{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T17:13:00Z","timestamp":1770138780363,"version":"3.49.0"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T00:00:00Z","timestamp":1578009600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Development Program of China","award":["2016YFB1102503"],"award-info":[{"award-number":["2016YFB1102503"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11290144"],"award-info":[{"award-number":["11290144"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As multisensor measurement technology is rapidly applied in industrial production, one key issue is the data fusion procedure by combining several datasets from multiple sensors to obtain the overall geometric measurement. In this paper, a multisensor data fusion method based on a Gaussian process model is proposed for complex surface measurements. A robust surface registration method based on the adaptive distance function is firstly used to unify the coordinate systems of different measurement datasets. By introducing an adjustment model, the residuals between several independent datasets from different sensors are then approximated to construct a Gaussian process model-based data fusion system. The proposed method is verified through both simulation verification and actual experiments, indicating that the proposed method can fuse multisensor measurement datasets with better fusion accuracy and faster computational efficiency compared to the existing method.<\/jats:p>","DOI":"10.3390\/s20010278","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T11:55:07Z","timestamp":1578052507000},"page":"278","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Multisensor Data Fusion Method Based on Gaussian Process Model for Precision Measurement of Complex Surfaces"],"prefix":"10.3390","volume":"20","author":[{"given":"Ji","family":"Ding","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering &amp; Automation, Beihang University, Beijing 100083, China"},{"name":"Beijing Engineering Technological Research Center of High-efficient &amp; Green CNC Machining Process and Equipment, Beijing 100083, China"}]},{"given":"Qiang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering &amp; Automation, Beihang University, Beijing 100083, China"},{"name":"Beijing Engineering Technological Research Center of High-efficient &amp; Green CNC Machining Process and Equipment, Beijing 100083, China"}]},{"given":"Mingxuan","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering &amp; Automation, Beihang University, Beijing 100083, China"},{"name":"Beijing Engineering Technological Research Center of High-efficient &amp; Green CNC Machining Process and Equipment, Beijing 100083, China"}]},{"given":"Pengpeng","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering &amp; Automation, Beihang University, Beijing 100083, China"},{"name":"Beijing Engineering Technological Research Center of High-efficient &amp; Green CNC Machining Process and Equipment, Beijing 100083, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1016\/j.cirp.2012.05.009","article-title":"Technological shifts in surface metrology","volume":"61","author":"Jiang","year":"2012","journal-title":"CIRP Ann."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1016\/j.cirp.2013.05.003","article-title":"Manufacturing and measurement of freeform optics","volume":"62","author":"Fang","year":"2013","journal-title":"CIRP Ann."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"023001","DOI":"10.1088\/2051-672X\/3\/2\/023001","article-title":"Review of the mathematical foundations of data fusion techniques in surface metrology","volume":"3","author":"Wang","year":"2015","journal-title":"Surf. Topogr. Metrol. Prop."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1016\/j.cirp.2009.09.008","article-title":"Multisensor data fusion in dimensional metrology","volume":"58","author":"Weckenmann","year":"2009","journal-title":"CIRP Ann."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.optlaseng.2016.01.005","article-title":"The use of low density high accuracy (LDHA) data for correction of high density low accuracy (HDLA) point cloud","volume":"81","author":"Rak","year":"2016","journal-title":"Opt. Lasers Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"22344","DOI":"10.1109\/ACCESS.2017.2759798","article-title":"An Efficient Pose Measurement Method of a Space Non-Cooperative Target Based on Stereo Vision","volume":"5","author":"Peng","year":"2017","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1109\/TIM.2019.2893010","article-title":"Virtual Stereovision Pose Measurement of Noncooperative Space Targets for a Dual-Arm Space Robot","volume":"69","author":"Peng","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1016\/j.measurement.2010.11.013","article-title":"The hybrid contact\u2013optical coordinate measuring system","volume":"44","author":"Kupiec","year":"2011","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.optlaseng.2014.12.023","article-title":"Proximity weighted correction of high density high uncertainty (HDHU) point cloud using low density low uncertainty (LDLU) reference point coordinates","volume":"68","author":"Rak","year":"2015","journal-title":"Opt. Lasers Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3008","DOI":"10.1109\/JSEN.2018.2889469","article-title":"Pose Measurement and Motion Estimation of Space Non-Cooperative Targets Based on Laser Radar and Stereo-Vision Fusion","volume":"19","author":"Peng","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1115\/1.2179459","article-title":"Building Surrogate Models Based on Detailed and Approximate Simulations","volume":"128","author":"Qian","year":"2006","journal-title":"J. Mech. Des."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Wang, Y., Ye, X., Wang, Z., Fu, L., Liu, C., and Wang, Z. (2018). Multi-Sensor Registration in High-Precision CMM Based on a Composite Standard. Sensors, 18.","DOI":"10.3390\/s18041220"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1109\/34.121791","article-title":"A method for registration of 3-D shapes","volume":"14","author":"Besl","year":"1992","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s11263-006-5167-2","article-title":"Geometry and convergence analysis of algorithms for registration of 3D shapes","volume":"67","author":"Pottmann","year":"2006","journal-title":"Int. J. Comput. Vis."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.cviu.2004.04.002","article-title":"Registration without ICP","volume":"95","author":"Pottmann","year":"2004","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1145\/1138450.1138453","article-title":"Fitting B-spline curves to point clouds by curvature-based squared distance minimization","volume":"25","author":"Wang","year":"2006","journal-title":"ACM Trans. Graph."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1049\/iet-cvi.2009.0032","article-title":"Three-dimensional point-based shape registration algorithm based on adaptive distance function","volume":"5","author":"Li","year":"2011","journal-title":"IET Comput. Vis."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Li, W.L., Yin, Z.P., and Xiong, Y.L. (2009, January 22\u201324). Adaptive Distance Function and its Application in Free-form Surface Localization. Proceedings of the Icia: 2009 International Conference on Information and Automation, Zhuhai, Macau, China.","DOI":"10.1109\/ICINFA.2009.5204889"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1115\/1.2356498","article-title":"A New Data Fusion Method for Scanned Models","volume":"6","author":"Jamshidi","year":"2006","journal-title":"J. Comput. Inf. Sci. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1198\/004017008000000082","article-title":"Bayesian Hierarchical Modeling for Integrating Low-Accuracy and High-Accuracy Experiments","volume":"50","author":"Qian","year":"2008","journal-title":"Technometrics"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1080\/0740817X.2010.521804","article-title":"Bayesian hierarchical model for combining misaligned two-resolution metrology data","volume":"43","author":"Xia","year":"2011","journal-title":"IIE Trans."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Kong, L.B., Ren, M.J., and Xu, M. (2017). Development of Data Registration and Fusion Methods for Measurement of Ultra-Precision Freeform Surfaces. Sensors, 17.","DOI":"10.3390\/s17051110"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Gong, M., Zhang, Z., Zeng, D., and Peng, T. (2019). Three-Dimensional Measurement Method of Four-View Stereo Vision Based on Gaussian Process Regression. Sensors, 19.","DOI":"10.3390\/s19204486"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.rcim.2012.07.003","article-title":"Point set augmentation through fitting for enhanced ICP registration of point clouds in multisensor coordinate metrology","volume":"29","author":"Senin","year":"2013","journal-title":"Robot. Comput. Integr. Manuf."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.precisioneng.2016.11.014","article-title":"A weighted least square based data fusion method for precision measurement of freeform surfaces","volume":"48","author":"Ren","year":"2017","journal-title":"Precis. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1080\/07408170801971502","article-title":"Gaussian process method for form error assessment using coordinate measurements","volume":"40","author":"Xia","year":"2008","journal-title":"IIE Trans."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.precisioneng.2014.11.011","article-title":"Multisensor data fusion via Gaussian process models for dimensional and geometric verification","volume":"40","author":"Colosimo","year":"2015","journal-title":"Precis. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1080\/00401706.2013.879075","article-title":"Geodesic Gaussian Processes for the Parametric Reconstruction of a Free-Form Surface","volume":"57","author":"Colosimo","year":"2015","journal-title":"Technometrics"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1080\/00224065.2014.11917956","article-title":"From Profile to Surface Monitoring: SPC for Cylindrical Surfaces Via Gaussian Processes","volume":"46","author":"Colosimo","year":"2014","journal-title":"J. Qual. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"075003","DOI":"10.1088\/1361-6501\/ab16ad","article-title":"A robust registration algorithm of point clouds based on adaptive distance function for surface inspection","volume":"30","author":"Ding","year":"2019","journal-title":"Meas. Sci. Technol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/1\/278\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:42:15Z","timestamp":1760362935000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/1\/278"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,3]]},"references-count":30,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["s20010278"],"URL":"https:\/\/doi.org\/10.3390\/s20010278","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,3]]}}}