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In order to address these issues, we provide a mathematical framework where we show how the use of coarse model parameters results in a new data assimilation problem. Understanding this new problem proves essential to derive sound inference algorithms. We introduce a model parameter specifically tailored for lidar data assimilation, which closely relates to the local mean free path. Using this new model parameter, we derive its associated forward model and we provide the resulting mapping algorithm. We further discuss how our proposed algorithm relates to usual occupancy grid mapping. Finally, we present an example with real lidar measurements.<\/jats:p>","DOI":"10.1017\/s0263574721000850","type":"journal-article","created":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T14:28:03Z","timestamp":1625063283000},"page":"862-887","source":"Crossref","is-referenced-by-count":5,"title":["A physics perspective on lidar data assimilation for mobile robots"],"prefix":"10.1017","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6747-8832","authenticated-orcid":false,"given":"Yann","family":"Berquin","sequence":"first","affiliation":[]},{"given":"Andreas","family":"Zell","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,6,30]]},"reference":[{"key":"S0263574721000850_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(00)00299-1"},{"key":"S0263574721000850_ref24","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/25\/11\/115008"},{"key":"S0263574721000850_ref5","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2019.2895264"},{"key":"S0263574721000850_ref13","unstructured":"[13] Burgard, W. , Fox, D. , Hennig, D. and Schmidt, T. , \u201cEstimating the Absolute Position of a Mobile Robot Using Position Probability Grids,\u201d Proceedings of the National Conference on Artificial Intelligence (Citeseer, 1996) pp. 896\u2013901."},{"key":"S0263574721000850_ref31","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00294"},{"key":"S0263574721000850_ref25","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/7\/5\/003"},{"key":"S0263574721000850_ref4","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA40945.2020.9196769"},{"key":"S0263574721000850_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574718000528"},{"key":"S0263574721000850_ref43","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574719000900"},{"key":"S0263574721000850_ref21","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511813559"},{"key":"S0263574721000850_ref40","doi-asserted-by":"publisher","DOI":"10.1109\/ICSensT.2015.7438508"},{"volume-title":"Foundations of the Theory of Probability","year":"1950","author":"Kolmogorov","key":"S0263574721000850_ref34"},{"volume-title":"Multiscale Methods: Averaging and Homogenization","year":"2008","author":"Pavliotis","key":"S0263574721000850_ref22"},{"key":"S0263574721000850_ref38","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2009.3.87"},{"key":"S0263574721000850_ref18","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717921"},{"key":"S0263574721000850_ref2","first-page":"4758","volume-title":"RSJ International Conference on Intelligent Robots and Systems (IROS)","author":"Shan","year":"2018"},{"key":"S0263574721000850_ref27","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.1984.tb05047.x"},{"key":"S0263574721000850_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574719000298"},{"volume-title":"Radiative Transfer","year":"1960","author":"Chandrasekhar","key":"S0263574721000850_ref39"},{"key":"S0263574721000850_ref42","first-page":"1729881417735401","article-title":"Training a terrain traversability classifier for a planetary rover through simulation","volume":"14","author":"Hewitt","year":"2017","journal-title":"Int. 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