Toward Consistent and Efficient Map-based Visual-inertial Localization: Theory Framework and Filter Design

TL;DR

This paper introduces a novel invariant EKF and Schmidt filter framework for map-based visual-inertial localization, ensuring consistency, efficiency, and proper observability handling in both theoretical and practical scenarios.

Contribution

It proposes a new Lie group-based invariant EKF, a Schmidt filter for map uncertainty, and an observability-constrained technique, advancing the state-of-the-art in visual-inertial localization.

Findings

The invariant EKF maintains correct observability properties.

The Schmidt filter effectively accounts for map uncertainty.

The system achieves high consistency, accuracy, and efficiency in experiments.

Abstract

This paper focuses on designing a consistent and efficient filter for map-based visual-inertial localization. First, we propose a new Lie group with its algebra, based on which a novel invariant extended Kalman filter (invariant EKF) is designed. We theoretically prove that, when we do not consider the uncertainty of the map information, the proposed invariant EKF can naturally maintain the correct observability properties of the system. To consider the uncertainty of the map information, we introduce a Schmidt filter. With the Schmidt filter, the uncertainty of the map information can be taken into consideration to avoid over-confident estimation while the computation cost only increases linearly with the size of the map keyframes. In addition, we introduce an easily implemented observability-constrained technique because directly combining the invariant EKF with the Schmidt filter cannot maintain the correct observability properties of the system that considers the uncertainty of the map information. Finally, we validate our proposed system's high consistency, accuracy, and efficiency via extensive simulations and real-world experiments.