{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T05:06:23Z","timestamp":1789103183157,"version":"build-2803163510"},"reference-count":28,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T00:00:00Z","timestamp":1788912000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Fundamental Research Funds for the Central Universities","award":["2572025BR94"],"award-info":[{"award-number":["2572025BR94"]}]},{"name":"Advanced Semiconductor Optoelectronic Devices and System Integration Open Project of Shanxi Provincial Key Laboratory in 2026","award":["2026SZKF02"],"award-info":[{"award-number":["2026SZKF02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>In Global Navigation Satellite System (GNSS)-denied deep-sea environments, traditional scalar gravity matching navigation methods frequently suffer severe performance degradation in weak-feature, highly repetitive gravity anomaly regions. Inspired by the hippocampal spatial memory mechanism and natural graded foraging behavior of benthic marine organisms, this paper proposes a full-chain bionic framework named the Physics-Consistent Multi-Scale Adaptive Particle Filter for Gravity Matching Navigation (PC-MAPF-GM). This method endows the particle filter with four layers of biologically mimicked autonomous regulation capabilities: quantitative gravity field local suitability assessment, dynamically adjusted time-varying search scope, three-level multi-scale stepwise matching, and along-track trajectory motion physics consistency constraint. The verification of long-term shipborne lake experiments confirms that the proposed method reduces the final gravity matching positioning root mean square error (RMSE) to only 528.2 m, which is more than 41% lower than the classical terrain contour matching (TERCOM) benchmark and 31% lower than iterative closest contour point (ICCP). This biomimetic full-design-chain solution provides a robust new practical navigation paradigm for long-endurance fully autonomous underwater vehicles operating without any external auxiliary positioning information.<\/jats:p>","DOI":"10.3390\/biomimetics11090651","type":"journal-article","created":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T15:01:56Z","timestamp":1788966116000},"page":"651","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Bio-Inspired Multi-Scale Adaptive Particle Filter for Scalar Gravity Matching Navigation in GNSS-Denied Underwater Environments"],"prefix":"10.3390","volume":"11","author":[{"given":"Xu","family":"Xia","sequence":"first","affiliation":[{"name":"School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China"},{"name":"Hunan Aerospace Electromechanical Equipment and Special Materials Research Institute, Changsha 410205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ningfang","family":"Song","sequence":"additional","affiliation":[{"name":"School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianze","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Control and Information Engineering, Northeast Forestry University, Harbin 150040, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Control and Information Engineering, Northeast Forestry University, Harbin 150040, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingchao","family":"Ban","sequence":"additional","affiliation":[{"name":"Hunan Aerospace Electromechanical Equipment and Special Materials Research Institute, Changsha 410205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenpeng","family":"Wang","sequence":"additional","affiliation":[{"name":"Sichuan Aerospace System Engineering Research Institute, Chengdu 610100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113861","DOI":"10.1016\/j.oceaneng.2023.113861","article-title":"Autonomous Underwater Vehicle Navigation: A Review","volume":"273","author":"Zhang","year":"2023","journal-title":"Ocean Eng."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Jalal, F., and Nasir, F. (2021). Underwater Navigation, Localization and Path Planning for Autonomous Vehicles: A Review. Proceedings of the 2021 International Bhurban Conference on Applied Sciences and Technologies (IBCAST), IEEE.","DOI":"10.1109\/IBCAST51254.2021.9393315"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2109","DOI":"10.1109\/TII.2023.3286901","article-title":"Underwater Downwelling Radiance Fields Enable Three-Dimensional Attitude and Heading Determination","volume":"20","author":"Hu","year":"2024","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3104","DOI":"10.1109\/LSP.2024.3484292","article-title":"Optimizing GNSS\/INS Integrated Navigation: A Deep Learning Approach for Error Compensation","volume":"31","author":"Wu","year":"2024","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"79033","DOI":"10.1109\/ACCESS.2023.3299290","article-title":"Research on GNSS INS & GNSS\/INS Integrated Navigation Method for Autonomous Vehicles: A Survey","volume":"11","author":"He","year":"2023","journal-title":"IEEE Access"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"135728","DOI":"10.1109\/ACCESS.2023.3338537","article-title":"A Real-Time Autonomous Gravity Measurement Method for Underwater Gravity-Aided Navigation","volume":"11","author":"Ai","year":"2023","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Shi, H., Tang, R., Wang, Q., and Song, T. (2024). Performance Evaluation of a Bioinspired Geomagnetic Sensor and Its Application for Geomagnetic Navigation in Simulated Environment. Sensors, 24.","DOI":"10.3390\/s24196477"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"101067","DOI":"10.1016\/j.ejcon.2024.101067","article-title":"Observer design for visual-inertial estimation of pose, linear velocity and gravity direction in planar environments","volume":"80","author":"Bouazza","year":"2024","journal-title":"Eur. J. Control"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Hassan, S., Wang, L., and Mahmud, K.R. (2024). Robotic Odor Source Localization via Vision and Olfaction Fusion Navigation Algorithm. Sensors, 24.","DOI":"10.20944\/preprints202402.1024.v1"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"133380","DOI":"10.1016\/j.neucom.2026.133380","article-title":"Bioinspired Extraction of Relative Nearness Map from Expanding Optic Flow for Collision Avoidance","volume":"681","author":"Zhou","year":"2026","journal-title":"Neurocomputing"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Li, X., Hao, S., Yu, M., Gao, Y., and Fan, S. (2026). Lightweight Low-Light Enhancement Network with Multi-Bio-Inspired Visual Mechanisms. Biomimetics, 11.","DOI":"10.3390\/biomimetics11060401"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1017\/S0373463313000660","article-title":"A Triangle Matching Algorithm for Gravity-Aided Navigation for Underwater Vehicles","volume":"67","author":"Yang","year":"2014","journal-title":"J. Navig."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1017\/S0373463324000250","article-title":"Gravity-Aided Navigation Using Viterbi Map Matching Algorithm","volume":"77","author":"Li","year":"2024","journal-title":"J. Navig."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2537","DOI":"10.1109\/JSEN.2016.2518686","article-title":"An Improved TERCOM-Based Algorithm for Gravity-Aided Navigation","volume":"16","author":"Han","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"97440","DOI":"10.1109\/ACCESS.2019.2929778","article-title":"Gravity Aided Positioning Based on Real-Time ICCP with Optimized Matching Sequence Length","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Dai, Z., and Kang, C. (2014). Geomagnetic Field Aided Inertial Navigation Using the SITAN Algorithm. Proceedings of the 2014 2nd International Conference on Systems and Informatics (ICSAI 2014), IEEE.","DOI":"10.1109\/ICSAI.2014.7009263"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"34851","DOI":"10.1109\/JSEN.2024.3439607","article-title":"A Gravity-Aided Navigation Matching Algorithm Based on Triangulation","volume":"24","author":"Wang","year":"2024","journal-title":"IEEE Sens. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1016\/j.isatra.2021.10.013","article-title":"Gravity Matching Navigation Algorithm Based on Multiscale Search and Hadamard Transformed Difference","volume":"128","author":"Liu","year":"2022","journal-title":"ISA Trans."},{"key":"ref_19","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_20","doi-asserted-by":"crossref","unstructured":"Zhao, X., Zheng, W., Xu, K., and Zhang, H. (2024). Optimizing the Matching Area for Underwater Gravity Matching Navigation Based on a New Gravity Field Feature Parameters Selection Method. Remote Sens., 16.","DOI":"10.3390\/rs16122202"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zhao, S., Zheng, W., Li, Z., Zhu, H., and Xu, A. (2022). 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. Remote Sens., 14.","DOI":"10.3390\/rs14092129"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4507","DOI":"10.1109\/TMECH.2022.3159596","article-title":"A Filtered-Marine Map-Based Matching Method for Gravity-Aided Navigation of Underwater Vehicles","volume":"27","author":"Wang","year":"2022","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"15415","DOI":"10.1109\/JIOT.2025.3527761","article-title":"ID2TM: A Novel Iterative Double-Cross Domain-Center Transfer-Matching Method for Underwater Gravity-Aided Navigation","volume":"12","author":"Zhao","year":"2025","journal-title":"IEEE Internet Things J."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Gao, S., Cai, T., and Fang, K. (2022). Gravity-Matching Algorithm Based on K-Nearest Neighbor. Sensors, 22.","DOI":"10.3390\/s22124454"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Mao, N., Li, A., Xu, J., and Qin, F. (2025). A Multi-Resolution Sequence Method with Strong Constraints for Marine Gravity Matching Navigation. J. Mar. Sci. Eng., 13.","DOI":"10.3390\/jmse13030542"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Kagioulis, E., Knight, J., Graham, P., Nowotny, T., and Philippides, A. (2024). Adaptive Route Memory Sequences for Insect-Inspired Visual Route Navigation. Biomimetics, 9.","DOI":"10.3390\/biomimetics9120731"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1109\/JSEN.2022.3226747","article-title":"An Improved Particle Filter Based on Gravity Measurement Feature in Gravity-Aided Inertial Navigation System","volume":"23","author":"Zhao","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Yu, H., Li, Z., Yang, W., Shen, T., Liang, D., and He, Q. (2023). Underwater Geomagnetic Localization Based on Adaptive Fission Particle-Matching Technology. J. Mar. Sci. Eng., 11.","DOI":"10.3390\/jmse11091739"}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/9\/651\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T04:17:02Z","timestamp":1789100222000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/9\/651"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,9]]},"references-count":28,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["biomimetics11090651"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics11090651","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,9]]}}}