{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T12:24:15Z","timestamp":1787833455514,"version":"build-2784847793"},"reference-count":20,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T00:00:00Z","timestamp":1787788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006141","name":"Military University of Technology in Warsaw","doi-asserted-by":"publisher","award":["531-000090-W500-22"],"award-info":[{"award-number":["531-000090-W500-22"]}],"id":[{"id":"10.13039\/501100006141","id-type":"DOI","asserted-by":"publisher"}]},{"award":["531-000090-W500-22"],"award-info":[{"award-number":["531-000090-W500-22"]}],"id":[{"id":"https:\/\/ror.org\/05fct5h31","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurate velocity estimation in GPS-denied environments remains a core challenge for autonomous unmanned aerial vehicle (UAV) navigation. Our previous work demonstrated that fusing optical flow (OF) with dead reckoning (DR) substantially reduces position drift compared to inertial-only solutions. However, velocity estimates derived from dense optical flow are degraded by two systematic effects: (1) incorrect metric scaling when the camera footprint covers heterogeneous terrain types\u2014particularly at forest\u2013field transitions where the visible surface elevation differs significantly from bare-ground elevation; and (2) flow magnitude bias introduced by scene texture and structural properties. This paper presents three targeted improvements to a software pipeline for optical flow-assisted UAV navigation. First, single-point above-ground-level (AGL) estimation is replaced by camera footprint area mean sampling over co-registered Digital Terrain Model (DTM) and Digital Surface Model (DSM) rasters, with the surface model adopted consistently for OF metric scaling. Second, a one-dimensional Kalman filter with an innovation gate suppresses velocity spikes caused by abrupt terrain transitions. Third, a compact data-driven correction module uses selected flow, texture, and terrain descriptors to estimate a multiplicative velocity correction factor aligned with GPS-derived reference speed available during calibration and offline evaluation but not required during GPS-denied operation. Experiments on three real PX4-logged flight missions (Log 258 for calibration and Logs 259\u2013260 for independent evaluation) totalling 7.3 min show terrain-dependent behaviour. On the mixed forest\u2013field validation flight (Log 260), the improved pipeline reduces velocity mean absolute error (MAE) by 71% (1.04 m\/s \u2192 0.30 m\/s) and dead-reckoning position MAE by 88% (59.8 m \u2192 7.1 m), compared to the baseline from our previous work. On a flat open-terrain validation flight (Log 259), the terrain-aware modifications leave the terrain-insensitive baseline essentially unchanged, providing a control case for the proposed DSM-based scaling mechanism.<\/jats:p>","DOI":"10.3390\/s26175421","type":"journal-article","created":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T12:03:43Z","timestamp":1787832223000},"page":"5421","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Improved Fusion of Optical Flow and Dead Reckoning for UAV Navigation Using Digital Terrain Models and Data-Driven Velocity Correction"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-4991-6431","authenticated-orcid":false,"given":"Jakub","family":"Walczak","sequence":"first","affiliation":[{"name":"Faculty of Cybernetics, Military University of Technology, 00-908 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-0947-7774","authenticated-orcid":false,"given":"Piotr","family":"Targowski","sequence":"additional","affiliation":[{"name":"Faculty of Cybernetics, Military University of Technology, 00-908 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-3030-2515","authenticated-orcid":false,"given":"Szymon","family":"Chmielewski","sequence":"additional","affiliation":[{"name":"Faculty of Cybernetics, Military University of Technology, 00-908 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4772-4084","authenticated-orcid":false,"given":"Sebastian","family":"\u0141eska","sequence":"additional","affiliation":[{"name":"Faculty of Cybernetics, Military University of Technology, 00-908 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4853-7363","authenticated-orcid":false,"given":"Janusz","family":"Furtak","sequence":"additional","affiliation":[{"name":"Faculty of Cybernetics, Military University of Technology, 00-908 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,27]]},"reference":[{"key":"ref_1","unstructured":"Groves, P.D. (2013). Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Artech House. [2nd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1242\/jeb.199.1.237","article-title":"Honeybee Navigation En Route to the Goal: Visual Flight Control and Odometry","volume":"199","author":"Srinivasan","year":"1996","journal-title":"J. Exp. Biol."},{"key":"ref_3","first-page":"1069","article-title":"Fusion of Optical Flow and Dead Reckoning Algorithms for UAV Navigation Without GPS","volume":"19","author":"Walczak","year":"2025","journal-title":"TransNav Int. J. Mar. Navig. Saf. Sea Transp."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/0004-3702(81)90024-2","article-title":"Determining Optical Flow","volume":"17","author":"Horn","year":"1981","journal-title":"Artif. Intell."},{"key":"ref_5","unstructured":"Lucas, B.D., and Kanade, T. (1981, January 24\u201328). An Iterative Image Registration Technique with an Application to Stereo Vision. Proceedings of the 7th International Joint Conference on Artificial Intelligence, Vancouver, BC, Canada."},{"key":"ref_6","unstructured":"Farneb\u00e4ck, G. (July, January 29). Two-Frame Motion Estimation Based on Polynomial Expansion. Proceedings of the 13th Scandinavian Conference on Image Analysis, Gothenburg, Sweden."},{"key":"ref_7","first-page":"120","article-title":"The OpenCV Library","volume":"25","author":"Bradski","year":"2000","journal-title":"Dr. Dobb\u2019s J. Softw. Tools"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Sun, D., Yang, X., Liu, M.-Y., and Kautz, J. (2018, January 18\u201322). PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00931"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Teed, Z., and Deng, J. (2020, January 23\u201328). RAFT: Recurrent All-Pairs Field Transforms for Optical Flow. Proceedings of the European Conference on Computer Vision (ECCV), Glasgow, UK.","DOI":"10.1007\/978-3-030-58536-5_24"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Sun, J., Shen, Z., Wang, Y., Bao, H., and Zhou, X. (2021, January 20\u201325). LoFTR: Detector-Free Local Feature Matching with Transformers. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Nashville, TN, USA.","DOI":"10.1109\/CVPR46437.2021.00881"},{"key":"ref_11","unstructured":"Teed, Z., and Deng, J. (2021, January 6\u201314). DROID-SLAM: Deep Visual SLAM for Monocular, Stereo, and RGB-D Cameras. Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), Virtual."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Barry, A.J., and Tedrake, R. (2015, January 26\u201330). Pushbroom Stereo for High-Speed Navigation in Cluttered Environments. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7139617"},{"key":"ref_13","unstructured":"Hollowell, J. (1990, January 20\u201323). Heli\/SITAN: A Terrain Referenced Navigation Algorithm for Helicopters. Proceedings of the IEEE Position Location and Navigation Symposium, Las Vegas, NV, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1109\/TRO.2011.2163435","article-title":"Landing a VTOL Unmanned Aerial Vehicle on a Moving Platform Using Optical Flow","volume":"28","author":"Hamel","year":"2012","journal-title":"IEEE Trans. Robot."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1109\/TIV.2020.2980758","article-title":"AI-IMU Dead-Reckoning","volume":"5","author":"Brossard","year":"2020","journal-title":"IEEE Trans. Intell. Veh."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1109\/TRO.2018.2858287","article-title":"Continuous-Time Visual-Inertial Trajectory Estimation with Event Cameras","volume":"34","author":"Mueggler","year":"2018","journal-title":"IEEE Trans. Robot."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1109\/TRO.2018.2853729","article-title":"VINS-Mono: A Robust and Versatile Monocular Visual-Inertial State Estimator","volume":"34","author":"Qin","year":"2018","journal-title":"IEEE Trans. Robot."},{"key":"ref_18","unstructured":"GDAL\/OGR Contributors (2026, June 01). GDAL\/OGR Geospatial Data Abstraction Software Library. Open Source Geospatial Foundation. Available online: https:\/\/gdal.org."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Meier, L., Honegger, D., and Pollefeys, M. (2015, January 26\u201330). PX4: A Node-Based Multithreaded Open Source Robotics Framework for Deeply Embedded Platforms. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7140074"},{"key":"ref_20","first-page":"2825","article-title":"Scikit-learn: Machine Learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/17\/5421\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T12:05:14Z","timestamp":1787832314000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/17\/5421"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,27]]},"references-count":20,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["s26175421"],"URL":"https:\/\/doi.org\/10.3390\/s26175421","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,27]]}}}