{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:28:25Z","timestamp":1767706105671,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2023,8,20]],"date-time":"2023-08-20T00:00:00Z","timestamp":1692489600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51979041","61973079"],"award-info":[{"award-number":["51979041","61973079"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The strap-down inertial navigation system (SINS) and Doppler velocity log (DVL) integrated navigation system are widely used for autonomous underwater vehicles (AUVs). Whereas DVL works in the water tracking mode, the velocity provided by DVL is relative to the current layer and cannot be directly used to suppress the divergence of SINS errors. Therefore, the estimation and compensation of the ocean current velocity play an essential role in improving navigation positioning accuracy. In recent works, ocean currents are considered constant over a short term in small areas. In the common KF algorithm with the ocean current as a state vector, the current velocity cannot be estimated because the current velocity and the SINS velocity error are coupled. In this paper, two virtual metrology filter (VMF) methods are proposed for estimating the velocity of ocean currents based on the properties that the currents remain unchanged at the adjacent moments. New measurement equations are constructed to decouple the current velocity and the SINS velocity error, respectively. Simulations and lake tests show that both proposed methods are effective in estimating the current velocity, and each has its advantages in estimating the ocean current velocity or the misalignment angle.<\/jats:p>","DOI":"10.3390\/rs15164097","type":"journal-article","created":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T01:46:56Z","timestamp":1692582416000},"page":"4097","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Virtual Metrology Filter-Based Algorithms for Estimating Constant Ocean Current Velocity"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3289-7380","authenticated-orcid":false,"given":"Yongjiang","family":"Huang","sequence":"first","affiliation":[{"name":"School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"},{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, Nanjing 210096, China"}]},{"given":"Xixiang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"},{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, Nanjing 210096, China"}]},{"given":"Qiantong","family":"Shao","sequence":"additional","affiliation":[{"name":"School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"},{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, Nanjing 210096, China"}]},{"given":"Zixuan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"},{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, Nanjing 210096, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1109\/JOE.2010.2100470","article-title":"Model-Aided INS With Sea Current Estimation for Robust Underwater Navigation","volume":"36","author":"Hegrenaes","year":"2011","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_2","first-page":"9567","article-title":"A Novel Calibration Method of SINS\/DVL Integration Navigation System Based on Quaternion","volume":"20","author":"Xu","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_3","first-page":"8504211","article-title":"A New Coupled Method of SINS\/DVL Integrated Navigation Based on Improved Dual Adaptive Factors","volume":"70","author":"Liu","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"9992041","DOI":"10.1155\/2021\/9992041","article-title":"Modified Sage-Husa Adaptive Kalman Filter-Based SINS\/DVL Integrated Navigation System for AUV","volume":"2021","author":"Liu","year":"2021","journal-title":"J. Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"102441","DOI":"10.1016\/j.apor.2020.102441","article-title":"A practical INS\/GPS\/DVL\/PS integrated navigation algorithm and its application on Autonomous Underwater Vehicle","volume":"106","author":"Mu","year":"2021","journal-title":"Appl. Ocean. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"106831","DOI":"10.1016\/j.measurement.2019.07.059","article-title":"Pseudo DVL reconstruction by an evolutionary TS-fuzzy algorithm for ocean vehicles","volume":"147","author":"Hashemi","year":"2019","journal-title":"Measurement"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1738","DOI":"10.1109\/TMECH.2021.3090428","article-title":"Inertial-Based Integration With Transformed INS Mechanization in Earth Frame","volume":"27","author":"Chang","year":"2022","journal-title":"IEEE-ASME Trans. Mech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1109\/JSEN.2021.3108497","article-title":"Strapdown Inertial Navigation System Initial Alignment Based on Group of Double Direct Spatial Isometries","volume":"22","author":"Chang","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2984","DOI":"10.1109\/JIOT.2021.3094305","article-title":"Efficient Velocity Estimation and Location Prediction in Underwater Acoustic Sensor Networks","volume":"9","author":"Song","year":"2022","journal-title":"IEEE Internet Things"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"035105","DOI":"10.1088\/1361-6501\/aca2cb","article-title":"GSCV-XGBoost based information reconstruction and fusion method for SINS\/DVL integrated navigation system","volume":"34","author":"Qin","year":"2023","journal-title":"Meas. Sci. Technol."},{"key":"ref_11","unstructured":"Wu, Y.L., Wang, X.S., Zhao, Y.W., and Tang, Y.J. (2020). AOPC 2020: Optical Sensing and Imaging Technology, CSOE."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"110325","DOI":"10.1016\/j.measurement.2021.110325","article-title":"A calibration method of DVL in integrated navigation system based on particle swarm optimization","volume":"187","author":"Li","year":"2022","journal-title":"Measurement"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"065003","DOI":"10.1088\/0957-0233\/27\/6\/065003","article-title":"A novel separation and calibration method for DVL and compass error in dead reckoning navigation systems","volume":"27","author":"Zhang","year":"2016","journal-title":"Meas. Sci. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1109\/TVT.2020.3048730","article-title":"A New Kalman Filter-Based In-Motion Initial Alignment Method for DVL-Aided Low-Cost SINS","volume":"70","author":"Luo","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1659","DOI":"10.1109\/TMECH.2020.2982199","article-title":"Robust Initial Alignment for SINS\/DVL Based on Reconstructed Observation Vectors","volume":"25","author":"Xu","year":"2020","journal-title":"IEEE-ASME Trans. Mech."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"5183","DOI":"10.1109\/TIM.2019.2955187","article-title":"A Novel SINS\/DVL Tightly Integrated Navigation Method for Complex Environment","volume":"69","author":"Wang","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"337","DOI":"10.3182\/20120410-3-PT-4028.00056","article-title":"GAS ocean current estimation with limited velocity readings","volume":"45","author":"Batista","year":"2012","journal-title":"IFAC Proc. Vol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.isatra.2020.05.033","article-title":"In-motion coarse alignment method for SINS\/DVL with the attitude dynamics","volume":"105","author":"Yao","year":"2020","journal-title":"ISA Trans."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2604","DOI":"10.1016\/j.automatica.2011.09.024","article-title":"Position USBL\/DVL sensor-based navigation filter in the presence of unknown ocean currents","volume":"47","author":"Morgado","year":"2011","journal-title":"Automatica"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"106148","DOI":"10.1016\/j.oceaneng.2019.106148","article-title":"Cooperative current estimation based multi-AUVs localization for deep ocean applications","volume":"188","author":"Wu","year":"2019","journal-title":"Ocean. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"He, K.F., Liu, H.M., and Wang, Z.J. (2020). A Novel Adaptive Two-Stage Information Filter Approach for Deep-Sea USBL\/DVL Integrated Navigation. Sensors, 20.","DOI":"10.3390\/s20216029"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3444","DOI":"10.1109\/LRA.2020.2976318","article-title":"2D Estimation of Velocity Relative to Water and Tidal Currents Based on Differential Pressure for Autonomous Underwater Vehicles","volume":"5","author":"Meurer","year":"2020","journal-title":"IEEE Robot. Autom. Let."},{"key":"ref_23","unstructured":"Saksvik, I.B., Alcocer, A., and Hassani, V. (2021). OCEANS 2021: San Diego\u2013Porto, IEEE."},{"key":"ref_24","unstructured":"Zang, X.L., Ben, Y.Y., and Li, Q. (2020). 2020 IEEE\/ION Position, Location and Navigation Symposium (PLANS), IEEE."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.1007\/s12083-022-01310-x","article-title":"An effective LS-SVM\/AKF aided SINS\/DVL integrated navigation system for underwater vehicles","volume":"15","author":"Sun","year":"2022","journal-title":"Peer Peer Netw. Appl."},{"key":"ref_26","unstructured":"Chang, D., Johnson-Roberson, M., and Sun, J. (2020). 2020 American Control Conference (ACC), IEEE."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2301","DOI":"10.1109\/TCST.2021.3139307","article-title":"An Active Perception Framework for Autonomous Underwater Vehicle Navigation Under Sensor Constraints","volume":"30","author":"Chang","year":"2022","journal-title":"IEEE Trans. Control Syst. Trans."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1108\/AA-05-2020-0072","article-title":"Self-aided SINS for spiral-diving human-occupied vehicle in midwater","volume":"41","author":"Liu","year":"2021","journal-title":"Assem. Autom."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"111763","DOI":"10.1016\/j.measurement.2022.111763","article-title":"A Self-Aided Strapdown inertial navigation method based on maneuver constraints and incremental observation","volume":"201","author":"Wu","year":"2022","journal-title":"Measurement"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1000215","DOI":"10.1109\/TIM.2020.3010042","article-title":"A Dual-State Filter for a Relative Velocity Aiding Strapdown Inertial Navigation System","volume":"70","author":"Ben","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"065112","DOI":"10.1063\/5.0089117","article-title":"A virtual velocity-based integrated navigation method for strapdown inertial navigation system and Doppler velocity log coupled with unknown current","volume":"93","author":"Wang","year":"2022","journal-title":"Rev. Sci. Instrum."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/16\/4097\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:38:09Z","timestamp":1760128689000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/16\/4097"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,20]]},"references-count":31,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["rs15164097"],"URL":"https:\/\/doi.org\/10.3390\/rs15164097","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,8,20]]}}}