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To deal with measurement outliers, the Euclidean distance of measurement error is introduced to detect and remove abnormal data. Then, we use dimension expansion methods to preprocess the data of heterogeneous sensors, such as UWB and IMU. An MHE-based method is proposed that deals with the localization of mobile robots with measurement outliers in the presence of bounded noise. An MHE-based estimator is obtained by solving a regularized least-squares problem. We analyze the convergence of the estimation error system using the properties of norm inequalities, and an upper bound is derived for the estimation error system by using norm inequality. Finally, simulation and experiment examples are given to verify the effectiveness and applicability of the proposed approach.<\/jats:p>","DOI":"10.1177\/09596518241240314","type":"journal-article","created":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T09:02:02Z","timestamp":1716195722000},"page":"1367-1379","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Moving horizon estimation for localization of mobile robots with measurement outliers"],"prefix":"10.1177","volume":"238","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2445-8457","authenticated-orcid":false,"given":"Andong","family":"Liu","sequence":"first","affiliation":[{"name":"College of Information Engineering, Zhejiang University of Technology, Zhejiang Provincial United Key Laboratory of Embedded Systems, Hangzhou, 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