On the Accuracy of the One-step UKF and the Two-step UKF

TL;DR

This paper introduces a modified one-step UKF that matches the classical Kalman filter's accuracy for linear systems and approaches the two-step UKF's accuracy in nonlinear systems with linear outputs, reducing computational costs.

Contribution

The paper develops a modified one-step UKF that recovers the classical Kalman filter for linear systems and matches the two-step UKF's accuracy in certain nonlinear systems.

Findings

Modified one-step UKF recovers classical Kalman filter accuracy for linear systems.

Modified one-step UKF achieves accuracy comparable to two-step UKF in specific nonlinear systems.

Numerical examples validate the improved accuracy of the proposed method.

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.