CT-ESKF: A General Framework of Covariance Transformation-Based Error-State Kalman Filter

TL;DR

This paper introduces the CT-ESKF framework that unifies error-state Kalman filters using covariance transformation, improving navigation accuracy in systems with global and body-frame observations.

Contribution

It reveals the covariance equivalence between InEKF and EKF and proposes a unified framework for enhanced error-state Kalman filtering algorithms.

Findings

CT-ESKF outperforms InEKF and EKF in navigation tasks.

Covariance transformation improves filter consistency and accuracy.

Unified framework enables development of novel filtering algorithms.

Abstract

Invariant extended Kalman filter (InEKF) possesses excellent trajectory-independent property and better consistency compared to conventional extended Kalman filter (EKF). However, when applied to scenarios involving both global-frame and body-frame observations, InEKF may fail to preserve its trajectory-independent property. This work introduces the concept of equivalence between error states and covariance matrices among different error-state Kalman filters, and shows that although InEKF exhibits trajectory independence, its covariance propagation is actually equivalent to EKF. A covariance transformation-based error-state Kalman filter (CT-ESKF) framework is proposed that unifies various error-state Kalman filtering algorithms. The framework gives birth to novel filtering algorithms that demonstrate improved performance in integrated navigation systems that incorporate both global and body-frame observations. Experimental results show that the EKF with covariance transformation outperforms both InEKF and original EKF in a representative INS/GNSS/Odometer integrated navigation system.