Affine EKF: Exploring and Utilizing Sufficient and Necessary Conditions for Observability Maintenance to Improve EKF Consistency

TL;DR

This paper introduces the affine EKF framework that maintains observability conditions to improve EKF consistency in state estimation, validated through theoretical proofs and SLAM experiments.

Contribution

It provides a theoretical foundation for observability maintenance and proposes a novel affine EKF method that ensures consistency in various SLAM scenarios.

Findings

Affine EKF naturally maintains correct observability.

The proposed method improves EKF consistency in SLAM.

Validated through Monte Carlo simulations.

Abstract

Inconsistency issue is one crucial challenge for the performance of extended Kalman filter (EKF) based methods for state estimation problems, which is mainly affected by the discrepancy of observability between the EKF model and the underlying dynamic system. In this work, some sufficient and necessary conditions for observability maintenance are first proved. We find that under certain conditions, an EKF can naturally maintain correct observability if the corresponding linearization makes unobservable subspace independent of the state values. Based on this theoretical finding, a novel affine EKF (Aff-EKF) framework is proposed to overcome the inconsistency of standard EKF (Std-EKF) by affine transformations, which not only naturally satisfies the observability constraint but also has a clear design procedure. The advantages of our Aff-EKF framework over some commonly used methods are demonstrated through mathematical analyses. The effectiveness of our proposed method is demonstrated on three simultaneous localization and mapping (SLAM) applications with different types of features, typical point features, point features on a horizontal plane and plane features. Specifically, following the proposed procedure, the naturally consistent Aff-EKFs can be explicitly derived for these problems. The consistency improvement of these Aff-EKFs are validated by Monte Carlo simulations.