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Reliability Assessment of an Unscented Kalman Filter by Using Ellipsoidal Enclosure Techniques

  • The Unscented Kalman Filter (UKF) is widely used for the state, disturbance, and parameter estimation of nonlinear dynamic systems, for which both process and measurement uncertainties are represented in a probabilistic form. Although the UKF can often be shown to be more reliable for nonlinear processes than the linearization-based Extended Kalman Filter (EKF) due to the enhanced approximation capabilities of its underlying probability distribution, it is not a priori obvious whether its strategy for selecting sigma points is sufficiently accurate to handle nonlinearities in the system dynamics and output equations. Such inaccuracies may arise for sufficiently strong nonlinearities in combination with large state, disturbance, and parameter covariances. Then, computationally more demanding approaches such as particle filters or the representation of (multi-modal) probability densities with the help of (Gaussian) mixture representations are possible ways to resolve this issue. To detect cases in a systematic manner that are not reliably handled by a standard EKF or UKF, this paper proposes the computation of outer bounds for state domains that are compatible with a certain percentage of confidence under the assumption of normally distributed states with the help of a set-based ellipsoidal calculus. The practical applicability of this approach is demonstrated for the estimation of state variables and parameters for the nonlinear dynamics of an unmanned surface vessel (USV).

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Metadaten
Author:Andreas RauhORCiDGND, Stefan WirtensohnORCiD, Patrick HoherORCiD, Johannes ReuterORCiD, Luc JaulinORCiD
DOI:https://doi.org/10.3390/math10163011
ISSN:2227-7390
Parent Title (English):Mathematics
Volume:10
Publisher:MDPI
Document Type:Article
Language:English
Year of Publication:2022
Release Date:2022/09/15
Tag:Unscented Kalman Filter; Ellipsoidal state estimation; Stochastic uncertainty; Bounded uncertainty; State and parameter estimation
Issue:16
Page Number:18
Article Number:3011
Institutes:Institut für Systemdynamik - ISD
Open Access?:Ja
Relevance:Peer reviewed Publikation in Master Journal List
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International