{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T07:48:19Z","timestamp":1769154499291,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2013,11,6]],"date-time":"2013-11-06T00:00:00Z","timestamp":1383696000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper deals with the attitude estimation of a rigid body equipped with angular velocity sensors and reference vector sensors. A quaternion-based nonlinear observer is proposed in order to fuse all information sources and to obtain an accurate estimation of the attitude. It is shown that the observer error dynamics can be separated into two passive subsystems connected in \u201cfeedback\u201d. Then, this property is used to show that the error dynamics is input-to-state stable when the measurement disturbance is seen as an input and the error as the state. These results allow one to affirm that the observer is \u201crobustly stable\u201d. The proposed observer is evaluated in real-time with the design and implementation of an Attitude and Heading Reference System (AHRS) based on low-cost MEMS (Micro-Electro-Mechanical Systems) Inertial Measure Unit (IMU) and magnetic sensors and a 16-bit microcontroller. The resulting estimates are compared with a high precision motion system to demonstrate its performance.<\/jats:p>","DOI":"10.3390\/s131115138","type":"journal-article","created":{"date-parts":[[2013,11,6]],"date-time":"2013-11-06T11:41:50Z","timestamp":1383738110000},"page":"15138-15158","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["A Robust Nonlinear Observer for Real-Time Attitude Estimation Using Low-Cost MEMS Inertial Sensors"],"prefix":"10.3390","volume":"13","author":[{"given":"Jos\u00e9","family":"Guerrero-Castellanos","sequence":"first","affiliation":[{"name":"Faculty of Electronic, Autonomous University of Puebla (BUAP), Ciudad universitaria, Puebla 72570, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heberto","family":"Madrigal-Sastre","sequence":"additional","affiliation":[{"name":"Faculty of Electronic, Autonomous University of Puebla (BUAP), Ciudad universitaria, Puebla 72570, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1529-098X","authenticated-orcid":false,"given":"Sylvain","family":"Durand","sequence":"additional","affiliation":[{"name":"Control Systems Department, GIPSA-lab laboratory, CNRS-University of Grenoble, ENSE3 BP 46, St Martin d'H\u00e8res Cedex 38402, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4937-4586","authenticated-orcid":false,"given":"Lizeth","family":"Torres","sequence":"additional","affiliation":[{"name":"Engineering Institute, Autonomous University of Mexico (UNAM), Circuito Escolar, Ciudad Universitaria, Mexico D.F. 04510, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"German","family":"Mu\u00f1oz-Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Faculty of Electronic, Autonomous University of Puebla (BUAP), Ciudad universitaria, Puebla 72570, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,11,6]]},"reference":[{"key":"ref_1","unstructured":"Wertz, J. 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