{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:39:25Z","timestamp":1760240365024,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T00:00:00Z","timestamp":1559088000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"INNOVATIVE doctoral programme","award":["665468"],"award-info":[{"award-number":["665468"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The dominant navigation system for low-cost, mass-market Unmanned Aerial Vehicles (UAVs) is based on an Inertial Navigation System (INS) coupled with a Global Navigation Satellite System (GNSS). However, problems tend to arise during periods of GNSS outage where the navigation solution degrades rapidly. Therefore, this paper details a model-based integration approach for fixed wing UAVs, using the Vehicle Dynamics Model (VDM) as the main process model aided by low-cost Micro-Electro-Mechanical Systems (MEMS) inertial sensors and GNSS measurements with moment of inertia calibration using an Unscented Kalman Filter (UKF). Results show that the position error does not exceed 14.5 m in all directions after 140 s of GNSS outage. Roll and pitch errors are bounded to 0.06 degrees and the error in yaw grows slowly to 0.65 degrees after 140 s of GNSS outage. The filter is able to estimate model parameters and even the moment of inertia terms even with significant coupling between them. Pitch and yaw moment coefficient terms present significant cross coupling while roll moment terms seem to be decorrelated from all of the other terms, whilst more dynamic manoeuvres could help to improve the overall observability of the parameters.<\/jats:p>","DOI":"10.3390\/s19112467","type":"journal-article","created":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T11:31:28Z","timestamp":1559129488000},"page":"2467","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Model-Based Autonomous Navigation with Moment of Inertia Estimation for Unmanned Aerial Vehicles"],"prefix":"10.3390","volume":"19","author":[{"given":"Hery","family":"Mwenegoha","sequence":"first","affiliation":[{"name":"Nottingham Geospatial Institute, University of Nottingham, Triumph Road, Nottingham NG7 2TU, UK"}]},{"given":"Terry","family":"Moore","sequence":"additional","affiliation":[{"name":"Nottingham Geospatial Institute, University of Nottingham, Triumph Road, Nottingham NG7 2TU, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6645-7212","authenticated-orcid":false,"given":"James","family":"Pinchin","sequence":"additional","affiliation":[{"name":"Nottingham Geospatial Institute, University of Nottingham, Triumph Road, Nottingham NG7 2TU, UK"}]},{"given":"Mark","family":"Jabbal","sequence":"additional","affiliation":[{"name":"Fluids and Thermal Engineering Research Group, University of Nottingham, Nottingham NG7 2RD, UK"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,29]]},"reference":[{"key":"ref_1","unstructured":"Kim, J., and Sukkarieh, S. (2003, January 22\u201325). A Baro-Altimeter Augmented INS\/GPS Navigation System for an Uninhabited Aerial Vehicle. Proceedings of the 6th International Symposium on Satellite Navigation Technology Including Mobile Positioning & Location Services, Melbourne, Australia."},{"key":"ref_2","unstructured":"George, M., and Sukkarieh, S. (2005, January 5\u20137). Tightly Coupled INS\/GPS with Bias Estimation for UAV Applications. Proceedings of the Australasian Conference on Robotics and Automation 2005, Sydney, Australia."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s10291-008-0097-9","article-title":"Ultra-tight GPS\/INS\/PL integration: A system concept and performance analysis","volume":"13","author":"Babu","year":"2009","journal-title":"GPS Solut."},{"key":"ref_4","unstructured":"Brown, R., and Hwang, P.Y. (2012). Introduction to Random Signals and Applied Kalman Filtering, John Wiley & Sons, Inc.. [4th ed.]."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Falco, G., Pini, M., and Marucco, G. (2017). Loose and tight GNSS\/INS integrations: Comparison of performance assessed in real Urban scenarios. Sensors, 17.","DOI":"10.3390\/s17020255"},{"key":"ref_6","unstructured":"Hide, C. (2003). Integration of GPS and Low Cost INS Measurements. [Ph.D. Dissertation, University of Nottingham]."},{"key":"ref_7","first-page":"963","article-title":"Integration of Gps\/Ins\/Vision Sensors to Navigate Unmanned Aerial Vehicles","volume":"37","author":"Wang","year":"2008","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1932","DOI":"10.1109\/TAES.2013.6558029","article-title":"Inertial-based localization for unmanned helicopters against GNSS outage","volume":"49","author":"Lau","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"9549","DOI":"10.3390\/s130809549","article-title":"A comparison between different error modeling of MEMS applied to GPS\/INS integrated systems","volume":"13","author":"Quinchia","year":"2013","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Papadimitratos, P., and Jovanovic, A. (2008, January 1\u20133). Protection and fundamental vulnerability of GNSS. Proceedings of the 2008 IEEE International Workshop on Satellite and Space Communications, Toulouse, France.","DOI":"10.1109\/IWSSC.2008.4656777"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3768","DOI":"10.3390\/s140203768","article-title":"Implementation and Performance of a GPS\/INS Tightly Coupled Assisted PLL Architecture Using MEMS Inertial Sensors","volume":"14","author":"Tawk","year":"2014","journal-title":"Sensors"},{"key":"ref_12","unstructured":"Groves, P.D. (2008). Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Artech House."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Madison, R., Andrews, G., DeBitetto, P., Rasmussen, S., and Bottkol, M. (2007, January 7\u201310). Vision-Aided Navigation for Small UAVs in GPS-Challenged Environments. Proceedings of the AIAA Infotech at Aerospace Conference, Rohnert Park, CA, USA.","DOI":"10.2514\/6.2007-2986"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Beard, R.W., and McLain, T.W. (2013). Small Unmanned Aircraft: Theory and Practice, Princeton University Press.","DOI":"10.1515\/9781400840601"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.conengprac.2009.11.004","article-title":"Embedded UAV model and LASER aiding techniques for inertial navigation systems","volume":"18","author":"Vasconcelos","year":"2010","journal-title":"Control Eng. Pract."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"8473","DOI":"10.3390\/s91108473","article-title":"A Rigorous Temperature-Dependent Stochastic Modelling and Testing for MEMS-Based Inertial Sensor Errors","volume":"9","author":"Pagiatakis","year":"2009","journal-title":"Sensors"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1109\/87.772164","article-title":"Inertial navigation system aided by aircraft dynamics","volume":"7","author":"Koifman","year":"1999","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_18","unstructured":"Bryson, M., and Sukkarieh, S. (2004, January 6\u20138). Vehicle Model Aided Inertial Navigation for a UAV using Low-cost Sensors. Proceedings of the Australasian Conference on Robotics and Automation 2004, Canberra, Australia."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1002\/navi.39","article-title":"Unified Model Technique for Inertial Navigation","volume":"60","author":"Crocoll","year":"2013","journal-title":"NAVIGATION"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1002\/navi.140","article-title":"Autonomous Vehicle Dynamic Model-Based Navigation for Small UAVs","volume":"63","author":"Khaghani","year":"2016","journal-title":"NAVIGATION"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1002\/navi.68","article-title":"Model-Aided Navigation for a Quadrotor Helicopter: A Novel Navigation System and First Experimental Results","volume":"61","author":"Crocoll","year":"2014","journal-title":"NAVIGATION"},{"key":"ref_22","unstructured":"Sendobry, A. (2014). Control System Theoretic Approach to Model Based Navigation, Technische Universit\u00e4t Darmstadt."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Lyu, P., Lai, J., Liu, J., Zhang, L., and Liu, S. (2018, January 23\u201326). A novel integrated navigation system based on the quadrotor dynamic model. Proceedings of the 2018 IEEE\/ION Position, Location and Navigation Symposium (PLANS), Monterey, CA, USA.","DOI":"10.1109\/PLANS.2018.8373444"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TRA.2002.805661","article-title":"On the Role of Process Models in Autonomous Land Vehicle Navigation Systems","volume":"19","author":"Julier","year":"2003","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_25","unstructured":"Vissi\u00e8re, D., Bristeau, P.-J., Martin, A.P., and Petit, N. (2008, January 6\u201311). Experimental autonomous flight of a small-scaled helicopter using accurate dynamics model and low-cost sensors. Proceedings of the 17th World Congress of the International Federation of Automatic Control, Seoul, Korea."},{"key":"ref_26","unstructured":"Dadkhah, N., Mettler, B., and Gebre-egziabher, D. (2008, January 16\u201319). A Model-Aided AHRS for Micro Aerial Vehicle Application. Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008), Savannah, GA, USA."},{"key":"ref_27","unstructured":"Crocoll, P., and Trommer, G.F. (2014, January 8\u201312). Quadrotor Inertial Navigation Aided by a Vehicle Dynamics Model with In-Flight Parameter Estimation. Proceedings of the 27th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2014), Tampa, FL, USA."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Mueller, K., Crocoll, P., and Trommer, G.F. (2016, January 25\u201328). Model-Aided Navigation with Wind Estimation for Robust Quadrotor Navigation. Proceedings of the 2016 International Technical Meeting of the Institute of Navigation, Monterey, CA, USA.","DOI":"10.33012\/2016.13466"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.robot.2018.05.007","article-title":"Assessment of VDM-based autonomous navigation of a UAV under operational conditions","volume":"106","author":"Khaghani","year":"2018","journal-title":"Rob. Auton. Syst."},{"key":"ref_30","unstructured":"Sendobry, A. (December, January 29). A Model Based Navigation Architecture for Small Unmanned Aerial Vehicles. Proceedings of the European Navigation Conference, London, UK."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Khaghani, M., and Skaloud, J. (2018, January 14\u201317). VDM-based UAV Attitude Determination in Absence of IMU Data. Proceedings of the European Navigation Conference, ENC 2018, Gothenburg, Sweden.","DOI":"10.1109\/EURONAV.2018.8433243"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1002\/navi.249","article-title":"Hybrid Machine Learning VDM for UAVs in GNSS-denied Environment","volume":"65","author":"Zahran","year":"2018","journal-title":"NAVIGATION"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1002\/navi.232","article-title":"A Model Aided Inertial Navigation System for Automatic Landing of Unmanned Aerial Vehicles","volume":"65","author":"Mohammadkarimi","year":"2018","journal-title":"NAVIGATION"},{"key":"ref_34","unstructured":"International Civil Aviation Organization (1993). Manual of the ICAO Standard Atmosphere Extended to 80 Kilometres (262,500 Feet), International Civil Aviation Organization. [3rd ed.]."},{"key":"ref_35","unstructured":"Ducard, G. (2007). Fault-Tolerant Flight Control and Guidance Systems for a Small Unmanned Aerial Vehicle, ETH."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Julier, S.J., and Uhlmann, J.K. (1997). New extension of the Kalman filter to nonlinear systems. Signal Process. Sensor Fusion Target Recogn.","DOI":"10.1117\/12.280797"},{"key":"ref_37","unstructured":"Julier, S.J., Uhlmann, J.K., and Durrant-whyte, H.F. (1995, January 21\u201323). A New Approach for Filtering Nonlinear Systems. Proceedings of the American Control Conference, Seattle, WA, USA."},{"key":"ref_38","unstructured":"Gelb, A., Kasper, J.F., Nash, R.A., Price, C.F., and Sutherland, A.A. (1974). Applied Optimal Estimation, MIT Press."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/11\/2467\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:54:36Z","timestamp":1760187276000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/11\/2467"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,29]]},"references-count":38,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["s19112467"],"URL":"https:\/\/doi.org\/10.3390\/s19112467","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,5,29]]}}}