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Advanced Kalman Filtering Approaches to Bayesian State Estimation
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. (Automatic Control)ORCID iD: 0000-0002-4812-346X
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Bayesian state estimation is a flexible framework to address relevant problems at the heart of existing and upcoming technologies. Application examples are obstacle tracking for driverless cars and indoor navigation using smartphone sensor data. Unfortunately, the mathematical solutions of the underlying theory cannot be translated to computer code in general. Therefore, this thesis discusses algorithms and approximations that are related to the Kalman filter (KF).

Four scientific articles and an introduction with the relevant background on Bayesian state estimation theory and algorithms are included. Two articles discuss nonlinear Kalman filters, which employ the KF measurement update in nonlinear models. The numerous variants are presented in a common framework and the employed moment approximations are analyzed. Furthermore, their application to target tracking problems is discussed. A third article analyzes the ensemble Kalman filter (EnKF), a Monte Carlo implementation of the KF that has been developed for high-dimensional geoscientific filtering problems. The EnKF is presented in a simple KF framework, including its challenges, important extensions, and relations to other filters. Whereas the aforementioned articles contribute to the understanding of existing algorithms, a fourth article devises novel filters and smoothers to address heavy-tailed noise. The development is based on Student’s t distribution and provides simple recursions in the spirit of the KF. The introduction and articles are accompanied by extensive simulation experiments.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. , p. 81
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1832
National Category
Signal Processing Control Engineering Computational Mathematics Computer Sciences Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-134867DOI: 10.3384/diss.diva-134867ISBN: 9789176855782 (print)OAI: oai:DiVA.org:liu-134867DiVA, id: diva2:1077486
Public defence
2017-04-21, Visionen, B-huset, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2017-03-22 Created: 2017-02-27 Last updated: 2018-02-09Bibliographically approved
List of papers
1. Nonlinear Kalman Filters Explained: A Tutorial on Moment Computations and Sigma Point Methods
Open this publication in new window or tab >>Nonlinear Kalman Filters Explained: A Tutorial on Moment Computations and Sigma Point Methods
2016 (English)In: Journal of Advances in Information Fusion, ISSN 1557-6418, Vol. 11, no 1, p. 47-70Article in journal (Refereed) Published
Abstract [en]

Nonlinear Kalman filters are algorithms that approximately solve the Bayesian filtering problem by employing the measurement update of the linear Kalman filter (KF). Numerous variants have been developed over the past decades, perhaps most importantly the popular sampling based sigma point Kalman filters.In order to make the vast literature accessible, we present nonlinear KF variants in a common framework that highlights the computation of mean values and covariance matrices as the main challenge. The way in which these moment integrals are approximated distinguishes, for example, the unscented KF from the divided difference KF.With the KF framework in mind, a moment computation problem is defined and analyzed. It is shown how structural properties can be exploited to simplify its solution. Established moment computation methods, and their basics and extensions, are discussed in an extensive survey. The focus is on the sampling based rules that are used in sigma point KF. More specifically, we present three categories of methods that use sigma-points 1) to represent a distribution (as in the UKF); 2) for numerical integration (as in Gauss-Hermite quadrature); 3) to approximate nonlinear functions (as in interpolation). Prospective benefits and downsides are listed for each of the categories and methods, including accuracy statements. Furthermore, the related KF publications are listed.The theoretical discussion is complemented with a comparative simulation study on instructive examples.

Place, publisher, year, edition, pages
International society of information fusion, 2016
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-129231 (URN)
Available from: 2016-06-14 Created: 2016-06-14 Last updated: 2017-11-28Bibliographically approved
2. The Ensemble Kalman filter: a signal processing perspective
Open this publication in new window or tab >>The Ensemble Kalman filter: a signal processing perspective
2017 (English)In: EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, E-ISSN 1687-6180, article id 56Article, review/survey (Refereed) Published
Abstract [en]

The ensemble Kalman filter (EnKF) is a Monte Carlo-based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear, and non-Gaussian state estimation problems. Its ability to handle state dimensions in the order of millions has made the EnKF a popular algorithm in different geoscientific disciplines. Despite a similarly vital need for scalable algorithms in signal processing, e.g., to make sense of the ever increasing amount of sensor data, the EnKF is hardly discussed in our field. This self-contained review is aimed at signal processing researchers and provides all the knowledge to get started with the EnKF. The algorithm is derived in a KF framework, without the often encountered geoscientific terminology. Algorithmic challenges and required extensions of the EnKF are provided, as well as relations to sigma point KF and particle filters. The relevant EnKF literature is summarized in an extensive survey and unique simulation examples, including popular benchmark problems, complement the theory with practical insights. The signal processing perspective highlights new directions of research and facilitates the exchange of potentially beneficial ideas, both for the EnKF and high-dimensional nonlinear and non-Gaussian filtering in general.

Place, publisher, year, edition, pages
SPRINGER INTERNATIONAL PUBLISHING AG, 2017
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-139901 (URN)10.1186/s13634-017-0492-x (DOI)000406890100001 ()
Note

Funding Agencies|project Scalable Kalman Filters - Swedish Research Council

Available from: 2017-08-24 Created: 2017-08-24 Last updated: 2018-02-09
3. EKF/UKF Maneuvering Target Tracking using Coordinated Turn Models with Polar/Cartesian Velocity
Open this publication in new window or tab >>EKF/UKF Maneuvering Target Tracking using Coordinated Turn Models with Polar/Cartesian Velocity
2014 (English)In: 17th International Conference on Information Fusion (FUSION), 2014, Institute of Electrical and Electronics Engineers (IEEE), 2014, p. 1-8Conference paper, Published paper (Refereed)
Abstract [en]

Nonlinear Kalman filter adaptations such as extended Kalman filters (EKF) or unscented Kalman filters (UKF) provide approximate solutions to state estimation problems in nonlinear models. The algorithms utilize mean values and covariance matrices to represent the probability densities in the otherwise intractable Bayesian filtering equations. As a consequence, their estimation performance can show significant dependence on the choice of state coordinates. The here considered problem of tracking maneuvering targets using coordinated turn (CT) models is one practically relevant example: The velocity in the target state can either be formulated in Cartesian or polar coordinates. We extend a previous study to a broader range of CT models that allow for changes in target speed and turn rate, and investigate UKF as well as EKF variants in terms of their performance and sensitivity to noise parameters. The results advocate for the use of polar CT models.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2014
Keywords
Coordinated turn model; Maneuvering target tracking
National Category
Control Engineering Signal Processing
Identifiers
urn:nbn:se:liu:diva-108957 (URN)000363896100153 ()978-849012355-3 (ISBN)
Conference
17th International Conference on Information Fusion, Salamanca, Spain, July 7-10, 2014
Funder
Security LinkSwedish Foundation for Strategic Research
Available from: 2014-07-14 Created: 2014-07-14 Last updated: 2017-02-27

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