MSCEqF: A Multi State Constraint Equivariant Filter for Vision-aided Inertial Navigation (2311.11649v1)

Abstract: This letter re-visits the problem of visual-inertial navigation system (VINS) and presents a novel filter design we dub the multi state constraint equivariant filter (MSCEqF, in analogy to the well known MSCKF). We define a symmetry group and corresponding group action that allow specifically the design of an equivariant filter for the problem of visual-inertial odometry (VIO) including IMU bias, and camera intrinsic and extrinsic calibration states. In contrast to state-of-the-art invariant extended Kalman filter (IEKF) approaches that simply tack IMU bias and other states onto the $\mathbf{SE}_2(3)$ group, our filter builds upon a symmetry that properly includes all the states in the group structure. Thus, we achieve improved behavior, particularly when linearization points largely deviate from the truth (i.e., on transients upon state disturbances). Our approach is inherently consistent even during convergence phases from significant errors without the need for error uncertainty adaptation, observability constraint, or other consistency enforcing techniques. This leads to greatly improved estimator behavior for significant error and unexpected state changes during, e.g., long-duration missions. We evaluate our approach with a multitude of different experiments using three different prominent real-world datasets.

• The paper introduces MSCEqF, an equivariant filter that enhances visual-inertial navigation robustness by integrating calibration and state estimation in a Lie group framework.
• It employs a semi-direct product symmetry group combining SE(3) with intrinsic camera calibration to improve linearization and reduce computational complexity.
• Experimental results on Euroc, TUM-VI, and UZH-FPV datasets demonstrate that MSCEqF outperforms OpenVINS, especially under significant extrinsic calibration errors.

Overview of the MSCEqF: A Multi State Constraint Equivariant Filter for Vision-aided Inertial Navigation

The paper under discussion introduces the Multi State Constraint Equivariant Filter (MSCEqF), a novel approach within visual-inertial navigation systems (VINS) to enhance the robustness and consistency of state estimation. The MSCEqF leverages the principles of equivariant filtering to address challenges associated with visual-inertial odometry (VIO) and simultaneous localization and mapping (SLAM) systems, particularly concerning the self-calibration of camera and IMU parameters.

Technical Contributions

The primary contribution is the development of the MSCEqF, an equivariant filter which contrasts with traditional approaches such as the invariant extended Kalman filter (IEKF) that faces limitations when explicit bias states are included. The MSCEqF employs a semi-direct product symmetry group that integrates the special Euclidean group SE(3) with intrinsic camera calibration states modeled as a Lie group, denoted as $\IN$. This formulation facilitates the handling of IMU biases correctly within the group structure, providing improved linearization characteristics even during transient phases after state disturbances.

The research presents a comprehensive mathematical derivation overlapping state-of-the-art algorithms in theoretical and practical performance. The authors provide analytical expressions for the filter matrices and state transition matrices, ensuring reduced computational complexity suitable for resource-limited applications like micro aerial vehicles and augmented reality devices.

Performance and Evaluation

A rigorous experimental evaluation was conducted using real-world datasets such as Euroc, TUM-VI, and UZH-FPV, aiming to assess the filter's capability in maintaining accuracy and robustness under adverse calibration conditions. The MSCEqF demonstrated superior performance compared to OpenVINS, notably in scenarios with significant extrinsic calibration errors, achieving an efficient trade-off between robustness and complexity.

The paper highlights several key findings:

• The filter remains robust under both known and unexpected errors, attributed to its equivariant nature, which inherently maintains consistency without the need for compensatory techniques like the first estimate Jacobian (FEJ).
• The MSCEqF achieves consistency naturally, benefitting from compatibility with reference frame transformations—a salient feature assessing performance during real-world deployments.

Implications and Future Work

The development of the MSCEqF offers significant implications for advancing autonomous systems' reliability and resilience. By minimizing the need for extensive tuning and eliminating reliance on ancillary health-check algorithms, the filter presents as a promising step toward universal applicability of VIO systems across diverse scenarios.

Future research should consider extending the MSCEqF model to incorporate more sophisticated feature management strategies, such as polar symmetry for explicit SLAM features. Further exploration into real-time adaptation strategies and integration with more extensive environmental understanding modules could enhance operational robustness.

Conclusion

The MSCEqF represents an impactful advancement in the domain of visual-inertial navigation, addressing core challenges of consistency and robustness head-on. Through rigorous mathematical foundations coupled with expansive practical evaluations, the paper sets a noteworthy precedent for subsequent research initiatives aiming to refine autonomous navigation systems. This work consequently opens new opportunities for deploying more intelligent and adaptive robotic solutions in the contemporary landscape.