Matthias Schmid

Saeed Maleki, John Crassidis, Yang Cheng et al.

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 Cramér-Rao lower bound under the small angle approximation of the attitude errors. Specifically, The Fisher Information Matrix and the Cramér-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.

Pardha Sai Krishna Ala, Ameya Salvi, Venkat Krovi et al.

Accurate state estimation requires careful consideration of uncertainty surrounding the process and measurement models; these characteristics are usually not well-known and need an experienced designer to select the covariance matrices. An error in the selection of covariance matrices could impact the accuracy of the estimation algorithm and may sometimes cause the filter to diverge. Identifying noise characteristics has long been a challenging problem due to uncertainty surrounding noise sources and difficulties in systematic noise modeling. Most existing approaches try identifying unknown covariance matrices through an optimization algorithm involving innovation sequences. In recent years, learning approaches have been utilized to determine the stochastic characteristics of process and measurement models. We present a learning-based methodology with different loss functions to identify noise characteristics and test these approaches' performance for real-time vehicle state estimation

Saeed Maleki, Yang Cheng, John Crassidis et al.

This work provides a theoretical framework for the pose estimation problem using total least squares for vector observations from landmark features. First, the optimization framework is formulated with observation vectors extracted from point cloud features. Then, error-covariance expressions are derived. The attitude and position solutions obtained via the derived optimization framework are proven to reach the bounds defined by the Cramér-Rao lower bound under the small-angle approximation of attitude errors. The measurement data for the simulation of this problem is provided through a series of vector observation scans, and 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. Here, previous derivations are expanded for the pose estimation problem to include more generic correlations in the errors than previous cases involving an isotropic noise assumption. The proposed solution is simulated in a Monte-Carlo framework to validate the error-covariance analysis.