{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T10:46:11Z","timestamp":1778496371312,"version":"3.51.4"},"reference-count":53,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2013,5,1]],"date-time":"2013-05-01T00:00:00Z","timestamp":1367366400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2013,5]]},"abstract":"<jats:p>In this paper, we focus on the problem of motion tracking in unknown environments using visual and inertial sensors. We term this estimation task visual\u2013inertial odometry (VIO), in analogy to the well-known visual-odometry problem. We present a detailed study of extended Kalman filter (EKF)-based VIO algorithms, by comparing both their theoretical properties and empirical performance. We show that an EKF formulation where the state vector comprises a sliding window of poses (the multi-state-constraint Kalman filter (MSCKF)) attains better accuracy, consistency, and computational efficiency than the simultaneous localization and mapping (SLAM) formulation of the EKF, in which the state vector contains the current pose and the features seen by the camera. Moreover, we prove that both types of EKF approaches are inconsistent, due to the way in which Jacobians are computed. Specifically, we show that the observability properties of the EKF\u2019s linearized system models do not match those of the underlying system, which causes the filters to underestimate the uncertainty in the state estimates. Based on our analysis, we propose a novel, real-time EKF-based VIO algorithm, which achieves consistent estimation by (i) ensuring the correct observability properties of its linearized system model, and (ii) performing online estimation of the camera-to-inertial measurement unit (IMU) calibration parameters. This algorithm, which we term MSCKF 2.0, is shown to achieve accuracy and consistency higher than even an iterative, sliding-window fixed-lag smoother, in both Monte Carlo simulations and real-world testing.<\/jats:p>","DOI":"10.1177\/0278364913481251","type":"journal-article","created":{"date-parts":[[2013,6,7]],"date-time":"2013-06-07T05:30:49Z","timestamp":1370583049000},"page":"690-711","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":706,"title":["High-precision, consistent EKF-based visual-inertial odometry"],"prefix":"10.1177","volume":"32","author":[{"given":"Mingyang","family":"Li","sequence":"first","affiliation":[]},{"given":"Anastasios I.","family":"Mourikis","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of California, Riverside, CA, USA"}]}],"member":"179","published-online":{"date-parts":[[2013,6,7]]},"reference":[{"key":"bibr1-0278364913481251","doi-asserted-by":"publisher","DOI":"10.1002\/0471221279"},{"key":"bibr2-0278364913481251","doi-asserted-by":"crossref","unstructured":"Brockers R, Susca S, Zhu D, Matthies L (2012) Fully self-contained vision-aided navigation and landing of a micro air vehicle independent from external sensor inputs, volumn 8387.","DOI":"10.1117\/12.919278"},{"key":"bibr3-0278364913481251","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2008.2003276"},{"key":"bibr4-0278364913481251","doi-asserted-by":"publisher","DOI":"10.1109\/ACVMOT.2005.48"},{"key":"bibr5-0278364913481251","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2011.5980267"},{"key":"bibr6-0278364913481251","first-page":"266","volume-title":"Proceedings of the Photogrammetric Computer Vision Conference","author":"Engels C","year":"2006"},{"key":"bibr7-0278364913481251","volume-title":"Aided navigation: GPS with high rate sensors","author":"Farrell J","year":"2008"},{"key":"bibr8-0278364913481251","doi-asserted-by":"publisher","DOI":"10.1109\/MCG.2005.140"},{"key":"bibr9-0278364913481251","volume-title":"Proceedings of the International Workshop on the Algorithmic Foundations of Robotics","author":"Hesch JA","year":"2012"},{"key":"bibr10-0278364913481251","doi-asserted-by":"publisher","DOI":"10.1177\/0278364909353640"},{"key":"bibr11-0278364913481251","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2008.4543252"},{"key":"bibr12-0278364913481251","doi-asserted-by":"publisher","DOI":"10.1177\/0278364910388963"},{"key":"bibr13-0278364913481251","volume-title":"Fundamentals of Statistical Signal Processing, Vol. 1: Estimation Theory","author":"Kay SM","year":"1993"},{"key":"bibr14-0278364913481251","first-page":"515","volume-title":"Proceedings of the International Symposium of Experimental Robotics","author":"Kelly J","year":"2008"},{"key":"bibr15-0278364913481251","doi-asserted-by":"publisher","DOI":"10.1177\/0278364910382802"},{"key":"bibr16-0278364913481251","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2006.06.006"},{"key":"bibr17-0278364913481251","doi-asserted-by":"publisher","DOI":"10.1109\/MFI.2010.5604453"},{"key":"bibr18-0278364913481251","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2008.2004832"},{"key":"bibr19-0278364913481251","first-page":"201","volume-title":"Proceedings of the International Symposium of Robotics Research","author":"Konolige K","year":"2011"},{"key":"bibr20-0278364913481251","volume-title":"Proceedings of the International Symposium on Experimental Robotics","author":"Kottas DG","year":"2012"},{"key":"bibr21-0278364913481251","unstructured":"Li M, Mourikis AI (2011) Consistency of EKF-based Visual\u2013Inertial Odometry. 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