{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T18:36:12Z","timestamp":1774722972516,"version":"3.50.1"},"reference-count":62,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,19]],"date-time":"2018-08-19T00:00:00Z","timestamp":1534636800000},"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>Wearable motion sensors are assumed to be correctly positioned and oriented in most of the existing studies. However, generic wireless sensor units, patient health and state monitoring sensors, and smart phones and watches that contain sensors can be differently oriented on the body. The vast majority of the existing algorithms are not robust against placing the sensor units at variable orientations. We propose a method that transforms the recorded motion sensor sequences invariantly to sensor unit orientation. The method is based on estimating the sensor unit orientation and representing the sensor data with respect to the Earth frame. We also calculate the sensor rotations between consecutive time samples and represent them by quaternions in the Earth frame. We incorporate our method in the pre-processing stage of the standard activity recognition scheme and provide a comparative evaluation with the existing methods based on seven state-of-the-art classifiers and a publicly available dataset. The standard system with fixed sensor unit orientations cannot handle incorrectly oriented sensors, resulting in an average accuracy reduction of 31.8%. Our method results in an accuracy drop of only 4.7% on average compared to the standard system, outperforming the existing approaches that cause an accuracy degradation between 8.4 and 18.8%. We also consider stationary and non-stationary activities separately and evaluate the performance of each method for these two groups of activities. All of the methods perform significantly better in distinguishing non-stationary activities, our method resulting in an accuracy drop of 2.1% in this case. Our method clearly surpasses the remaining methods in classifying stationary activities where some of the methods noticeably fail. The proposed method is applicable to a wide range of wearable systems to make them robust against variable sensor unit orientations by transforming the sensor data at the pre-processing stage.<\/jats:p>","DOI":"10.3390\/s18082725","type":"journal-article","created":{"date-parts":[[2018,8,20]],"date-time":"2018-08-20T11:23:06Z","timestamp":1534764186000},"page":"2725","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Activity Recognition Invariant to Wearable Sensor Unit Orientation Using Differential Rotational Transformations Represented by Quaternions"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6213-5427","authenticated-orcid":false,"given":"Aras","family":"Yurtman","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Bilkent University, Bilkent, Ankara 06800, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Billur","family":"Barshan","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Bilkent University, Bilkent, Ankara 06800, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5333-0201","authenticated-orcid":false,"given":"Bar\u0131\u015f","family":"Fidan","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1109\/SURV.2012.110112.00192","article-title":"A survey on human activity recognition using wearable sensors","volume":"15","author":"Lara","year":"2013","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1145\/2629633","article-title":"Wearables: Has the age of smartwatches finally arrived?","volume":"58","author":"Rawassizadeh","year":"2015","journal-title":"Commun. ACM"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"26783","DOI":"10.3390\/s151026783","article-title":"Can smartwatches replace smartphones for posture tracking?","volume":"15","author":"Mortazavi","year":"2015","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5561","DOI":"10.3390\/s110605561","article-title":"Wearable and implantable wireless sensor network solutions for healthcare monitoring","volume":"11","author":"Darwish","year":"2011","journal-title":"Sensors"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TSMCC.2009.2032660","article-title":"A survey on wearable sensor-based systems for health monitoring and prognosis","volume":"40","author":"Pantelopoulos","year":"2010","journal-title":"IEEE Trans. Syst. Man Cybern. Part C"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1080\/08839514.2016.1138787","article-title":"Human activity recognition using tag-based radio frequency localization","volume":"30","author":"Yurtman","year":"2016","journal-title":"Appl. Artif. Intell."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.cmpb.2014.07.003","article-title":"Automated evaluation of physical therapy exercises using multi-template dynamic time warping on wearable sensor signals","volume":"117","author":"Yurtman","year":"2014","journal-title":"Comput. Methods Progr. Biomed."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1016\/j.sna.2016.06.024","article-title":"Improvements in deterministic error modeling and calibration of inertial sensors and magnetometers","volume":"247","author":"Barshan","year":"2016","journal-title":"Sens. Actuators A Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.bbe.2017.04.004","article-title":"Physical activity recognition by smartphones, a survey","volume":"37","author":"Morales","year":"2017","journal-title":"Biocybern. Biomed. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/MPRV.2014.73","article-title":"Sensor placement variations in wearable activity recognition","volume":"13","author":"Kunze","year":"2014","journal-title":"IEEE Pervasive Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1145\/1689239.1689243","article-title":"Using mobile phones to determine transportation modes","volume":"6","author":"Reddy","year":"2010","journal-title":"ACM Trans. Sens. Netw."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.pmcj.2014.05.006","article-title":"Using unlabeled data in a sparse-coding framework for human activity recognition","volume":"15","author":"Bhattacharya","year":"2014","journal-title":"Pervasive Mob. Comput."},{"key":"ref_13","first-page":"548","article-title":"Activity recognition on an accelerometer embedded mobile phone with varying positions and orientations","volume":"Volume 6406","author":"Yu","year":"2010","journal-title":"Lecture Notes in Computer Science, Proceedings of the 7th International Conference on Ubiquitous Intelligence and Computing, Xi\u2019an, China, 26\u201329 October 2010"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"10146","DOI":"10.3390\/s140610146","article-title":"Fusion of smartphone motion sensors for physical activity recognition","volume":"14","author":"Shoaib","year":"2014","journal-title":"Sensors"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Janidarmian, M., Fekr, A.R., Radecka, K., and Zilic, Z. (2017). A comprehensive analysis on wearable acceleration sensors in human activity recognition. Sensors, 17.","DOI":"10.3390\/s17030529"},{"key":"ref_16","first-page":"38","article-title":"Recognizing human activities user-independently on smartphones based on accelerometer data","volume":"1","author":"Siirtola","year":"2012","journal-title":"Int. J. Interact. Multimed. Artif. Intell."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Yang, Y. (2009, January 23). Toward physical activity diary: Motion recognition using simple acceleration features with mobile phones. Proceedings of the 1st International Workshop on Interactive Multimedia for Consumer Electronics, Beijing, China.","DOI":"10.1145\/1631040.1631042"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Lu, H., Yang, J., Liu, Z., Lane, N.D., Choudhury, T., and Campbell, A.T. (2010, January 3\u20135). The Jigsaw continuous sensing engine for mobile phone applications. Proceedings of the 8th ACM Conference on Embedded Networked Sensor Systems, Z\u00fcrich, Switzerland.","DOI":"10.1145\/1869983.1869992"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2506","DOI":"10.1109\/TBME.2010.2049357","article-title":"Can triaxial accelerometry accurately recognize inclined walking terrains?","volume":"57","author":"Wang","year":"2010","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Henpraserttae, A., Thiemjarus, S., and Marukatat, S. (2011, January 23\u201325). Accurate activity recognition using a mobile phone regardless of device orientation and location. Proceedings of the International Conference on Body Sensor Networks, Dallas, TX, USA.","DOI":"10.1109\/BSN.2011.8"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/s00779-011-0493-y","article-title":"Unsupervised adaptation for acceleration-based activity recognition: Robustness to sensor displacement and rotation","volume":"17","author":"Chavarriaga","year":"2011","journal-title":"Pers. Ubiquitous Comput."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Ustev, Y.E., \u0130ncel, \u00d6.D., and Ersoy, C. (2013, January 8\u201312). User, device and orientation independent human activity recognition on mobile phones: Challenges and a proposal. Proceedings of the ACM Conference on Pervasive and Ubiquitous Computing, Z\u00fcrich, Switzerland.","DOI":"10.1145\/2494091.2496039"},{"key":"ref_23","first-page":"90300I-1","article-title":"Human activity recognition by smartphones regardless of device orientation","volume":"Volume 9030","author":"Creutzburg","year":"2014","journal-title":"Proceedings of the SPIE-IS&T Electronic Imaging: Mobile Devices and Multimedia: Enabling Technologies, Algorithms, and Applications"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"9995","DOI":"10.3390\/s140609995","article-title":"Dealing with the effects of sensor displacement in wearable activity recognition","volume":"14","author":"Banos","year":"2014","journal-title":"Sensors"},{"key":"ref_25","unstructured":"Yang, J.B., Nguyen, M.N., San, P.P., Li, X.L., and Krishnaswamy, S. (2015, January 25\u201331). Deep convolutional neural networks on multichannel time series for human activity recognition. Proceedings of the 24th International Conference on Artificial Intelligence (IJCAI\u201915), Buenos Aires, Argentina."},{"key":"ref_26","unstructured":"Alsheikh, M.A., Selim, A., Niyato, D., Doyle, L., Lin, S., and Tan, H.-P. (2016, January 12\u201317). Deep activity recognition models with triaxial accelerometers. Proceedings of the Workshop at the Thirtieth AAAI Conference on Artificial Intelligence: Artificial Intelligence Applied to Assistive Technologies and Smart Environments, Phoenix, AZ, USA."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1109\/JBHI.2016.2633287","article-title":"A deep learning approach to on-node sensor data analytics for mobile or wearable devices","volume":"21","author":"Ravi","year":"2017","journal-title":"IEEE J. Biomed. Health"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Thiemjarus, S. (2010, January 7\u20139). A device-orientation independent method for activity recognition. Proceedings of the International Conference on Body Sensor Networks, Biopolis, Singapore.","DOI":"10.1109\/BSN.2010.55"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1088\/0967-3334\/32\/3\/006","article-title":"A method to deal with installation errors of wearable accelerometers for human activity recognition","volume":"32","author":"Jiang","year":"2011","journal-title":"Physiol. Meas."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Kunze, K., and Lukowicz, P. (2008, January 21\u201324). Dealing with sensor displacement in motion-based onbody activity recognition systems. Proceedings of the 10th International Conference on Ubiquitous Computing, Seoul, Korea.","DOI":"10.1145\/1409635.1409639"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"F\u00f6rster, K., Roggen, D., and Troster, G. (2009, January 4\u20137). Unsupervised classifier self-calibration through repeated context occurrences: Is there robustness against sensor displacement to gain?. Proceedings of the International Symposium on Wearable Computers, Linz, Austria.","DOI":"10.1109\/ISWC.2009.12"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1109\/MRA.2007.901320","article-title":"Limitations of attitude estimation algorithms for inertial\/magnetic sensor modules","volume":"14","author":"Bachmann","year":"2007","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_33","first-page":"1","article-title":"Attitude determination by combining arrays of MEMS accelerometers, gyros, and magnetometers via quaternion-based complementary filter","volume":"31","author":"Homaeinezhad","year":"2018","journal-title":"Int. J. Numer. Model. Electron. Netw. Devices Fields"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Yurtman, A., and Barshan, B. (2017). Activity recognition invariant to sensor orientation with wearable motion sensors. Sensors, 17.","DOI":"10.3390\/s17081838"},{"key":"ref_35","unstructured":"Yurtman, A., and Barshan, B. (2017, January 1\u20133). Recognizing activities of daily living regardless of wearable device orientation. Proceedings of the Fifth International Symposium on Engineering, Artificial Intelligence, and Applications, Book of Abstracts, Kyrenia, Turkish Republic of Northern Cyprus."},{"key":"ref_36","unstructured":"Yurtman, A., and Barshan, B. (2018, January 25\u201329). Classifying daily activities regardless of wearable motion sensor orientation. Proceedings of the Eleventh International Conference on Advances in Computer-Human Interactions (ACHI), Rome, Italy."},{"key":"ref_37","unstructured":"Zhong, Y., and Deng, Y. (October, January 29). Sensor orientation invariant mobile gait biometrics. Proceedings of the IEEE International Joint Conference on Biometrics, Clearwater, FL, USA."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1093\/comjnl\/bxv093","article-title":"Investigating inter-subject and inter-activity variations in activity recognition using wearable motion sensors","volume":"59","author":"Barshan","year":"2016","journal-title":"Comput. J."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Cai, G., Chen, B.M., and Lee, T.H. (2011). Chapter 2: On Coordinate Systems and Transformations. Unmanned Rotorcraft Systems, Springer.","DOI":"10.1007\/978-0-85729-635-1_2"},{"key":"ref_40","unstructured":"Comotti, D. (2011). Orientation Estimation Based on Gauss-Newton Method and Implementation of a Quaternion Complementary Filter, Department of Computer Science and Engineering, University of Bergamo. Available online: https:\/\/storage.googleapis.com\/google-code-archive-downloads\/v2\/code.google.com\/9dof-orientation-estimation\/GaussNewton_QuaternionComplemFilter_V13.pdf."},{"key":"ref_41","unstructured":"Spong, M.W., Hutchinson, S., and Vidyasagar, M. (2006). Section 2.3: On Rotational Transformations. Robot Modeling and Control, John Wiley & Sons."},{"key":"ref_42","unstructured":"Chen, C.-T. (1999). Section 3.4: On Similarity Transformation. Linear System Theory and Design, Oxford University Press."},{"key":"ref_43","unstructured":"Altun, K., and Barshan, B. (2013). Daily and Sports Activities Dataset. UCI Machine Learning Repository, School of Information and Computer Sciences, University of California, Irvine. Available online: http:\/\/archive.ics.uci.edu\/ml\/datasets\/Daily+and+Sports+Activities."},{"key":"ref_44","unstructured":"Xsens Technologies B.V. (2018). MTi, MTx, and XM-B User Manual and Technical Documentation, Xsens. Available online: http:\/\/www.xsens.com."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"3605","DOI":"10.1016\/j.patcog.2010.04.019","article-title":"Comparative study on classifying human activities with miniature inertial and magnetic sensors","volume":"43","author":"Altun","year":"2010","journal-title":"Pattern Recognit."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.1093\/comjnl\/bxt075","article-title":"Recognizing daily and sports activities in two open source machine learning environments using body-worn sensor units","volume":"57","author":"Barshan","year":"2014","journal-title":"Comput. J."},{"key":"ref_47","first-page":"38","article-title":"Human activity recognition using inertial\/magnetic sensor units","volume":"Volume 6219","author":"Salah","year":"2010","journal-title":"Lecture Notes in Computer Science, Proceedings of the International Workshop on Human Behaviour Understanding, Istanbul, Turkey, 22 August 2010"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1515\/bmt-2012-4137","article-title":"Method for daily-life movement classification of elderly people","volume":"57","author":"Rulsch","year":"2012","journal-title":"Biomed. Eng."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"10691","DOI":"10.3390\/s140610691","article-title":"Detecting falls with wearable sensors using machine learning techniques","volume":"14","author":"Barshan","year":"2014","journal-title":"Sensors"},{"key":"ref_50","unstructured":"Diebel, J. (2006). Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors, Department of Aeronautics and Astronautics, Stanford University. Available online: http:\/\/www.swarthmore.edu\/NatSci\/mzucker1\/papers\/diebel2006attitude.pdf."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Yurtman, A., and Barshan, B. (2018). Choosing Sensory Data Type and Rotational Representation for Activity Recognition Invariant to Wearable Sensor Orientation Using Differential Rotational Transformations, Department of Electrical and Electronics Engineering, Bilkent University. Technical Report.","DOI":"10.3390\/s18082725"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Webb, A. (2002). Statistical Pattern Recognition, John Wiley & Sons.","DOI":"10.1002\/0470854774"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.1162\/089976603321891855","article-title":"Asymptotic behaviors of support vector machines with Gaussian kernel","volume":"15","author":"Keerthi","year":"2003","journal-title":"Neural Comput."},{"key":"ref_54","first-page":"278","article-title":"Which is the best multiclass SVM method? An empirical study","volume":"Volume 3541","author":"Nikunj","year":"2005","journal-title":"Lecture Notes in Computer Science, Proceedings of the 6th International Workshop on Multiple Classifier Systems, Seaside, CA, USA, 13\u201315 June 2005"},{"key":"ref_55","unstructured":"Hsu, C.W., Chang, C.C., and Lin, C.J. (2003). A Practical Guide to Support Vector Classification, Department of Computer Science, National Taiwan University. Technical Report."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1145\/1961189.1961199","article-title":"LIBSVM: A library for support vector machines","volume":"2","author":"Chang","year":"2011","journal-title":"ACM Trans. Intell. Syst. Technol."},{"key":"ref_57","unstructured":"Duda, R.O., Hart, P.E., and Stork, D.G. (2000). Pattern Classification, John Wiley & Sons."},{"key":"ref_58","unstructured":"Haykin, S. (1998). Neural Networks: A Comprehensive Foundation, Prentice Hall. [2nd ed.]."},{"key":"ref_59","unstructured":"Witten, I.H., Frank, E., Hall, M.A., and Pal, C.J. (2016). Data Mining: Practical Machine Learning Tools and Techniques, Elsevier. [4th ed.]."},{"key":"ref_60","unstructured":"Pati, Y.C., Rezaiifar, R., and Krishnaprasad, P.S. (1993, January 1\u20133). Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition. Proceedings of the 27th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA."},{"key":"ref_61","unstructured":"Wang, L., Cheng, L., and Zhao, G. (2000). Machine Learning for Human Motion Analysis: Theory and Practice, IGI Global."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1109\/MPRV.2018.011591063","article-title":"NoCloud: Exploring network disconnection through on-device data analysis","volume":"17","author":"Rawassizadeh","year":"2018","journal-title":"IEEE Pervasive Comput."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/8\/2725\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:19:35Z","timestamp":1760195975000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/8\/2725"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,19]]},"references-count":62,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2018,8]]}},"alternative-id":["s18082725"],"URL":"https:\/\/doi.org\/10.3390\/s18082725","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,19]]}}}