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In recent years, Visual-Inertial Odometry (VIO) has achieved many significantprogresses. However, VIO methods suffer from localization drift over longtrajectories. In this paper, we propose a First-Estimates JacobianVisual-Inertial-Ranging Odometry (FEJ-VIRO) to reduce the localization driftsof VIO by incorporating ultra-wideband (UWB) ranging measurements into the VIOframework \textit{consistently}. Considering that the initial positions of UWBanchors are usually unavailable, we propose a long-short window structure toinitialize the UWB anchors' positions as well as the covariance for stateaugmentation. After initialization, the FEJ-VIRO estimates the UWB anchors'positions simultaneously along with the robot poses. We further analyze theobservability of the visual-inertial-ranging estimators and proved that thereare \textit{four} unobservable directions in the ideal case, while one of themvanishes in the actual case due to the gain of spurious information. Based onthese analyses, we leverage the FEJ technique to enforce the unobservabledirections, hence reducing inconsistency of the estimator. Finally, we validateour analysis and evaluate the proposed FEJ-VIRO with both simulation andreal-world experiments.

FEJ-VIRO: A Consistent First-Estimate Jacobian Visual-Inertial-Ranging Odometry