  This work provides a theoretical analysis for optimally solving the pose
estimation problem using total least squares for vector observations from
landmark features, which is central to applications involving simultaneous
localization and mapping. First, the optimization process is formulated with
observation vectors extracted from point-cloud features. Then, error-covariance
expressions are derived. The attitude and position estimates obtained via the
derived optimization process are proven to reach the bounds defined by the
Cram\'er-Rao lower bound under the small-angle approximation of attitude
errors. A fully populated observation noise-covariance matrix is assumed as the
weight in the cost function to cover the most general case of the sensor
uncertainty. This includes more generic correlations in the errors than
previous cases involving an isotropic noise assumption. The proposed solution
is verified using Monte Carlo simulations and an experiment with an actual
LIDAR to validate the error-covariance analysis.
