{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T17:27:36Z","timestamp":1777656456676,"version":"3.51.4"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2016,2,20]],"date-time":"2016-02-20T00:00:00Z","timestamp":1455926400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Technology of PR China","award":["2013AA041105"],"award-info":[{"award-number":["2013AA041105"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To provide a long-time reliable orientation, sensor fusion technologies are widely used to integrate available inertial sensors for the low-cost orientation estimation. In this paper, a novel dual-linear Kalman filter was designed for a multi-sensor system integrating MEMS gyros, an accelerometer, and a magnetometer. The proposed filter precludes the impacts of magnetic disturbances on the pitch and roll which the heading is subjected to. The filter can achieve robust orientation estimation for different statistical models of the sensors. The root mean square errors (RMSE) of the estimated attitude angles are reduced by 30.6% under magnetic disturbances. Owing to the reduction of system complexity achieved by smaller matrix operations, the mean total time consumption is reduced by 23.8%. Meanwhile, the separated filter offers greater flexibility for the system configuration, as it is possible to switch on or off the second stage filter to include or exclude the magnetometer compensation for the heading. Online experiments were performed on the homemade miniature orientation determination system (MODS) with the turntable. The average RMSE of estimated orientation are less than 0.4\u00b0 and 1\u00b0 during the static and low-dynamic tests, respectively. More realistic tests on two-wheel self-balancing vehicle driving and indoor pedestrian walking were carried out to evaluate the performance of the designed MODS when high accelerations and angular rates were introduced. Test results demonstrate that the MODS is applicable for the orientation estimation under various dynamic conditions. This paper provides a feasible alternative for low-cost orientation determination.<\/jats:p>","DOI":"10.3390\/s16020264","type":"journal-article","created":{"date-parts":[[2016,2,22]],"date-time":"2016-02-22T10:24:17Z","timestamp":1456136657000},"page":"264","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["A Dual-Linear Kalman Filter for Real-Time Orientation Determination System Using Low-Cost MEMS Sensors"],"prefix":"10.3390","volume":"16","author":[{"given":"Shengzhi","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanical &amp; Engineering, Huazhong University of Science &amp; Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuai","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Mechanical &amp; Engineering, Huazhong University of Science &amp; Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chaojun","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical &amp; Engineering, Huazhong University of Science &amp; Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuebing","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Mechanical &amp; Engineering, Huazhong University of Science &amp; Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sheng","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical &amp; Engineering, Huazhong University of Science &amp; Technology, Wuhan 430074, China"},{"name":"School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,2,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4465","DOI":"10.1109\/TIE.2011.2163913","article-title":"UAV attitude estimation using unscented kalman filter and TRIAD","volume":"59","author":"Pereda","year":"2012","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1016\/j.measurement.2012.10.003","article-title":"Strapdown gyrocompass algorithm for AUV attitude determination using a digital filter","volume":"46","author":"Wei","year":"2013","journal-title":"Measurement"},{"key":"ref_3","unstructured":"Berger, C., Al Mamun, M.A., and Hansson, J. (2013, January 24\u201327). COTS-architecture with a real-time OS for a self-driving miniature vehicle. Proceedings of the Workshop on Architecting Safety in Collaborative Mobile Systems (ASCoMS) of the 32nd International Conference on Computer Safety, Reliability and Security, Toulouse, France."},{"key":"ref_4","first-page":"1","article-title":"Estimating the orientation of a rigid body moving in space using inertial sensors","volume":"2014","author":"Peng","year":"2014","journal-title":"Mutibody Syst. Dyn."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Al Delail, B., Weruaga, L., Zemerly, M.J., and Ng, J.W.P. (2013, January 8\u201311). Indoor localization and navigation using smartphones augmented reality and inertial tracking. Proceedings of the IEEE International Conference on Electronics, Circuits, and Systems, Abu Dhabi, UAE.","DOI":"10.1109\/ICECS.2013.6815564"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/MCG.2005.140","article-title":"Pedestrian tracking with shoe-mounted inertial sensors","volume":"25","author":"Foxlin","year":"2005","journal-title":"IEEE Comput. Graph. Appl."},{"key":"ref_7","first-page":"50","article-title":"Comparative analysis of different adaptive filters for tracking lower segments of a human body using inertial motion sensors","volume":"24","author":"Grip","year":"2013","journal-title":"Meas. Sci. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.sna.2014.03.004","article-title":"Localization and velocity tracking of human via 3 IMU sensors","volume":"212","author":"Yuan","year":"2014","journal-title":"Sens. Actuators A Phys."},{"key":"ref_9","unstructured":"Farrell, J., and Barth, M. (1999). The Global Positioning System and Inertial Navigation, McGraw-Hill."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.2514\/1.49410","article-title":"Feedback control with nominal inputs for agile satellites using control moment gyros","volume":"34","author":"Kusuda","year":"2012","journal-title":"J. Guid. Control Dynam."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"533","DOI":"10.2514\/1.32395","article-title":"Attitude estimation for sounding rockets using microelectromechanical system gyros","volume":"31","author":"Bekkeng","year":"2012","journal-title":"J. Guid. Control Dynam."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1080\/01621459.2013.799920","article-title":"Wavelet-variance-based estimation for composite stochastic processes","volume":"108","author":"Guerrier","year":"2013","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1109\/TIM.2007.911646","article-title":"A simplified quaternion-based algorithm for orientation estimation from earth gravity and magnetic field measurements","volume":"57","author":"Yun","year":"2008","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1693","DOI":"10.2514\/1.57344","article-title":"Magnetometer-only attitude determination using novel two-step Kalman filter approach","volume":"35","author":"Searcy","year":"2012","journal-title":"J. Guid. Control Dynam."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"22864","DOI":"10.3390\/s141222864","article-title":"Magnetic, acceleration fields and gyro quaternion (MAGYQ)-based attitude estimation with smartphone sensors for indoor pedestrian navigation","volume":"14","author":"Renaudin","year":"2014","journal-title":"Sensors"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3816","DOI":"10.3390\/s110403816","article-title":"Gain-scheduled complementary filter design for a MEMS based attitude and heading reference system","volume":"11","author":"Yoo","year":"2011","journal-title":"Sensors"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3390\/s120100001","article-title":"Attitude determination using a MEMS-based flight information measurement unit","volume":"12","author":"Ma","year":"2012","journal-title":"Sensors"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.measurement.2006.05.020","article-title":"A linear fusion algorithm for attitude determination using low cost MEMS-based sensors","volume":"40","author":"Zhu","year":"2007","journal-title":"Measurement"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1017\/S0373463311000233","article-title":"A novel method to integrate IMU and magnetometers in attitude and heading reference systems","volume":"64","author":"Han","year":"2011","journal-title":"J. Navig."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1017\/S0373463312000331","article-title":"Effective adaptive Kalman filter for MEMS-IMU\/magnetometers integrated attitude and heading reference systems","volume":"66","author":"Li","year":"2013","journal-title":"J. Navig."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1109\/TIM.2012.2218692","article-title":"A double-stage Kalman filter for orientation tracking with an integrated processor in 9-D IMU","volume":"62","author":"Sabatelli","year":"2013","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"10872","DOI":"10.3390\/s150510872","article-title":"Quaternion-based unscented Kalman filter for accurate indoor heading estimation using wearable multi-sensor system","volume":"15","author":"Yuan","year":"2015","journal-title":"Sensors"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Titterton, D.H., and Weston, J.L. (2004). Strapdown Inertial Navigation Technology, Institution of Electronical Engineers. [2nd ed.].","DOI":"10.1049\/PBRA017E"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"9182","DOI":"10.3390\/s111009182","article-title":"Kalman-filter-based orientation determination using inertial\/magnetic sensors: observability analysis and performance evaluation","volume":"11","author":"Sabatini","year":"2011","journal-title":"Sensors"},{"key":"ref_25","first-page":"23","article-title":"Complete triaxis magnetometer calibration in the magnetic domain","volume":"115","author":"Renaudin","year":"2010","journal-title":"J. Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2852","DOI":"10.1088\/0957-0233\/23\/10\/105105","article-title":"A new calibration method for tri-axial field sensors in strap-down navigation systems","volume":"23","author":"Li","year":"2012","journal-title":"Meas. Sci. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"125106","DOI":"10.1088\/0957-0233\/25\/12\/125106","article-title":"Calibration of an inertial-magnetic measurement unit without external equipment, in the presence of dynamic magnetic disturbances","volume":"25","author":"Metge","year":"2014","journal-title":"Meas. Sci. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1109\/TIM.2013.2281562","article-title":"Calibration of miniature inertial and magnetic sensor units for robust attitude estimation","volume":"63","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_29","unstructured":"Xsens Technologies B.V. MTi300 datasheet. Available online: https:\/\/www.xsens.com\/products\/mti-100-series\/."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/2\/264\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:19:27Z","timestamp":1760210367000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/2\/264"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,20]]},"references-count":29,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,2]]}},"alternative-id":["s16020264"],"URL":"https:\/\/doi.org\/10.3390\/s16020264","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,20]]}}}