Attitude Uncertainty Analysis of a Three-Vehicle Constrained Formation
The uncertainty analysis of attitude estimates enables the comparison between different methods, and, thus, it is important for practical applications. This work studies the uncertainty for the attitude determination of a three-vehicle constrained formation. Moreover, the existing solution is improv...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/22/10/3879 |
| _version_ | 1797495595454169088 |
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| author | Pedro Cruz Pedro Batista |
| author_facet | Pedro Cruz Pedro Batista |
| author_sort | Pedro Cruz |
| collection | DOAJ |
| description | The uncertainty analysis of attitude estimates enables the comparison between different methods, and, thus, it is important for practical applications. This work studies the uncertainty for the attitude determination of a three-vehicle constrained formation. Moreover, the existing solution is improved by including the uncertainty results in a weighted orthogonal Procrustes problem. In the formation considered herein, the vehicles measure inertial references and relative line-of-sight vectors. Nonetheless, the line of sight between two elements of the formation is restricted. The uncertainty analysis uses perturbation theory and, consequently, considers a small first-order perturbation in the measurements. The covariance matrices are obtained for all relative and inertial attitude candidates from the linearization of the solution using a first-order Taylor expansion. Then, the uncertainty is completed by considering the covariance for the weighted orthogonal Procrustes problem, from the literature, and the definition of covariance for the remaining attitudes. The uncertainty characterization is valid for configurations with a unique solution. Finally, the theoretical results are validated by applying Monte Carlo simulations, which show that the predicted errors are statistically consistent with the numerical implementation of the solution with noise. Furthermore, the theoretical uncertainty predicts the accuracy changes near special configurations where there is loss of information. |
| first_indexed | 2024-03-10T01:52:52Z |
| format | Article |
| id | doaj.art-57d3b7e2ecd34dd086464b5c4f8d98b8 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-10T01:52:52Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-57d3b7e2ecd34dd086464b5c4f8d98b82023-11-23T13:02:49ZengMDPI AGSensors1424-82202022-05-012210387910.3390/s22103879Attitude Uncertainty Analysis of a Three-Vehicle Constrained FormationPedro Cruz0Pedro Batista1Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, PortugalInstituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, PortugalThe uncertainty analysis of attitude estimates enables the comparison between different methods, and, thus, it is important for practical applications. This work studies the uncertainty for the attitude determination of a three-vehicle constrained formation. Moreover, the existing solution is improved by including the uncertainty results in a weighted orthogonal Procrustes problem. In the formation considered herein, the vehicles measure inertial references and relative line-of-sight vectors. Nonetheless, the line of sight between two elements of the formation is restricted. The uncertainty analysis uses perturbation theory and, consequently, considers a small first-order perturbation in the measurements. The covariance matrices are obtained for all relative and inertial attitude candidates from the linearization of the solution using a first-order Taylor expansion. Then, the uncertainty is completed by considering the covariance for the weighted orthogonal Procrustes problem, from the literature, and the definition of covariance for the remaining attitudes. The uncertainty characterization is valid for configurations with a unique solution. Finally, the theoretical results are validated by applying Monte Carlo simulations, which show that the predicted errors are statistically consistent with the numerical implementation of the solution with noise. Furthermore, the theoretical uncertainty predicts the accuracy changes near special configurations where there is loss of information.https://www.mdpi.com/1424-8220/22/10/3879uncertainty analysisattitude determinationformation of vehiclesconstrained formation |
| spellingShingle | Pedro Cruz Pedro Batista Attitude Uncertainty Analysis of a Three-Vehicle Constrained Formation Sensors uncertainty analysis attitude determination formation of vehicles constrained formation |
| title | Attitude Uncertainty Analysis of a Three-Vehicle Constrained Formation |
| title_full | Attitude Uncertainty Analysis of a Three-Vehicle Constrained Formation |
| title_fullStr | Attitude Uncertainty Analysis of a Three-Vehicle Constrained Formation |
| title_full_unstemmed | Attitude Uncertainty Analysis of a Three-Vehicle Constrained Formation |
| title_short | Attitude Uncertainty Analysis of a Three-Vehicle Constrained Formation |
| title_sort | attitude uncertainty analysis of a three vehicle constrained formation |
| topic | uncertainty analysis attitude determination formation of vehicles constrained formation |
| url | https://www.mdpi.com/1424-8220/22/10/3879 |
| work_keys_str_mv | AT pedrocruz attitudeuncertaintyanalysisofathreevehicleconstrainedformation AT pedrobatista attitudeuncertaintyanalysisofathreevehicleconstrainedformation |