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Rather than using discrete sampling of the measurement dynamics as in current methods, we derive the closed-form solutions to the preintegration equations, yielding improved accuracy in state estimation. We advocate two new different inertial models for preintegration: (i) the model that assumes piecewise constant measurements; and (ii) the model that assumes piecewise constant local true acceleration. Through extensive Monte Carlo simulations, we show the effect that the choice of preintegration model has on estimation performance. To validate the proposed preintegration theory, we develop both direct and indirect visual\u2013inertial navigation systems (VINSs) that leverage our preintegration. In the first, within a tightly coupled, sliding-window optimization framework, we jointly estimate the features in the window and the IMU states while performing marginalization to bound the computational cost. In the second, we loosely couple the IMU preintegration with a direct image alignment that estimates relative camera motion by minimizing the photometric errors (i.e., image intensity difference), allowing for efficient and informative loop closures. Both systems are extensively validated in real-world experiments and are shown to offer competitive performance to state-of-the-art methods.<\/jats:p>","DOI":"10.1177\/0278364919835021","type":"journal-article","created":{"date-parts":[[2019,4,4]],"date-time":"2019-04-04T01:36:12Z","timestamp":1554341772000},"page":"563-586","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":79,"title":["Closed-form preintegration methods for graph-based visual\u2013inertial navigation"],"prefix":"10.1177","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6985-3210","authenticated-orcid":false,"given":"Kevin","family":"Eckenhoff","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, and Computer and Information Sciences, 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":"Department of Mechanical Engineering, and Computer and Information Sciences, University of Delaware, Newark, DE, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guoquan","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, and Computer and Information Sciences, University of Delaware, Newark, DE, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2019,4,3]]},"reference":[{"key":"bibr1-0278364919835021","unstructured":"Agarwal S, Mierle K and Others (2018) Ceres solver. http:\/\/ceres-solver.org"},{"key":"bibr2-0278364919835021","doi-asserted-by":"publisher","DOI":"10.1023\/B:VISI.0000011205.11775.fd"},{"key":"bibr3-0278364919835021","doi-asserted-by":"publisher","DOI":"10.1177\/0278364917728574"},{"key":"bibr4-0278364919835021","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2015.7353389"},{"key":"bibr5-0278364919835021","doi-asserted-by":"publisher","DOI":"10.1177\/0278364915620033"},{"key":"bibr6-0278364919835021","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2016.2624754"},{"key":"bibr7-0278364919835021","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2015.7353366"},{"key":"bibr8-0278364919835021","doi-asserted-by":"publisher","DOI":"10.2514\/4.866463"},{"key":"bibr9-0278364919835021","volume-title":"Stochastic Models, Information Theory, and Lie Groups, Volume 2: Analytic Methods and Modern Applications","author":"Chirikjian G","year":"2011"},{"key":"bibr10-0278364919835021","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2008.2003276"},{"key":"bibr11-0278364919835021","unstructured":"Dellaert F (2012) Factor graphs and GTSAM: A hands-on introduction. 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