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This work provides a theoretical analysis for optimally solving the poseestimation problem using total least squares for vector observations fromlandmark features, which is central to applications involving simultaneouslocalization and mapping. First, the optimization process is formulated withobservation vectors extracted from point-cloud features. Then, error-covarianceexpressions are derived. The attitude and position estimates obtained via thederived optimization process are proven to reach the bounds defined by theCram\'er-Rao lower bound under the small-angle approximation of attitudeerrors. A fully populated observation noise-covariance matrix is assumed as theweight in the cost function to cover the most general case of the sensoruncertainty. This includes more generic correlations in the errors thanprevious cases involving an isotropic noise assumption. The proposed solutionis verified using Monte Carlo simulations and an experiment with an actualLIDAR to validate the error-covariance analysis.

Optimal Pose Estimation and Covariance Analysis with Simultaneous Localization and Mapping Applications