On the Accuracy of the One-step UKF and the Two-step UKF
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2022-08-18
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Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
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Abstract
The most accurate version of the unscented
Kalman filter (UKF) involves the construction of two ensembles. To reduce computational cost, however, UKF is often
implemented without the second ensemble. This simplification
comes at a price, however, since, for linear systems, the one-step
variation of the two-step UKF does not specialize to the classical
Kalman filter, with an associated loss of accuracy. This paper
remedies this drawback by developing a modified one-step UKF
that recovers the classical Kalman filter for linear systems.
Numerical examples show that the modified one-step UKF also
recovers the accuracy of the two-step UKF in nonlinear systems
with linear outputs.