{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,10,23]],"date-time":"2024-10-23T04:25:18Z","timestamp":1729657518853,"version":"3.28.0"},"reference-count":45,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T00:00:00Z","timestamp":1687219200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004585","name":"Faculty of Mechanical Engineering, Brno University of Technology","doi-asserted-by":"publisher","award":["FSI-S-20-6407"],"id":[{"id":"10.13039\/501100004585","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"Planar fiducial markers are commonly used to estimate a pose of a camera relative to the marker. This information can be combined with other sensor data to provide a global or local position estimate of the system in the environment using a state estimator such as the Kalman filter. To achieve accurate estimates, the observation noise covariance matrix must be properly configured to reflect the sensor output\u2019s characteristics. However, the observation noise of the pose obtained from planar fiducial markers varies across the measurement range and this fact needs to be taken into account during the sensor fusion to provide a reliable estimate. In this work, we present experimental measurements of the fiducial markers in real and simulation scenarios for 2D pose estimation. Based on these measurements, we propose analytical functions that approximate the variances of pose estimates. We demonstrate the effectiveness of our approach in a 2D robot localisation experiment, where we present a method for estimating covariance model parameters based on user measurements and a technique for fusing pose estimates from multiple markers.<\/jats:p>","DOI":"10.3390\/s23125746","type":"journal-article","created":{"date-parts":[[2023,6,21]],"date-time":"2023-06-21T06:30:51Z","timestamp":1687329051000},"page":"5746","source":"Crossref","is-referenced-by-count":4,"title":["Analytical Models for Pose Estimate Variance of Planar Fiducial Markers for Mobile Robot Localisation"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-8026-5740","authenticated-orcid":false,"given":"Roman","family":"Ad\u00e1mek","sequence":"first","affiliation":[{"name":"Faculty of Mechanical Engineering, Brno University of Technology, Technick\u00e1 2896\/2, 616 69 Brno, Czech Republic"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-8675-8060","authenticated-orcid":false,"given":"Martin","family":"Brablc","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Brno University of Technology, Technick\u00e1 2896\/2, 616 69 Brno, Czech Republic"}]},{"given":"Patrik","family":"V\u00e1vra","sequence":"additional","affiliation":[{"name":"Independent Researcher, 74 401 Fren\u0161t\u00e1t pod Radho\u0161t\u011bm, Czech Republic"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0351-9671","authenticated-orcid":false,"given":"Barnab\u00e1s","family":"Dobossy","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Brno University of Technology, Technick\u00e1 2896\/2, 616 69 Brno, Czech Republic"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-0269-1506","authenticated-orcid":false,"given":"Martin","family":"Form\u00e1nek","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Brno University of Technology, Technick\u00e1 2896\/2, 616 69 Brno, Czech Republic"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-5594-6085","authenticated-orcid":false,"given":"Filip","family":"Radil","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Brno University of Technology, Technick\u00e1 2896\/2, 616 69 Brno, Czech Republic"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"114195","DOI":"10.1016\/j.eswa.2020.114195","article-title":"A state-of-the-art review on mobile robotics tasks using artificial intelligence and visual data","volume":"167","author":"Cebollada","year":"2021","journal-title":"Expert Syst. 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