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The accurate determination of the magnetic field by measurement is critical for the prediction of the particle beam trajectory and hence the design of the accelerator complex. In this context, state-of-the-art numerical field computation makes use of boundary-element methods (BEM) to express the magnetic field. This enables the accurate computation of higher-order partial derivatives and local expansions of magnetic potentials used in efficient numerical codes for particle tracking. In this paper, we present an approach to infer the boundary data of an indirect BEM formulation from magnetic field measurements by ensemble K\u00e1lm\u00e1n filtering. In this way, measurement uncertainties can be propagated to the boundary data, magnetic field and potentials, and to the beam related quantities derived from particle tracking. We provide results obtained from real measurement data of a curved dipole magnet using a Hall probe mapper system.<\/jats:p>","DOI":"10.1515\/cmam-2022-0121","type":"journal-article","created":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T11:37:38Z","timestamp":1671017858000},"page":"405-424","source":"Crossref","is-referenced-by-count":6,"title":["BEM-Based Magnetic Field Reconstruction by Ensemble K\u00e1lm\u00e1n Filtering"],"prefix":"10.1515","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2022-105X","authenticated-orcid":false,"given":"Melvin","family":"Liebsch","sequence":"first","affiliation":[{"name":"CERN , TE-MSC-TM , 1211 Meyrin , Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3370-7419","authenticated-orcid":false,"given":"Stephan","family":"Russenschuck","sequence":"additional","affiliation":[{"name":"CERN , TE-MSC-TM , 1211 Meyrin , Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Kurz","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology , University of Jyv\u00e4skyl\u00e4 , 40014 Jyv\u00e4skyl\u00e4 , Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2022,12,15]]},"reference":[{"key":"2023033113095745239_j_cmam-2022-0121_ref_001","doi-asserted-by":"crossref","unstructured":"J. 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