  State estimation problems without absolute position measurements routinely
arise in navigation of unmanned aerial vehicles, autonomous ground vehicles,
etc., whose proper operation relies on accurate state estimates and reliable
covariances. Unaware of absolute positions, these problems have immanent
unobservable directions. Traditional causal estimators, however, usually gain
spurious information on the unobservable directions, leading to over-confident
covariance inconsistent with actual estimator errors. The consistency problem
of fixed-lag smoothers (FLSs) has only been attacked by the first estimate
Jacobian (FEJ) technique because of the complexity to analyze their
observability property. But the FEJ has several drawbacks hampering its wide
adoption. To ensure the consistency of a FLS, this paper introduces the right
invariant error formulation into the FLS framework. To our knowledge, we are
the first to analyze the observability of a FLS with the right invariant error.
Our main contributions are twofold. As the first novelty, to bypass the
complexity of analysis with the classic observability matrix, we show that
observability analysis of FLSs can be done equivalently on the linearized
system. Second, we prove that the inconsistency issue in the traditional FLS
can be elegantly solved by the right invariant error formulation without
artificially correcting Jacobians. By applying the proposed FLS to the
monocular visual inertial simultaneous localization and mapping (SLAM) problem,
we confirm that the method consistently estimates covariance similarly to a
batch smoother in simulation and that our method achieved comparable accuracy
as traditional FLSs on real data.

Robotics;Systems and Control;Systems and Control