  As autonomous systems increasingly rely on onboard sensing for localization
and perception, the parallel tasks of motion planning and state estimation
become more strongly coupled. This coupling is well-captured by augmenting the
planning objective with a posterior-covariance penalty -- however, prediction
of the estimator covariance is challenging when the observation model depends
on unknown landmarks, as is the case in Simultaneous Localization and Mapping
(SLAM). This paper addresses these challenges in the case of landmark- and
SLAM-based estimators, enabling efficient prediction (and ultimately
minimization) of this performance metric. First, we provide an interval-based
filtering approximation of the SLAM inference process which allows for
recursive propagation of the ego-covariance while avoiding the quadratic
complexity of explicitly tracking landmark uncertainty. Secondly, we introduce
a Lie-derivative measurement bundling scheme that simplifies the recursive
"bundled" update, representing significant computational savings for high-rate
sensors such as cameras. Finally, we identify a large class of measurement
models (which includes orthographic camera projection) for which the
contributions from each landmark can be directly combined, making evaluation of
the information gained at each timestep (nearly) independent of the number of
landmarks. This also enables the generalization from finite sets of landmarks
$\{\ell^{(n)} \}$ to distributions, foregoing the need for fully-specified
linearization points at planning time and allowing for new landmarks to be
anticipated. Taken together, these contributions allow SLAM performance to be
accurately and efficiently predicted, paving the way for online,
observability-aware trajectory optimization in unknown space.
