  It is often convenient to separate a state estimation task into smaller
"local" tasks, where each local estimator estimates a subset of the overall
system state. However, neglecting cross-covariance terms between state
estimates can result in overconfident estimates, which can ultimately degrade
the accuracy of the estimator. Common cascaded filtering techniques focus on
the problem of modelling cross-covariances when the local estimators share a
common state vector. This letter introduces a novel cascaded and decentralized
filtering approach that approximates the cross-covariances when the local
estimators consider distinct state vectors. The proposed estimator is validated
in simulations and in experiments on a three-dimensional attitude and position
estimation problem. The proposed approach is compared to a naive cascaded
filtering approach that neglects cross-covariance terms, a sigma point-based
Covariance Intersection filter, and a full-state filter. In both simulations
and experiments, the proposed filter outperforms the naive and the Covariance
Intersection filters, while performing comparatively to the full-state filter.
