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

Andreas Rauh (), Stefan Wirtensohn, Patrick Hoher, Johannes Reuter and Luc Jaulin
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Andreas Rauh: Group: Distributed Control in Interconnected Systems, Department of Computing Science, Carl von Ossietzky Universität Oldenburg, D-26111 Oldenburg, Germany
Stefan Wirtensohn: Institute of System Dynamics, University of Applied Sciences Konstanz, D-78462 Konstanz, Germany
Patrick Hoher: Institute of System Dynamics, University of Applied Sciences Konstanz, D-78462 Konstanz, Germany
Johannes Reuter: Institute of System Dynamics, University of Applied Sciences Konstanz, D-78462 Konstanz, Germany
Luc Jaulin: Lab-STICC, ENSTA Bretagne, 29806 Brest, France

Mathematics, 2022, vol. 10, issue 16, 1-18

Abstract: 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).

Keywords: Unscented Kalman Filters; ellipsoidal state estimation; stochastic uncertainty; bounded uncertainty; state and parameter estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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