Equivariant Filter Transformations for Consistent and Efficient Visual--Inertial Navigation

TL;DR

This paper introduces an equivariant filter transformation method for visual-inertial navigation that enhances consistency and efficiency by systematically managing symmetries and unobservable states, validated through simulations and real-world tests.

Contribution

It formalizes the transformation between different equivariant filters, enabling systematic consistency design and proposing efficient implementation strategies to reduce computational load.

Findings

Improved navigation accuracy demonstrated in simulations and experiments.

Enhanced computational efficiency with proposed Jacobian-based strategies.

Validated the approach's effectiveness in real-world scenarios.

Abstract

This paper presents an equivariant filter (EqF) transformation approach for visual--inertial navigation. By establishing analytical links between EqFs with different symmetries, the proposed approach enables systematic consistency design and efficient implementation. First, we formalize the mapping from the global system state to the local error-state and prove that it induces a nonsingular linear transformation between the error-states of any two EqFs. Second, we derive transformation laws for the associated linearized error-state systems and unobservable subspaces. These results yield a general consistency design principle: for any unobservable system, a consistent EqF with a state-independent unobservable subspace can be synthesized by transforming the local coordinate chart, thereby avoiding ad hoc symmetry analysis. Third, to mitigate the computational burden arising from the non-block-diagonal Jacobians required for consistency, we propose two efficient implementation strategies. These strategies exploit the Jacobians of a simpler EqF with block-diagonal structure to accelerate covariance operations while preserving consistency. Extensive Monte Carlo simulations and real-world experiments validate the proposed approach in terms of both accuracy and runtime.