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The new algorithms continue to produce good estimates of parameters or state in the presence of observation outliers. The approach is based on replacing the traditional $L_2$ norm formulation of data assimilation problems with formulations based on $L_1$ and Huber norms. Numerical experiments using the Lorenz-96 and the shallow water on the sphere models illustrate how the new algorithms outperform traditional data assimilation approaches in the presence of data outliers.<\/jats:p>","DOI":"10.1137\/15m1045910","type":"journal-article","created":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T12:09:43Z","timestamp":1498133383000},"page":"B548-B570","source":"Crossref","is-referenced-by-count":18,"title":["Robust Data Assimilation Using $L_1$ and Huber Norms"],"prefix":"10.1137","volume":"39","author":[{"given":"Vishwas","family":"Rao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adrian","family":"Sandu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Ng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elias D.","family":"Nino-Ruiz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,6,22]]},"reference":[{"key":"atypb1","first-page":"125","author":"Anderson E.","year":"1999","journal-title":"Q. 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