A Systematization of the Unscented Kalman Filter Theory
@article{Menegaz2015ASO, title={A Systematization of the Unscented Kalman Filter Theory}, author={Henrique Marra Menegaz and Jo{\~a}o Yoshiyuki Ishihara and Geovany de Ara{\'u}jo Borges and Alessandro N. Vargas}, journal={IEEE Transactions on Automatic Control}, year={2015}, volume={60}, pages={2583-2598} }
In this paper, we propose a systematization of the (discrete-time) Unscented Kalman Filter (UKF) theory. We gather all available UKF variants in the literature, present corrections to theoretical inconsistencies, and provide a tool for the construction of new UKF's in a consistent way. This systematization is done, mainly, by revisiting the concepts of Sigma-Representation, Unscented Transformation (UT), Scaled Unscented Transformation (SUT), UKF, and Square-Root Unscented Kalman Filter (SRUKF…
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References
SHOWING 1-10 OF 77 REFERENCES
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…
Some Relations Between Extended and Unscented Kalman Filters
- MathematicsIEEE Transactions on Signal Processing
- 2012
It is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model, and a less cited version of the EKf based on a second-order Taylor expansion is shown to be quite closely related to UKF.
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.
Unscented Kalman filtering for additive noise case: augmented versus nonaugmented
- Computer ScienceIEEE Signal Processing Letters
- 2005
Under the condition of n+/spl kappa/=const, the basic difference between the unscented Kalman filtering for the nonlinear dynamic systems with additive process and measurement noises is that the augmented UKF draws a sigma set only once within a filtering recursion, while the nonaugmented UKF has to redraw a new set of sigma points to incorporate the effect of additive process noise.
On nonlinear transformations of stochastic variables and its application to nonlinear filtering
- Mathematics2008 IEEE International Conference on Acoustics, Speech and Signal Processing
- 2008
A class of nonlinear transformation-based filters (NLTF) for state estimation is proposed, which includes first (TT1) and second (TT2) order Taylor expansions, the unscented transformation (UT), and the Monte Carlo transformation (MCT) approximation.
Aspects and comparison of matrix decompositions in unscented Kalman filter
- Engineering2013 American Control Conference
- 2013
It is shown that different decompositions may lead to significant differences in quality of approximations provided by the transform, which is a core of the unscented Kalman filter.
On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear Systems
- MathematicsIEEE Transactions on Automatic Control
- 2007
This paper considers the application of the unscented Kalman filter (UKF) to continuous-time filtering problems, where both the state and measurement processes are modeled as stochastic differential…
Cubature Kalman Filtering for Continuous-Discrete Systems: Theory and Simulations
- MathematicsIEEE Transactions on Signal Processing
- 2010
Results indicate that the CD-CKF markedly outperforms existing continuous-discrete filters in the context of radar in two respects- high dimensionality of the state and increasing degree of nonlinearity.
An improved square root unscented Kalman filter for projectile's attitude determination
- Engineering2010 5th IEEE Conference on Industrial Electronics and Applications
- 2010
In this paper, considering the performance of short-time working, inertial flight and high impulse of launch for projectile, an improved square root unscented Kalman filter (UKF) is used. According…
New extension of the Kalman filter to nonlinear systems
- Mathematics, EngineeringDefense, Security, and Sensing
- 1997
It is argued that the ease of implementation and more accurate estimation features of the new filter recommend its use over the EKF in virtually all applications.