{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T16:00:25Z","timestamp":1786118425820,"version":"build-2736575974"},"reference-count":24,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T00:00:00Z","timestamp":1785974400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The Velocity-Aided Navigation (VAN) method for determining latitude, longitude, and altitude is proposed when global navigation satellite system (GNSS) signals are unavailable. Currently, GNSS receivers are the primary navigation systems that meet consumer demand for location accuracy. However, GNSS receivers are not autonomous. Strapdown inertial navigation systems (SINSs), unlike GNSSs, are autonomous. Their operating principle is based on double integration of accelerometer output signals. However, they have a significant drawback: SINS errors increase significantly over time. Two approaches are used to improve accuracy. The first involves using expensive, high-precision gyroscopes and accelerometers. The other involves correcting the SINS by integrating it with navigation systems built on physical principles different from those of the SINS. An alternative method, based on VAN and an inertial measurement unit (IMU), for determining navigation parameters is proposed and does not require double integration of accelerometer output signals. Analytical expressions for the errors of the new method are derived. Calculations showed that the errors of the new method are significantly smaller than those of the autonomous SINS. Experimental testing confirmed the calculation results and demonstrated that the errors of the new method are comparable to those of the SINS integrated with GNSS using a Kalman filter. The proposed alternative VAN method for determining latitude, longitude, and altitude can be used independently, as an alternative to GNSS for integration with the SINS, and can also serve as a backup navigation system.<\/jats:p>","DOI":"10.3390\/s26155006","type":"journal-article","created":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T15:52:30Z","timestamp":1786031550000},"page":"5006","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Velocity-Aided Navigation in GNSS-Denied Environments"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3875-0646","authenticated-orcid":false,"given":"Vadym","family":"Avrutov","sequence":"first","affiliation":[{"name":"Department of Computer-Integrated Optical and Navigation Systems, National Technical University of Ukraine \u2018Igor Sikorsky Kyiv Polytechnic Institute\u2019, 03056 Kyiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6848-816X","authenticated-orcid":false,"given":"Nadiia","family":"Bouraou","sequence":"additional","affiliation":[{"name":"Department of Computer-Integrated Optical and Navigation Systems, National Technical University of Ukraine \u2018Igor Sikorsky Kyiv Polytechnic Institute\u2019, 03056 Kyiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Oleg","family":"Nesterenko","sequence":"additional","affiliation":[{"name":"Inertial Labs UA, 01010 Kyiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sergii","family":"Holovach","sequence":"additional","affiliation":[{"name":"Joint Stock Company \u2018ELMIZ\u2019, 02099 Kyiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Oleksii","family":"Hehelskyi","sequence":"additional","affiliation":[{"name":"Department of Computer-Integrated Optical and Navigation Systems, National Technical University of Ukraine \u2018Igor Sikorsky Kyiv Polytechnic Institute\u2019, 03056 Kyiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Olha","family":"Pazdrii","sequence":"additional","affiliation":[{"name":"Department of Computer-Integrated Optical and Navigation Systems, National Technical University of Ukraine \u2018Igor Sikorsky Kyiv Polytechnic Institute\u2019, 03056 Kyiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1134\/S207510871902007X","article-title":"GPS Based Navigation Systems in Difficult Environments","volume":"10","author":"Schmidt","year":"2019","journal-title":"Gyroscopy Navig."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1186\/s43020-025-00162-z","article-title":"Gnss-denied unmanned aerial vehicle navigation: Analyzing computational complexity, sensor fusion, and localization methodologies","volume":"6","author":"Jarraya","year":"2025","journal-title":"Satell. Navig."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Tal, A., Klein, I., and Katz, R. (2017). Inertial Navigation System\/Doppler Velocity Log (INS\/DVL) Fusion with Partial DVL Measurements. Sensors, 17.","DOI":"10.3390\/s17020415"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1017\/S0373463315000703","article-title":"Underwater Doppler Navigation with Self-calibration","volume":"69","author":"Pan","year":"2016","journal-title":"J. Navig."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1046","DOI":"10.3390\/s130101046","article-title":"A Novel Scheme for DVL-Aided SINS In-Motion Alignment Using UKF Techniques","volume":"13","author":"Li","year":"2013","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Cohen, N., and Klein, I. (2024). Seamless Underwater Navigation with Limited Doppler Velocity Log Measurements. IEEE Trans. Intell. Veh., early access.","DOI":"10.1109\/TIV.2024.3457772"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"13519","DOI":"10.1109\/JSEN.2026.3674924","article-title":"A Hybrid Physics\u2013Data-Driven Navigation Method for AUVs Fusing Hydrographic Information with INS\/DVL Integration","volume":"26","author":"Mo","year":"2026","journal-title":"IEEE Sens. J."},{"key":"ref_8","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."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"29258","DOI":"10.1109\/JIOT.2026.3686859","article-title":"An INS\/DVL\/PS Integrated Underwater System Based on NLS-Transformer-LSTM Velocity Prediction Model","volume":"13","author":"Zhang","year":"2026","journal-title":"IEEE Internet Things J."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Mourikis, A., Trawny, N., Roumeliotis, S.I., Johnson, A.E., and Matthies, L.H. (2008). Vision-Aided Inertial Navigation for Precise Planetary Landing: Analysis and Experiments. Robotics: Science and Systems III, MIT Press.","DOI":"10.15607\/RSS.2007.III.019"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Serio, P., Ryals, A.D., Piana, F., Gentilini, L., and Pollini, L. (2026). Vision-Aided Velocity Estimation in GNSS Degraded or Denied Environments. Sensors, 26.","DOI":"10.3390\/s26030786"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Li, X., Liu, C., and Yan, X. (2025). Robust Visual-Inertial Odometry with Learning-Based Line Features in a Illumination-Changing Environment. Sensors, 25.","DOI":"10.3390\/s25165029"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"7838","DOI":"10.1109\/JSEN.2024.3406948","article-title":"Low Latency Visual Inertial Odometry with On-Sensor Accelerated Optical Flow for Resource-Constrained UAVs","volume":"25","author":"Magno","year":"2025","journal-title":"IEEE Sens. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"8526","DOI":"10.1109\/TIE.2022.3212421","article-title":"A Bioinspired Navigation System for Multirotor UAV by Integrating Polarization Compass\/Magnetometer\/INS\/GNSS","volume":"70","author":"Wang","year":"2023","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"10816422","DOI":"10.1109\/ACCESS.2024.3523249","article-title":"Bio-Inspired Polarization Compass for Solar Azimuth Prediction Under Clear and Cloudy Sky Conditions","volume":"13","author":"Agarwal","year":"2025","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zhang, L., Cao, X., Su, M., and Sui, Y. (2025). Collaborative Integrated Navigation for Unmanned Aerial Vehicle Swarms Under Multiple Uncertainties. Sensors, 25.","DOI":"10.3390\/s25030617"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Arshid, K., Krayani, A., Marcenaro, L., Gomez, D.M., and Regazzoni, C. (2025). Toward Autonomous UAV Swarm Navigation: A Review of Trajectory Design Paradigms. Sensors, 25.","DOI":"10.3390\/s25185877"},{"key":"ref_18","first-page":"318","article-title":"Overview of Mutual Localization Techniques Between Unmanned Aerial Vehicles in Swarm","volume":"19","author":"Czaja","year":"2025","journal-title":"TransNav Int. J. Mar. Navig. Saf. Sea Transp."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.ifacol.2023.02.059","article-title":"Constructive Equivariant Observer Design for Inertial Velocity-Aided Attitude","volume":"56","author":"Hamel","year":"2023","journal-title":"IFAC-PapersOnLine"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"de Vries, P.S., Rojer, J., and Kalff, F.E. (2023). Quantum-Based Relative Inertial Navigation with Velocity-Aided Alignment and Initialization. Eng. Proc., 54.","DOI":"10.3390\/ENC2023-15437"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Titterton, D.H., and Weston, J.L. (2004). Strapdown Inertial Navigation Technology, IET.","DOI":"10.1049\/PBRA017E"},{"key":"ref_22","unstructured":"McManus, D., Wiltshire, P., Gibson, M., and Roberts, L. (2026, August 02). Laser Velocity Sensor (LVS): A High-Accuracy Velocity Aid for GNSS-Denied Navigation. Available online: https:\/\/www.advancednavigation.com\/tech-articles\/laser-velocity-sensor-lvs-high-accuracy-velocity-aid-gnss-denied-navigation\/."},{"key":"ref_23","unstructured":"Matveev, V.V. (2014). The Engineering Analysis of Lapses of Strapdown Inertial Navigational System, Bulletin of Tula State University. (In Russian)."},{"key":"ref_24","unstructured":"Popov, E.P. (1978). Theory of the Linear Automatic Regulation and Control Systems, Nauka. (In Russian)."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/15\/5006\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T15:52:52Z","timestamp":1786031572000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/15\/5006"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,6]]},"references-count":24,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["s26155006"],"URL":"https:\/\/doi.org\/10.3390\/s26155006","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,6]]}}}