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This letter re-visits the problem of visual-inertial navigation system (VINS)and presents a novel filter design we dub the multi state constraintequivariant filter (MSCEqF, in analogy to the well known MSCKF). We define asymmetry group and corresponding group action that allow specifically thedesign of an equivariant filter for the problem of visual-inertial odometry(VIO) including IMU bias, and camera intrinsic and extrinsic calibrationstates. 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 properlyincludes all the states in the group structure. Thus, we achieve improvedbehavior, particularly when linearization points largely deviate from the truth(i.e., on transients upon state disturbances). Our approach is inherentlyconsistent even during convergence phases from significant errors without theneed for error uncertainty adaptation, observability constraint, or otherconsistency enforcing techniques. This leads to greatly improved estimatorbehavior for significant error and unexpected state changes during, e.g.,long-duration missions. We evaluate our approach with a multitude of differentexperiments using three different prominent real-world datasets.

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