{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T16:56:37Z","timestamp":1783529797125,"version":"3.55.0"},"reference-count":26,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,4,28]],"date-time":"2022-04-28T00:00:00Z","timestamp":1651104000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2021M701537"],"award-info":[{"award-number":["2021M701537"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["41774014"],"award-info":[{"award-number":["41774014"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["41574014"],"award-info":[{"award-number":["41574014"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["XLYC2002082"],"award-info":[{"award-number":["XLYC2002082"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["085015"],"award-info":[{"award-number":["085015"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China","award":["2021M701537"],"award-info":[{"award-number":["2021M701537"]}]},{"name":"National Natural Science Foundation of China","award":["41774014"],"award-info":[{"award-number":["41774014"]}]},{"name":"National Natural Science Foundation of China","award":["41574014"],"award-info":[{"award-number":["41574014"]}]},{"name":"National Natural Science Foundation of China","award":["XLYC2002082"],"award-info":[{"award-number":["XLYC2002082"]}]},{"name":"National Natural Science Foundation of China","award":["085015"],"award-info":[{"award-number":["085015"]}]},{"DOI":"10.13039\/501100018617","name":"Liaoning Revitalization Talents Program","doi-asserted-by":"publisher","award":["2021M701537"],"award-info":[{"award-number":["2021M701537"]}],"id":[{"id":"10.13039\/501100018617","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018617","name":"Liaoning Revitalization Talents Program","doi-asserted-by":"publisher","award":["41774014"],"award-info":[{"award-number":["41774014"]}],"id":[{"id":"10.13039\/501100018617","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018617","name":"Liaoning Revitalization Talents Program","doi-asserted-by":"publisher","award":["41574014"],"award-info":[{"award-number":["41574014"]}],"id":[{"id":"10.13039\/501100018617","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018617","name":"Liaoning Revitalization Talents Program","doi-asserted-by":"publisher","award":["XLYC2002082"],"award-info":[{"award-number":["XLYC2002082"]}],"id":[{"id":"10.13039\/501100018617","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018617","name":"Liaoning Revitalization Talents Program","doi-asserted-by":"publisher","award":["085015"],"award-info":[{"award-number":["085015"]}],"id":[{"id":"10.13039\/501100018617","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Frontier Science and Technology Innovation Project and the Innovation Workstation Project of Science and Technology Commission of the Central Military Commission","award":["2021M701537"],"award-info":[{"award-number":["2021M701537"]}]},{"name":"Frontier Science and Technology Innovation Project and the Innovation Workstation Project of Science and Technology Commission of the Central Military Commission","award":["41774014"],"award-info":[{"award-number":["41774014"]}]},{"name":"Frontier Science and Technology Innovation Project and the Innovation Workstation Project of Science and Technology Commission of the Central Military Commission","award":["41574014"],"award-info":[{"award-number":["41574014"]}]},{"name":"Frontier Science and Technology Innovation Project and the Innovation Workstation Project of Science and Technology Commission of the Central Military Commission","award":["XLYC2002082"],"award-info":[{"award-number":["XLYC2002082"]}]},{"name":"Frontier Science and Technology Innovation Project and the Innovation Workstation Project of Science and Technology Commission of the Central Military Commission","award":["085015"],"award-info":[{"award-number":["085015"]}]},{"name":"Outstanding Youth Fund of China Academy of Space Technology","award":["2021M701537"],"award-info":[{"award-number":["2021M701537"]}]},{"name":"Outstanding Youth Fund of China Academy of Space Technology","award":["41774014"],"award-info":[{"award-number":["41774014"]}]},{"name":"Outstanding Youth Fund of China Academy of Space Technology","award":["41574014"],"award-info":[{"award-number":["41574014"]}]},{"name":"Outstanding Youth Fund of China Academy of Space Technology","award":["XLYC2002082"],"award-info":[{"award-number":["XLYC2002082"]}]},{"name":"Outstanding Youth Fund of China Academy of Space Technology","award":["085015"],"award-info":[{"award-number":["085015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>This paper mainly studies the improvement of the efficiency and out-of-domain reliability of gravity matching navigation for underwater vehicles. To overcome the traversal low-efficiency problem of the traditional terrain contour matching (TERCOM) algorithm and improve the positioning reliability of its out-of-domain mismatches, a novel soft-margin local semicircular-domain re-searching model (SLSR) is proposed by integrating the soft-margin circular grid matching (SCGM) mechanism and the local semicircular grid re-matching (LSGR) mechanism. SCGM uses three times the inertial navigation cumulative error and adds the unit grid resolution as the soft margin boundary to generate the soft-margin circular domain, which contributes to reducing in-domain matching grid points and enhancing the matching efficiency of algorithms. Then the optimal matching position in this soft-margin circular domain is obtained by using the optimization principle of matching indices. LSGR is triggered when the optimal matching position of SCGM is located near the soft-margin circular-domain boundary. It employs this optimal matching point as the center and the unit inertial navigation error as the radius to recreate the semicircular local re-searching matched grid domain (termed as semicircular domain). Moreover, the optimal matching point in this semicircular domain is obtained by the matching index optimization principle, and then it is compared and updated to obtain the final best matching position of SLSR. The simulation results show that SCGM and LSGR of the proposed SLSR method can effectively improve the matching efficiency and out-of-domain matching reliability of underwater navigation, respectively. Under the same testing conditions for the tracking starting points from three gravity regions, the number of out-of-domain mismatches of SLSR, compared with TERCOM, are lower up to 92.68%, 90.24% and 98.62%, while the average matching accuracies are relatively improved by 88.37%, 85.48% and 83.66%, which verifies the validity and feasibility of the proposed SLSR model on improving the efficiency and out-of-domain reliability of underwater gravity matching navigation.<\/jats:p>","DOI":"10.3390\/rs14092129","type":"journal-article","created":{"date-parts":[[2022,4,28]],"date-time":"2022-04-28T22:20:06Z","timestamp":1651184406000},"page":"2129","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Improving Matching Efficiency and Out-of-domain Reliability of Underwater Gravity Matching Navigation Based on a Novel Soft-margin Local Semicircular-domain Re-searching Model"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5861-0798","authenticated-orcid":false,"given":"Shijie","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"},{"name":"Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, China"},{"name":"Institute for Optimization and Decision Analytics, Liaoning Technical University, Fuxin 123000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"},{"name":"Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhaowei","family":"Li","sequence":"additional","affiliation":[{"name":"Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huizhong","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aigong","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhao, S., Zheng, W., Li, Z., Xu, A., and Zhu, H. (2021). Improving Matching Accuracy of Underwater Gravity Matching Navigation Based on Iterative Optimal Annulus Point Method with a Novel Grid Topology. Remote Sens., 13.","DOI":"10.3390\/rs13224616"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8441","DOI":"10.1109\/TVT.2021.3099126","article-title":"Variational Bayesian-Based Filter for Inaccurate Input in Underwater Navigation","volume":"70","author":"Huang","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1109\/TMECH.2018.2806350","article-title":"A Matching Algorithm Based on the Nonlinear Filter and Similarity Transformation for Gravity-Aided Underwater Navigation","volume":"23","author":"Han","year":"2018","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5206","DOI":"10.1109\/TIE.2020.2988227","article-title":"Improved Particle Filter-Based Matching Method with Gravity Sample Vector for Underwater Gravity-Aided Navigation","volume":"68","author":"Wang","year":"2020","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1731","DOI":"10.1109\/JSEN.2017.2779463","article-title":"Grid Design for Efficient and Accurate Point Mass Filter-Based Terrain Referenced Navigation","volume":"18","author":"Jeon","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1109\/TGRS.2014.2335773","article-title":"Automated Generation of a Digital Elevation Model Over Steep Terrain in Antarctica From High-Resolution Satellite Imagery","volume":"53","author":"Lee","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Liu, H., Wu, L., Bao, L., Li, Q., Zhang, P., and Wang, Y. (2021). Gravity matching navigation algorithm based on multiscale search and Hadamard transformed difference. ISA Trans., in press.","DOI":"10.1016\/j.isatra.2021.10.013"},{"key":"ref_8","first-page":"8500418","article-title":"A Computationally Efficient Outlier-Robust Cubature Kalman Filter for Underwater Gravity Matching Navigation","volume":"71","author":"Wang","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1109\/TAES.2019.2911766","article-title":"Parameter Estimation of Radar Noise Model for Terrain Referenced Navigation Using a New EM Initialization Method","volume":"56","author":"Park","year":"2019","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1109\/TMECH.2016.2519925","article-title":"A Particle Filter-Based Matching Algorithm with Gravity Sample Vector for Underwater Gravity Aided Navigation","volume":"21","author":"Wang","year":"2016","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1117\/12.959127","article-title":"Terrain contour matching (TERCOM): A cruise missile guidance aid","volume":"Volume 238","author":"Golden","year":"1980","journal-title":"Image Processing for Missile Guidance"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1017\/S0373463319000535","article-title":"An Improved ICCP Matching Algorithm for use in an Interference Environment during Geomagnetic Navigation","volume":"73","author":"Xiao","year":"2020","journal-title":"J. Navig."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1017\/S0373463315000235","article-title":"Research on the Relative Positions-Constrained Pattern Matching Method for Underwater Gravity-Aided Inertial Navigation","volume":"68","author":"Wu","year":"2015","journal-title":"J. Navig."},{"key":"ref_14","unstructured":"Wang, S., Cheng, G., and Zhao, J. (2011, January 15\u201317). The study on the TERCOM mismatch diagnostic based on detecting the extreme value of similarity. Proceedings of the 2011 Second International Conference on Mechanic Automation and Control Engineering, Hohhot, China."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2880","DOI":"10.1109\/JSEN.2017.2685429","article-title":"A Mismatch Diagnostic Method for TERCOM-Based Underwater Gravity-Aided Navigation","volume":"17","author":"Han","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Dai, T., Miao, L., and Guo, Y. (2019). A Real-Time Mismatch Detection Method for Underwater Database-Referenced Navigation. Sensors, 19.","DOI":"10.3390\/s19020307"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1631\/FITEE.1900556","article-title":"Terrain matching localization for hybrid underwater vehicle in the Challenger Deep of the Mariana Trench","volume":"21","author":"Wang","year":"2020","journal-title":"Front. Inf. Technol. Electron. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1109\/TMECH.2020.3012499","article-title":"A Delaunay Triangulation-Based Matching Area Selection Algorithm for Underwater Gravity-Aided Inertial Navigation","volume":"26","author":"Wang","year":"2021","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.isatra.2020.10.004","article-title":"High-precision initialization and acceleration of particle filter convergence to improve the accuracy and stability of terrain aided navigation","volume":"110","author":"Wang","year":"2021","journal-title":"ISA Trans."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Yuan, G., Zhang, H., Yuan, K., and Tao, C. (2011, January 15\u201319). A Combinational Underwater Aided Navigation Algorithm Based on TERCOM\/ICCP and Kalman Filter. Proceedings of the 2011 Fourth International Joint Conference on Computational Sciences and Optimization, Kunming and Lijiang City, China.","DOI":"10.1109\/CSO.2011.23"},{"key":"ref_21","first-page":"2405","article-title":"Improving the matching efficiency of underwater gravity matching navigation based on a new hierarchical neighborhood threshold method","volume":"62","author":"Li","year":"2019","journal-title":"Chin. J. Geophys."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Li, Z., Zheng, W., and Wu, F. (2019). Geodesic-Based Method for Improving Matching Efficiency of Underwater Terrain Matching Navigation. Sensors, 19.","DOI":"10.3390\/s19122709"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1124","DOI":"10.1109\/JSEN.2014.2360916","article-title":"A Novel Terrain-Aided Navigation Algorithm Combined with the TERCOM Algorithm and Particle Filter","volume":"15","author":"Zhao","year":"2014","journal-title":"IEEE Sens. J."},{"key":"ref_24","first-page":"2503212","article-title":"Geomagnetic Gradient-Assisted Evolutionary Algorithm for Long-Range Underwater Navigation","volume":"70","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1080\/00207721.2019.1567866","article-title":"A robust underwater navigation method fusing data of gravity anomaly and magnetic anomaly","volume":"50","author":"Dai","year":"2019","journal-title":"Int. J. Syst. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1109\/JOE.2021.3085941","article-title":"Terrain-Aided Navigation with Coarse Maps\u2014Toward an Arctic Crossing with an AUV","volume":"46","author":"Salavasidis","year":"2021","journal-title":"IEEE J. Ocean. Eng."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/9\/2129\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:03:39Z","timestamp":1760137419000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/9\/2129"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,28]]},"references-count":26,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["rs14092129"],"URL":"https:\/\/doi.org\/10.3390\/rs14092129","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,28]]}}}