{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T07:08:44Z","timestamp":1768979324362,"version":"3.49.0"},"reference-count":43,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2020,12,5]],"date-time":"2020-12-05T00:00:00Z","timestamp":1607126400000},"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>Inertial navigation systems provides the platform\u2019s position, velocity, and attitude during its operation. As a dead-reckoning system, it requires initial conditions to calculate the navigation solution. While initial position and velocity vectors are provided by external means, the initial attitude can be determined using the system\u2019s inertial sensors in a process known as coarse alignment. When considering low-cost inertial sensors, only the initial roll and pitch angles can be determined using the accelerometers measurements. The accuracy, as well as time required for the for the coarse alignment process are critical for the navigation solution accuracy, particularly for pure-inertial scenarios, because of the navigation solution drift. In this paper, a machine learning framework for the stationary coarse alignment stage is proposed. To that end, classical machine learning approaches are used in a two-stage approach to regress the roll and pitch angles. Alignment results obtained both in simulations and field experiments, using a smartphone, shows the benefits of using the proposed approach instead of the commonly used analytical coarse alignment procedure.<\/jats:p>","DOI":"10.3390\/s20236959","type":"journal-article","created":{"date-parts":[[2020,12,7]],"date-time":"2020-12-07T21:37:42Z","timestamp":1607377062000},"page":"6959","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["MLCA\u2014A Machine Learning Framework for INS Coarse Alignment"],"prefix":"10.3390","volume":"20","author":[{"given":"Idan","family":"Zak","sequence":"first","affiliation":[{"name":"Autonomous Systems Program, Technion\u2013Israel Institute of Technology, Haifa 3200003, Israel"}]},{"given":"Reuven","family":"Katz","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Technion\u2013Israel Institute of Technology, Haifa 3200003, Israel"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7846-0654","authenticated-orcid":false,"given":"Itzik","family":"Klein","sequence":"additional","affiliation":[{"name":"Department of Marine Technologies, University of Haifa, Haifa 3498838, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Titterton, D.H., and Weston, J.L. (2004). Strapdown Inertial Navigation Technology, The American Institute of Aeronautics and Astronautics and the Institution of Electrical Engineers. [2nd ed.].","DOI":"10.1049\/PBRA017E"},{"key":"ref_2","unstructured":"Groves, P.D. (2013). Principles of GNSS, Inertial and Multisensor Integrated Navigation Systems, Artech House. [2nd ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Noureldin, A., Karamat, T., and Georgy, J. (2012). Fundamentals of Inertial Navigation, Satellite-Based Positioning and Their Integration, Springer.","DOI":"10.1007\/978-3-642-30466-8"},{"key":"ref_4","unstructured":"Farrell, J. (2008). Aided Navigation: GPS with High Rate Sensors, McGraw-Hill."},{"key":"ref_5","unstructured":"Aggarwal, P., Syed, Z., Noureldin, A., and El-Sheimy, N. (2010). MEMS-Based Integrated Navigation, Artech House, Inc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1119\/1.3081061","article-title":"An introduction to inertial navigation","volume":"77","author":"Baird","year":"2009","journal-title":"Am. J. Phys."},{"key":"ref_7","first-page":"731530","article-title":"Performance Analysis of Alignment Process of MEMS IMU","volume":"2012","author":"Bistrov","year":"2012","journal-title":"Int. J. Navig. Obs."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wang, H., Li, G., and Shi, Z. (2017). Overview of Initial Alignment Method for Strap down Inertial Navigation System. Advances in Materials, Machinery, Electrical Engineering, Atlantis Press. Tianjin, China, 10\u201311 June 2017.","DOI":"10.2991\/ammee-17.2017.30"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1017\/S0373463310000214","article-title":"A Novel Initial Alignment Scheme for Low-Cost INS Aided by GPS for Land Vehicle Applications","volume":"63","author":"Han","year":"2010","journal-title":"J. Navig."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1134\/S2075108716020115","article-title":"Coarse leveling of gyro-free INS","volume":"7","author":"Vaknin","year":"2016","journal-title":"Gyroscopy Navig."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1109\/TAES.2017.2760520","article-title":"Analytic Evaluation of Fine Alignment for Velocity Aided INS","volume":"54","author":"Tsukerman","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1017\/S0373463314000198","article-title":"An Improved Optimal Method for Initial Alignment","volume":"67","author":"Li","year":"2014","journal-title":"J. Navig."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Yu, F., Gao, W., and Wang, Y. (2018). An Improved Strapdown Inertial Navigation System Initial Alignment Algorithm for Unmanned Vehicles. Sensors, 18.","DOI":"10.3390\/s18103297"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Dong, Q., Li, Y., Sun, Q., and Zhang, Y. (2017). An Adaptive Initial Alignment Algorithm Based on Variance Component Estimation for a Strapdown Inertial Navigation System for AUV. Symmetry, 9.","DOI":"10.3390\/sym9080129"},{"key":"ref_15","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_16","doi-asserted-by":"crossref","unstructured":"Liu, M., Gao, Y., Li, G., Guang, X., and Li, S. (2016). An improved alignment method for the Strapdown Inertial Navigation System (SINS). Sensors, 16.","DOI":"10.3390\/s16050621"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"21807","DOI":"10.3390\/s150921807","article-title":"Initial Alignment of Large Azimuth Misalignment Angles in SINS Based on Adaptive UPF","volume":"15","author":"Sun","year":"2015","journal-title":"Sensors"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1017\/S0373463312000318","article-title":"A fast SINS initial alignment scheme for underwater vehicle applications","volume":"66","author":"Li","year":"2013","journal-title":"J. Navig."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"85706","DOI":"10.1109\/ACCESS.2020.2993534","article-title":"StepNet\u2014Deep Learning Approaches for Step Length Estimation","volume":"8","author":"Klein","year":"2020","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Jamil, F., Iqbal, N., Ahmad, S., and Kim, D.H. (2020). Toward Accurate Position Estimation Using Learning to Prediction Algorithm in Indoor Navigation. Sensors, 20.","DOI":"10.3390\/s20164410"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Deng, J., Xu, Q., Ren, A., Duan, Y., Zahid, A., and Abbasi, Q.H. (2020, January 20\u201321). Machine Learning Driven Method for Indoor Positioning Using Inertial Measurement Unit. Proceedings of the International Conference on UK-China Emerging Technologies (UCET), Glasgow, UK.","DOI":"10.1109\/UCET51115.2020.9205369"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Brossard, M., Barrau, A., and Bonnabel, S. (2019, January 3\u20138). RINS-W: Robust Inertial Navigation System on Wheels. Proceedings of the 2019 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Macau, China.","DOI":"10.1109\/IROS40897.2019.8968593"},{"key":"ref_23","first-page":"616","article-title":"Nonlinear Initial Alignment of Strapdown Inertial Navigation System Using CSVM","volume":"148\u2013149","author":"Wang","year":"2012","journal-title":"Applied Mechanics and Materials"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Cort\u00e9s, S., Solin, A., and Kannala, J. (2018, January 17\u201320). Deep learning based speed estimation for constraining strapdown inertial navigation on smartphones. Proceedings of the IEEE 28th International Workshop on Machine Learning for Signal Processing, Aalborg, Denmark.","DOI":"10.1109\/MLSP.2018.8516710"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Chen, H., Aggarwal, P., Taha, T.M., and Chodavarapu, V.P. (2018, January 23\u201326). Improving Inertial Sensor by Reducing Errors using Deep Learning Methodology. Proceedings of the NAECON 2018-IEEE National Aerospace and Electronics Conference, Dayton, OH, USA.","DOI":"10.1109\/NAECON.2018.8556718"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Pukhov, E., and Cohen, H.I. (2020, January 20\u201323). Novel Approach to Improve Performance of Inertial Navigation System Via Neural Network. Proceedings of the 2020 IEEE\/ION Position, Location and Navigation Symposium, Portland, OR, USA.","DOI":"10.1109\/PLANS46316.2020.9110180"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zak, I., Klein, I., and Katz, R. (2018, January 15\u201330). A Feasibility Study of Machine Learning Based Coarse Alignment. Proceedings of the 5th International Electronic Conference on Sensors and Applications, Online.","DOI":"10.3390\/ecsa-5-05735"},{"key":"ref_28","unstructured":"Woodman, O. (2007). An introduction to inertial navigation. UCAM-CL-TR, Computer Laboratory, University Cambridge."},{"key":"ref_29","first-page":"1080","article-title":"Initial alignment for SINS based on low-cost IMU","volume":"6","author":"Jiong","year":"2011","journal-title":"J. Comput."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Brockwell, P.J., and Davis, R.A. (2002). Introduction to Time Series and Forecasting, Springer.","DOI":"10.1007\/b97391"},{"key":"ref_31","unstructured":"Chatfield, C. (2016). The Analysis of Time Series: An Introduction, Chapman and Hall\/CRC."},{"key":"ref_32","first-page":"1157","article-title":"An introduction to variable and feature selection","volume":"3","author":"Guyon","year":"2003","journal-title":"J. Mach. Learn. Res."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Chen, X., and Jeong, J.C. (2007, January 13\u201315). Enhanced recursive feature elimination. Proceedings of the Sixth International Conference on Machine Learning and Applications, Cincinnati, OH, USA.","DOI":"10.1109\/ICMLA.2007.35"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Darst, B.F., Malecki, K.C., and Engelman, C.D. (2018). Using recursive feature elimination in random forest to account for correlated variables in high dimensional data. BMC Genet., 19.","DOI":"10.1186\/s12863-018-0633-8"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random Forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10994-006-6226-1","article-title":"Extremely randomized trees","volume":"63","author":"Geurts","year":"2006","journal-title":"Machine Learning"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Chen, T., and Guestrin, C. (2016, January 22\u201327). XGBoost: A scalable tree boosting system. Proceedings of the 22nd ACM Sigkdd International Conference on Knowledge Discovery and Data Mining, San Diego, CA, USA.","DOI":"10.1145\/2939672.2939785"},{"key":"ref_38","unstructured":"Ke, G., Meng, Q., Finley, T., Wang, T., Chen, W., Ma, W., Ye, Q., and Liu, T. (2017, January 4\u20139). LightGBM: A highly efficient gradient boosting decision tree. Proceedings of the Advances in Neural Information Processing Systems, Long Beach, CA, USA."},{"key":"ref_39","unstructured":"Prokhorenkova, L., Gusev, G., Vorobev, A., Dorogush, A.V., and Gulin, A. (2018, January 3\u20138). CatBoost: Unbiased boosting with categorical features. Proceedings of the Advances in Neural Information Processing Systems, Montr\u00e9al, QC, Canada."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Dietterich, T.G. (2000). Ensemble Methods in Machine Learning. International Workshop on Multiple Classifier Systems, Springer.","DOI":"10.1007\/3-540-45014-9_1"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"79","DOI":"10.3354\/cr030079","article-title":"Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance","volume":"30","author":"Willmott","year":"2005","journal-title":"Clim. Res."},{"key":"ref_42","first-page":"781","article-title":"Platform for teaching sensor fusion using a smartphone","volume":"33","author":"Hendeby","year":"2017","journal-title":"Int. J. Eng. Educ."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Madgwick, S.O., Harrison, A.J., and Vaidyanathan, R. (July, January 29). Estimation of IMU and MARG orientation using a gradient descent algorithm. Proceedings of the 2011 IEEE International Conference on Rehabilitation Robotics, Zurich, Switzerland.","DOI":"10.1109\/ICORR.2011.5975346"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/23\/6959\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:41:57Z","timestamp":1760179317000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/23\/6959"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,5]]},"references-count":43,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["s20236959"],"URL":"https:\/\/doi.org\/10.3390\/s20236959","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,5]]}}}