Observation-centered Kalman filters

TL;DR

This paper introduces observation-centered variants of Kalman filters, OCEKF and OCUKF, which outperform traditional EKF and UKF in certain nonlinear filtering scenarios, especially with small observation errors.

Contribution

The paper proposes two new nonlinear Kalman filters, OCEKF and OCUKF, that improve filtering performance in specific nonlinear problems compared to existing methods.

Findings

OCEKF and OCUKF outperform EKF and UKF in certain cases.

Performance depends on tuning parameters and observation error size.

The paper provides detailed analysis of the filters' behavior.

Abstract

Various methods have been proposed for the nonlinear filtering problem, including the extended Kalman filter (EKF), iterated extended Kalman filter (IEKF), unscented Kalman filter (UKF) and iterated unscented Kalman filter (IUKF). In this paper two new nonlinear Kalman filters are proposed and investigated, namely the observation-centered extended Kalman filter (OCEKF) and observation-centered unscented Kalman filter (OCUKF). Although the UKF and EKF are common default choices for nonlinear filtering, there are situations where they are bad choices. Examples are given where the EKF and UKF perform very poorly, and the IEKF and OCEKF perform well. In addition the IUKF and OCUKF are generally similar to the IEKF and OCEKF, and also perform well, though care is needed in the choice of tuning parameters when the observation error is small. The reasons for this behaviour are explored in detail.