{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:51:26Z","timestamp":1767707486817,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T00:00:00Z","timestamp":1710288000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"ANID\/FONDECYT","award":["1220178","FB210024"],"award-info":[{"award-number":["1220178","FB210024"]}]},{"name":"Basal funding for Scientific and Technological Center of Excellence","award":["1220178","FB210024"],"award-info":[{"award-number":["1220178","FB210024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This work is focused on developing a self-calibration algorithm for an orientation estimation of cattle movements based on a quaternion Kalman filter. The accelerometer signals in the earth\u2019s frame provide more information to confirm that the cow is performing a jump to mount another cow. To obtain the measurements in the earth\u2019s frame, we propose a self-calibration method based on a strapdown inertial navigation system (SINS), which does not require intervention by the user once deployed in the field. The self-calibration algorithm uses a quaternion-based Kalman filter to predict the angular orientation with bias correction, and update it based on the measurements of accelerometers and magnetometers. The paper also depicts an alternate update to adjust the inclination using only the accelerometer measurements. We conducted experiments to compare the accuracy of the orientation estimation when the body moves similarly to cow mount movements. The comparison is between the proposed self-calibration algorithm with the IvenSense MPU9250 and Bosch BNO055 and the quaternion attitude estimation provided in the BNO055. The auto-calibrating algorithm presents a mean error of 0.149 rads with a mean consumption of 308.5 mW, and the Bosch algorithm shows an average error of 0.139 rads with a mean consumption of 307.5 mW. When we executed this algorithm in an MPU9250, the average error was 0.077 rads, and the mean consumption was 277.7 mW.<\/jats:p>","DOI":"10.3390\/s24061849","type":"journal-article","created":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T13:08:43Z","timestamp":1710335323000},"page":"1849","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["IMU Auto-Calibration Based on Quaternion Kalman Filter to Identify Movements of Dairy Cows"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7737-3102","authenticated-orcid":false,"given":"Carlos","family":"Mu\u00f1oz-Poblete","sequence":"first","affiliation":[{"name":"Electrical Engineering Department, Universidad de La Frontera, Temuco 4811230, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cristian","family":"Gonz\u00e1lez-Aguirre","sequence":"additional","affiliation":[{"name":"Magister en Ciencias de la Ingenier\u00eda, Universidad de La Frontera, Temuco 4811230, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4140-0997","authenticated-orcid":false,"given":"Robert H.","family":"Bishop","sequence":"additional","affiliation":[{"name":"Electrical Engineering, University of South Florida, 4202 E. Fowler Ave., Tampa, FL 33620, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3470-0270","authenticated-orcid":false,"given":"David","family":"Cancino-Baier","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias Agropecuarias y Medioambiente, Universidad de La Frontera, Temuco 4811230, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1080\/01652176.1996.9694615","article-title":"Detection of oestrus in dairy cows: A new approach to an old problem","volume":"18","author":"Loeffler","year":"1996","journal-title":"Vet. Q."},{"key":"ref_2","unstructured":"Vanrell, S.R., Chelotti, J.O., Galli, J.R., Rufiner, H.L., and Milone, D.H. (2014, January 2\u20133). 3D Acceleration for Heat Detection in Dairy Cows. Proceedings of the Sexto Congreso Argentino de Agroinformatica, Buenos Aires, Argentina."},{"key":"ref_3","first-page":"2415","article-title":"The Sensor Technologies for More Efficient Cow Reproduction Systems","volume":"6","author":"Koluman","year":"2019","journal-title":"Int. Res. J. Eng. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"104876","DOI":"10.1016\/j.prevetmed.2019.104876","article-title":"An observational study of the dry period length and its relation to milk yield, health, and fertility in two dairy cow breeds","volume":"175","author":"Holtenius","year":"2020","journal-title":"Prev. Vet. Med."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"619","DOI":"10.11118\/actaun201866020619","article-title":"Several methods of estrus detection in cattle dams: A review","volume":"66","year":"2018","journal-title":"Acta Univ. Agric. Silvic. Mendel. Brun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.compag.2007.08.014","article-title":"ALT pedometer\u2014New sensor-aided measurement system for improvement in oestrus detection","volume":"62","author":"Brehme","year":"2008","journal-title":"Comput. Electron. Agric."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/978-981-13-0869-7_30","article-title":"A study on estrus detection of cattle combining video image and sensor information","volume":"Volume 744","author":"Hirata","year":"2019","journal-title":"Proceedings of the Advances in Intelligent Systems and Computing"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"249","DOI":"10.3168\/jds.2008-1721","article-title":"On the use of physical activity monitoring for estrus detection in dairy cows","volume":"93","author":"Chagunda","year":"2010","journal-title":"J. Dairy Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2645","DOI":"10.3168\/jds.2018-14738","article-title":"Automated estrous detection using multiple commercial precision dairy monitoring technologies in synchronized dairy cows","volume":"102","author":"Mayo","year":"2019","journal-title":"J. Dairy Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"492","DOI":"10.3168\/jds.2019-17063","article-title":"Evaluation of activity meters for estrus detection: A stochastic bioeconomic modeling approach","volume":"103","author":"Pfeiffer","year":"2020","journal-title":"J. Dairy Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.theriogenology.2016.08.025","article-title":"Automated activity monitoring and visual observation of estrus in a herd of loose housed Hereford cattle: Diagnostic accuracy and time to ovulation","volume":"87","author":"Nelson","year":"2017","journal-title":"Theriogenology"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3703","DOI":"10.2527\/jas.2016-0469","article-title":"Using estrus detection patches to optimally time insemination improved pregnancy risk in suckled beef cows enrolled in a fixed-time artificial insemination program","volume":"94","author":"Hill","year":"2016","journal-title":"J. Anim. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.theriogenology.2020.11.002","article-title":"Monitoring estrous activity in pasture-based dairy cows","volume":"160","author":"Moore","year":"2021","journal-title":"Theriogenology"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3706","DOI":"10.3168\/jds.2018-15544","article-title":"Symposium review: Selection for fertility in the modern dairy cow\u2014Current status and future direction for genetic selection","volume":"102","author":"Lucy","year":"2019","journal-title":"J. Dairy Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2318","DOI":"10.3168\/jds.2020-18922","article-title":"Estimates of intra- and interclass correlation coefficients for rump touches and the number of steps during estrus in postpartum cows","volume":"104","author":"Kumro","year":"2021","journal-title":"J. Dairy Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.livsci.2016.12.011","article-title":"Automatic classification system for grazing, ruminating and resting behaviour of dairy sheep using a tri-axial accelerometer","volume":"196","author":"Giovanetti","year":"2017","journal-title":"Livest. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Munoz, C., Huircan, J.I., Huenupan, F., and Pinilla, D. (2022, January 24\u201328). Database generation to identify cow\u2019s movements for detecting estrus and lameness. Proceedings of the 2022 IEEE International Conference on Automation\/25th Congress of the Chilean Association of Automatic Control: For the Development of Sustainable Agricultural Systems, ICA-ACCA 2022, Curic\u00f3, Chile.","DOI":"10.1109\/ICA-ACCA56767.2022.10006230"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.3168\/jds.2022-22350","article-title":"Classification of cow behavior patterns using inertial measurement units and a fully convolutional network model","volume":"106","author":"Liu","year":"2023","journal-title":"J. Dairy Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.compag.2017.05.020","article-title":"Development of an open-source algorithm based on inertial measurement units (IMU) of a smartphone to detect cattle grass intake and ruminating behaviors","volume":"139","author":"Andriamandroso","year":"2017","journal-title":"Comput. Electron. Agric."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1134\/S0005117918010058","article-title":"Formalizing a Sequential Calibration Scheme for a Strapdown Inertial Navigation System","volume":"79","author":"Derevyankin","year":"2018","journal-title":"Autom. Remote. Control."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Xu, X., Xu, X., Zhang, T., Li, Y., and Tong, J. (2017). A kalman filter for sins self-alignment based on vector observation. Sensors, 17.","DOI":"10.3390\/s17020264"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1049\/iet-smt.2012.0071","article-title":"Strapdown inertial navigation system alignment based on marginalised unscented Kalman filter","volume":"7","author":"Chang","year":"2013","journal-title":"Iet Sci. Meas. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1109\/TAES.2012.6129652","article-title":"A Quaternion-Based Method for SINS\/SAR Integrated Navigation System","volume":"48","author":"Zhong","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhu, X., Gao, B., Zhong, Y., Gu, C., and Choi, K.S. (2021). Extended Kalman filter for online soft tissue characterization based on Hunt-Crossley contact model. J. Mech. Behav. Biomed. Mater., 123.","DOI":"10.1016\/j.jmbbm.2021.104667"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1017\/S0373463316000722","article-title":"The Standing Calibration Method of MEMS Gyro Bias for Autonomous Pedestrian Navigation System","volume":"70","author":"Zhang","year":"2017","journal-title":"J. Navig."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5416","DOI":"10.1109\/JSEN.2015.2439719","article-title":"A Novel Self-Calibration Method for MIMU","volume":"15","author":"Ren","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1016\/j.sna.2009.10.008","article-title":"Calibration methods for inertial and magnetic sensors","volume":"156","author":"Bonnet","year":"2009","journal-title":"Sens. Actuators A Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1109\/LRA.2020.2967308","article-title":"A Stable Adaptive Observer for Hard-Iron and Soft-Iron Bias Calibration and Compensation for Two-Axis Magnetometers: Theory and Experimental Evaluation","volume":"5","author":"Spielvogel","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_29","unstructured":"(2023, December 28). Bosch Sensortec. BNO055 Intelligent 9-Axis Absolute Orientation Sensor. Document Number: BST-BNO055-DS000-12. Available online: https:\/\/cdn-shop.adafruit.com\/datasheets\/BST_BNO055_DS000_12.pdf."},{"key":"ref_30","unstructured":"(2023, December 28). InvenSense. MPU-9250 Product Specification. Document Number: PS-MPU-9250A-01. Revision 1.1. Available online: https:\/\/invensense.tdk.com\/wp-content\/uploads\/2015\/02\/PS-MPU-9250A-01-v1.1.pdf."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1109\/TAES.1978.308627","article-title":"Analysis Strapdown Navigation Using Quaternions","volume":"AES-14","author":"Friedland","year":"1978","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1109\/TAES.2006.1603421","article-title":"Strapdown inertial navigation using dual quaternion algebra: Error analysis","volume":"42","author":"Wu","year":"2006","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1109\/TAES.2005.1413751","article-title":"Strapdown inertial navigation system algorithms based on dual quaternions","volume":"41","author":"Wu","year":"2005","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2413","DOI":"10.1109\/TMECH.2018.2865757","article-title":"Common Frame Based Unscented Quaternion Estimator for Inertial-Integrated Navigation","volume":"23","author":"Li","year":"2018","journal-title":"IEEE\/ASME Trans. Mechatronics"},{"key":"ref_35","unstructured":"Grewal, M., and Andrews, A. (1993). Kalman Filtering: Theory and Practice, Prentice-Hall. Number pt. 3 in Kalman Filtering: Theory and Practice."},{"key":"ref_36","unstructured":"Apkarian., J., L\u00e9vis, M., and Gurocak, H. (2023, December 28). User Manual SRV02 Rotary Servo Base Unit Solutions for Teaching and Research. Made in Canada. Available online: http:\/\/www.quanser.com."},{"key":"ref_37","unstructured":"Joulescope LLC (2023, December 03). Joulescope. Computer Software. 2018\u20132023. Available online: https:\/\/www.joulescope.com."},{"key":"ref_38","unstructured":"Jamovi Project Team (2023, December 03). Jamovi. Computer Software. Available online: https:\/\/www.jamovi.org."},{"key":"ref_39","unstructured":"Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences, Lawrence Erlbaum Associates. [2nd ed.]."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Pititeeraphab, Y., Jusing, T., Chotikunnan, P., Thongpance, N., Lekdee, W., and Teerasoradech, A. (2016, January 7\u20139). The effect of average filter for complementary filter and Kalman filter based on measurement angle. Proceedings of the The 2016 Biomedical Engineering International Conference (BMEiCON 2016), Laung Prabang, Laos.","DOI":"10.1109\/BMEiCON.2016.7859621"},{"key":"ref_41","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 Rehab Week Zurich, ETH, Zurich Science City, Zurich, Switzerland.","DOI":"10.1109\/ICORR.2011.5975346"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/6\/1849\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:13:08Z","timestamp":1760105588000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/6\/1849"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,13]]},"references-count":41,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["s24061849"],"URL":"https:\/\/doi.org\/10.3390\/s24061849","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2024,3,13]]}}}