{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T05:16:27Z","timestamp":1788498987825,"version":"build-2803163510"},"reference-count":24,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T00:00:00Z","timestamp":1788134400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]},{"id":[{"id":"https:\/\/ror.org\/01h531d29","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Passive magnetic localization for wireless capsule endoscopy degrades under involuntary gastrointestinal motion: displacement toward one sensor layer simultaneously saturates near-side magnetometers while driving far-side sensors below the noise floor, a failure mode we term asymmetric layer visibility. Existing single-layer and multi-layer systems do not model this explicitly, and full-array Jacobian conditioning degrades progressively with displacement even where a layer-conditioned decomposition remains comparatively stable. We present a two-layer magnetometer array with three algorithmic contributions: per-sensor SNR gating excluding saturated or low-SNR sensors before optimization; layer-conditioned Levenberg\u2013Marquardt estimation on a five-dimensional manifold via spherical parameterization; and SNR-weighted fusion with geodesic interpolation on S2, combined with layer-wise ellipsoid calibration and neural network initialization. Eight LIS3MDL tri-axial magnetometers in a 15\u00d715\u00d730 cm3 two-layer array were validated across 150 Monte Carlo trials using a 4-DOF robotic arm. Mean positional error was 2.32\u00b10.35 mm and orientational error 2.15\u00b10.88\u00b0 at 12.4 Hz, with 93.85% convergence success under displacement-induced asymmetric visibility events of 1.00\u20134.00 cm\u2014over 70% reduction over single-layer and layer-agnostic baselines. Hardware generalization was confirmed across three magnetometer types. The SNR weight ratio also yields a passive discriminant between capsule displacement and global array motion, cross-validated AUC 0.924\u00b10.045, requiring no additional hardware. Reported accuracy is specific to the LIS3MDL magnetometer used in this study.<\/jats:p>","DOI":"10.3390\/s26175536","type":"journal-article","created":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T03:19:26Z","timestamp":1788232766000},"page":"5536","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["SNR-Weighted Layer-Conditioned Magnetometer Array with Ellipsoid Calibration and Neural Network Initialization for Capsule Endoscopy Localization Under Asymmetric Sensor Visibility"],"prefix":"10.3390","volume":"26","author":[{"given":"Omid","family":"Yaghoobian","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, SK S7N 5A2, Canada"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0125-9789","authenticated-orcid":false,"given":"Khan A.","family":"Wahid","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, SK S7N 5A2, Canada"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1038\/35013140","article-title":"Wireless capsule endoscopy","volume":"405","author":"Iddan","year":"2000","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1109\/JSEN.2016.2645945","article-title":"Localization of wireless capsule endoscope: A systematic review","volume":"17","author":"Mateen","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1055\/s-0034-1391855","article-title":"Small-bowel capsule endoscopy and device-assisted enteroscopy for diagnosis and treatment of small-bowel disorders: European Society of Gastrointestinal Endoscopy (ESGE) Clinical Guideline","volume":"47","author":"Pennazio","year":"2015","journal-title":"Endoscopy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4597","DOI":"10.1038\/s41467-024-49019-0","article-title":"Robotic wireless capsule endoscopy: Recent advances and upcoming technologies","volume":"15","author":"Cao","year":"2024","journal-title":"Nat. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/j.gie.2009.09.031","article-title":"Indications and detection, completion, and retention rates of small-bowel capsule endoscopy: A systematic review","volume":"71","author":"Liao","year":"2010","journal-title":"Gastrointest. Endosc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3462","DOI":"10.1109\/JSEN.2019.2894386","article-title":"A novel passive magnetic localization wearable system for wireless capsule endoscopy","volume":"19","author":"Shao","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1849","DOI":"10.1109\/JSEN.2017.2652470","article-title":"Design and optimization strategy of sensor array layout for magnetic localization system","volume":"17","author":"Song","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_8","first-page":"1","article-title":"A compensation method for relative movement between a sensor array and the abdomen for magnetic localization of capsule endoscopes","volume":"71","author":"Zeising","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIM.2022.3204103","article-title":"MagnetOFuse: A hybrid tracking algorithm for wireless capsule endoscopy within the GI track","volume":"71","author":"Vedaei","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4324","DOI":"10.1109\/TIM.2019.2947173","article-title":"An optimal design for passive magnetic localization system based on SNR evaluation","volume":"69","author":"Shao","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_11","first-page":"1","article-title":"Magnetic tracking of wireless capsule endoscope in mobile setup based on differential signals","volume":"70","author":"Song","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_12","first-page":"1","article-title":"Design of a reconfigurable sensor array for localization of magnetic capsule endoscope","volume":"73","author":"Liu","year":"2024","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1109\/JSEN.2009.2035711","article-title":"A cubic 3-axis magnetic sensor array for wirelessly tracking magnet position and orientation","volume":"10","author":"Hu","year":"2010","journal-title":"IEEE Sens. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1109\/TMECH.2015.2488361","article-title":"A 5-D localization method for a magnetically manipulated untethered robot using a 2-D array of Hall-effect sensors","volume":"21","author":"Son","year":"2016","journal-title":"IEEE ASME Trans. Mechatron."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"13667","DOI":"10.1109\/JSEN.2021.3071432","article-title":"Model-aided real-time localization and parameter identification of a magnetic endoscopic capsule using extended Kalman filter","volume":"21","author":"Boroujeni","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"11204","DOI":"10.1038\/s41598-021-90523-w","article-title":"A localization method for wireless capsule endoscopy using side wall cameras and IMU sensor","volume":"11","author":"Vedaei","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_17","first-page":"1","article-title":"Magnetic localization method of capsule endoscope based on hybrid model","volume":"72","author":"Zhang","year":"2023","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Ali, M.A., Tom, N., Alsunaydih, F.N., and Yuce, M.R. (2025). Recent advancements in localization technologies for wireless capsule endoscopy: A technical review. Sensors, 25.","DOI":"10.3390\/s25010253"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"110196","DOI":"10.1109\/ACCESS.2026.3713825","article-title":"Layer-Conditioned Magnetic Localization With Residual-Weighted Fusion for Wireless Capsule Endoscopy Under Asymmetric Sensor Visibility and GI Motion","volume":"14","author":"Yaghoobian","year":"2026","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1293","DOI":"10.1109\/TAES.2011.5751259","article-title":"Geometric Approach to Strapdown Magnetometer Calibration in Sensor Frame","volume":"47","author":"Vasconcelos","year":"2011","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Yaghoobian, O., and Wahid, K.A. (2025, January 19\u201321). A New Localization Algorithm for a Two-Layer Magnetic Sensor Array in Capsule Endoscopy. Proceedings of the 28th International Conference on Computer and Information Technology (ICCIT 2025), Cox\u2019s Bazar, Bangladesh.","DOI":"10.1109\/ICCIT68739.2025.11490218"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"26","DOI":"10.5946\/ce.2016.49.1.26","article-title":"Challenges and future of wireless capsule endoscopy","volume":"49","author":"Camus","year":"2016","journal-title":"Clin. Endosc."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Han, J., Nguyen, K.T., Kim, E.S., Park, J.O., Choe, E., Moon, C.b., and Kim, J. (2026). Posture Tracking of Active Capsule Endoscopes Integrated with Magnetic Actuation Using Hall-Effect Sensors. Micromachines, 17.","DOI":"10.3390\/mi17030327"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"20393","DOI":"10.1038\/s41598-026-47589-1","article-title":"Two-stage cylindrical magnetic localization with neural network calibration for wearable capsule endoscopy","volume":"16","author":"Yaghoobian","year":"2026","journal-title":"Sci. Rep."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/17\/5536\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T04:27:14Z","timestamp":1788496034000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/17\/5536"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,31]]},"references-count":24,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["s26175536"],"URL":"https:\/\/doi.org\/10.3390\/s26175536","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,31]]}}}