{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T07:04:56Z","timestamp":1780556696022,"version":"3.54.1"},"reference-count":58,"publisher":"SAGE Publications","issue":"13","license":[{"start":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T00:00:00Z","timestamp":1724630400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"name":"NSF USA","award":["IIS-1924897"],"award-info":[{"award-number":["IIS-1924897"]}]},{"DOI":"10.13039\/100006094","name":"University of Delaware","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006094","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Google AR Core"},{"name":"University Doctoral Fellowship"},{"name":"NASA DE"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p>\n                    In this paper, we study state estimation of multi-visual-inertial systems (MVIS) and develop sensor fusion algorithms to optimally fuse an arbitrary number of asynchronous inertial measurement units (IMUs) or gyroscopes and global and\/or rolling shutter cameras. We are especially interested in the full calibration of the associated visual-inertial sensors, including the IMU\/camera intrinsics and the IMU-IMU\/camera spatiotemporal extrinsics as well as the image readout time of rolling-shutter cameras (if used). To this end, we develop a new analytic combined IMU integration with inertial intrinsics\u2014termed ACI\n                    <jats:sup>3<\/jats:sup>\n                    \u2014to pre-integrate IMU measurements, which is leveraged to fuse auxiliary IMUs and\/or gyroscopes alongside a base IMU. We model the multi-inertial measurements to include all the necessary inertial intrinsic and IMU-IMU spatiotemporal extrinsic parameters, while leveraging IMU-IMU rigid-body constraints to eliminate the necessity of auxiliary inertial poses and thus reducing computational complexity. By performing observability analysis of MVIS, we prove that the standard four unobservable directions remain\u2014no matter how many inertial sensors are used, and also identify, for the first time, degenerate motions for IMU-IMU spatiotemporal extrinsics and auxiliary inertial intrinsics. In addition to extensive simulations that validate our analysis and algorithms, we have built our own MVIS sensor rig and collected over 25 real-world datasets to experimentally verify the proposed calibration against the state-of-the-art calibration method Kalibr. We show that the proposed MVIS calibration is able to achieve competing accuracy with improved convergence and repeatability, which is open sourced to better benefit the community.\n                  <\/jats:p>","DOI":"10.1177\/02783649241245726","type":"journal-article","created":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T09:53:57Z","timestamp":1724666037000},"page":"1995-2026","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":11,"title":["Multi-visual-inertial system: Analysis, calibration, and estimation"],"prefix":"10.1177","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9675-9147","authenticated-orcid":false,"given":"Yulin","family":"Yang","sequence":"first","affiliation":[{"name":"Robot Perception and Navigation Group, University of Delaware, Newark, DE, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2179-3447","authenticated-orcid":false,"given":"Patrick","family":"Geneva","sequence":"additional","affiliation":[{"name":"Robot Perception and Navigation Group, University of Delaware, Newark, DE, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9932-0685","authenticated-orcid":false,"given":"Guoquan","family":"Huang","sequence":"additional","affiliation":[{"name":"Robot Perception and Navigation Group, University of Delaware, Newark, DE, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2024,8,26]]},"reference":[{"key":"bibr1-02783649241245726","volume-title":"Ceres Solver","author":"Agarwal S","year":"2023"},{"key":"bibr2-02783649241245726","doi-asserted-by":"publisher","DOI":"10.1017\/9781316671528"},{"key":"bibr3-02783649241245726","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2015.7353389"},{"key":"bibr4-02783649241245726","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2021.3100156"},{"key":"bibr5-02783649241245726","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2021.3075644"},{"key":"bibr6-02783649241245726","doi-asserted-by":"publisher","DOI":"10.1109\/IROS47612.2022.9982263"},{"key":"bibr7-02783649241245726","volume-title":"Stochastic Models, Information Theory, and Lie Groups, Volume 2: Analytic Methods and Modern Applications","volume":"2","author":"Chirikjian GS","year":"2011"},{"key":"bibr8-02783649241245726","volume-title":"Factor Graphs and Gtsam: A Hands-On Introduction","author":"Dellaert F","year":"2012"},{"key":"bibr9-02783649241245726","doi-asserted-by":"publisher","DOI":"10.1177\/0278364919835021"},{"key":"bibr10-02783649241245726","doi-asserted-by":"crossref","unstructured":"Eckenhoff K, Geneva P, Huang G (2019b) Sensor-failure-resilient multi-imu visual-inertial navigation. 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