Error-Covariance Analysis of Monocular Pose Estimation Using Total Least Squares

TL;DR

This paper develops a theoretical framework for monocular pose estimation using total least squares, demonstrating that the estimates reach the Cramér-Rao lower bound and validating the approach through extensive Monte Carlo simulations.

Contribution

It introduces a novel optimization framework for monocular pose estimation that achieves optimality under small angle assumptions and rigorously compares theoretical bounds with empirical results.

Findings

Estimates reach the Cramér-Rao lower bound under small angle approximation.

The proposed method is validated with 10,000 Monte Carlo simulations.

Error-covariance expressions are derived and confirmed through simulation.

Abstract

This study presents a theoretical structure for the monocular pose estimation problem using the total least squares. The unit-vector line-of-sight observations of the features are extracted from the monocular camera images. First, the optimization framework is formulated for the pose estimation problem with observation vectors extracted from unit vectors from the camera center-of-projection, pointing towards the image features. The attitude and position solutions obtained via the derived optimization framework are proven to reach the Cram\'er-Rao lower bound under the small angle approximation of the attitude errors. Specifically, The Fisher Information Matrix and the Cram\'er-Rao bounds are evaluated and compared to the analytical derivations of the error-covariance expressions to rigorously prove the optimality of the estimates. The sensor data for the measurement model is provided through a series of vector observations, and two fully populated noise-covariance matrices are assumed for the body and reference observation data. The inverse of the former matrices appear in terms of a series of weight matrices in the cost function. The proposed solution is simulated in a Monte-Carlo framework with 10,000 samples to validate the error-covariance analysis.