that needs neither Jacobian nor Hessian (or numerical approximations of these) and scales as n4x, which is an order of magnitude better than the EKF2 algorithm presented in literature.

Alternative framework for the iterated unscented Kalman filter

- MathematicsIET Signal Process.
- 2017

A new framework is proposed based on the statistical linear regression (SLR) perspective of the UT and the framework of the iterated extended Kalman filter (IEKF) implying that in each iteration, the linearised equation is used to correct the a priori estimate rather than the latest estimate.

A Hybrid, Coupled Approach to the Continuous-Discrete Kalman Filter

- EngineeringIEEE Control Systems Letters
- 2021

A novel approach to continuous-discrete Kalman filtering that uses unscented transforms to extract a pair of matrices, each made up of a linear combination of derivatives, that are used in its place, making the process of state estimation for stiff systems more efficient.

Do the Contemporary Cubature and Unscented Kalman Filtering Methods Outperform Always the Traditional Extended Kalman Filter?

- EngineeringArXiv
- 2016

Truncated Unscented Kalman Filtering

- MathematicsIEEE Transactions on Signal Processing
- 2012

A filtering algorithm to approximate the first two moments of the posterior probability density function (PDF) and is referred to as truncated unscented KF, which can vastly improve the performance of the conventional Kalman filter.

Comparison of stochastic integration filter with the Unscented Kalman filter for maneuvering targets

- EngineeringNAECON 2014 - IEEE National Aerospace and Electronics Conference
- 2014

Sigma-Point Filtering (SPF) has become popular to increase the accuracy in estimation of tracking parameters such as the mean and variance. A recent development in SPF is the stochastic integration…

Correlational inference-based adaptive unscented Kalman filter with application in GNSS/IMU-integrated navigation

- EngineeringGPS Solutions
- 2018

Simulation and a field test prove that the AUKF outperforms the conventional UKF regarding positioning and velocity estimates, as well as the innovation-based adaptive estimation (IAE) method, which has similar performance with IAE-based A UKF, but requires less computation time.

A Systematization of the Unscented Kalman Filter Theory

- MathematicsIEEE Transactions on Automatic Control
- 2015

With the proposed systematization of the Unscented Kalman Filter theory, the symmetric sets of sigma points in the literature are formally justified, and the proposed SRUKF has improved computational properties when compared to state-of-the-art methods.

The Level Set Kalman Filter for State Estimation of Continuous-Discrete Systems

- Computer ScienceIEEE Transactions on Signal Processing
- 2022

The LSKF improves the time-update step compared to existing methods, such as the continuous-discrete cubature Kalman filter (CD-CKF), by reformulating the underlying Fokker-Planck equation as an ordinary differential equation for the Gaussian, thereby avoiding the need for the explicit expression of the higher derivatives.

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