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Some Relations Between Extended and Unscented Kalman Filters
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1971-4295
2012 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 2, 545-555 p.Article in journal (Refereed) Published
Abstract [en]

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 system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.

Place, publisher, year, edition, pages
IEEE Signal Processing Society, 2012. Vol. 60, no 2, 545-555 p.
Keyword [en]
Extended Kalman filter (EKF), Transformations, Unscented Kalman filter (UKF)
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-75272DOI: 10.1109/TSP.2011.2172431ISI: 000299434300001OAI: diva2:505951
Swedish Research Council
Available from: 2012-02-27 Created: 2012-02-24 Last updated: 2015-09-22

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