{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T10:05:16Z","timestamp":1771236316334,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2015,4,22]],"date-time":"2015-04-22T00:00:00Z","timestamp":1429660800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"China High-Tech 863 Program","award":["2001AA415340"],"award-info":[{"award-number":["2001AA415340"]}]},{"name":"China High-Tech 863 Program","award":["2007AA04Z1A6"],"award-info":[{"award-number":["2007AA04Z1A6"]}]},{"name":"China Natural Science Foundation","award":["61174168"],"award-info":[{"award-number":["61174168"]}]},{"DOI":"10.13039\/501100012130","name":"Aviation Science Foundation of China","doi-asserted-by":"publisher","award":["20100758002"],"award-info":[{"award-number":["20100758002"]}],"id":[{"id":"10.13039\/501100012130","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012130","name":"Aviation Science Foundation of China","doi-asserted-by":"publisher","award":["20128058006"],"award-info":[{"award-number":["20128058006"]}],"id":[{"id":"10.13039\/501100012130","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>This paper presents a non-linear state observer-based integrated navigation scheme for estimating the attitude, position and velocity of micro aerial vehicles (MAV) operating in GPS-denied indoor environments, using the measurements from low-cost MEMS (micro electro-mechanical systems) inertial sensors and an RGB-D camera.  A robust RGB-D visual odometry (VO) approach was developed to estimate the MAV\u2019s relative motion by extracting and matching features captured by the RGB-D camera from the environment. The state observer of the RGB-D visual-aided inertial navigation was then designed based on the invariant observer theory for systems possessing symmetries. The motion estimates from the RGB-D VO were fused with inertial and magnetic measurements from the onboard MEMS sensors via the state observer, providing the MAV with accurate estimates of its full six degree-of-freedom states. Implementations on a quadrotor MAV and indoor flight test results demonstrate that the resulting state observer is effective in estimating the MAV\u2019s states without relying on external navigation aids such as GPS. The properties of computational efficiency and simplicity in gain tuning make the proposed invariant observer-based navigation scheme appealing for actual MAV applications in indoor environments.<\/jats:p>","DOI":"10.3390\/mi6040487","type":"journal-article","created":{"date-parts":[[2015,4,22]],"date-time":"2015-04-22T12:14:23Z","timestamp":1429704863000},"page":"487-522","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Invariant Observer-Based State Estimation for Micro-Aerial Vehicles in GPS-Denied Indoor Environments Using an RGB-D Camera and MEMS Inertial Sensors"],"prefix":"10.3390","volume":"6","author":[{"given":"Dachuan","family":"Li","sequence":"first","affiliation":[{"name":"Department of Automation, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qing","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Automation, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liangwen","family":"Tang","sequence":"additional","affiliation":[{"name":"National Key Laboratory on Flight Vehicle Control Integrated Technology, Flight Automatic Control Research Institute, Xi'an 710065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sheng","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Automation, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nong","family":"Cheng","sequence":"additional","affiliation":[{"name":"Department of Automation, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingyan","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Automation, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,4,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s10846-010-9483-y","article-title":"Towards palm-size autonomous helicopters","volume":"61","author":"Bouabdallah","year":"2011","journal-title":"J. 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