{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T03:37:04Z","timestamp":1761709024579,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2014,11,7]],"date-time":"2014-11-07T00:00:00Z","timestamp":1415318400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>In this paper, the dynamic performance of a Kalman filter (KF) was analyzed, which is used to combine multiple measurements of a gyroscopes array to reduce the noise and improve the accuracy of the individual sensors. A principle for accuracy improvement by the KF was briefly presented to obtain an optimal estimate of input rate signal. In particular, the influences of some crucial factors on the KF dynamic performance were analyzed by simulations such as the factors input signal frequency, signal sampling, and KF filtering rate. Finally, a system that was comprised of a six-gyroscope array was designed and implemented to test the dynamic performance. Experimental results indicated that the 1\u03c3 error for the combined rate signal was reduced to about 0.2\u00b0\/s in the constant rate test, which was a reduction by a factor of more than eight compared to the single gyroscope. The 1\u03c3 error was also reduced from 1.6\u00b0\/s to 0.48\u00b0\/s in the swing test. It showed that the estimated angular rate signal could well reflect the dynamic characteristic of the input signal in dynamic conditions.<\/jats:p>","DOI":"10.3390\/mi5041034","type":"journal-article","created":{"date-parts":[[2014,11,7]],"date-time":"2014-11-07T08:18:31Z","timestamp":1415348311000},"page":"1034-1050","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Analysis of Dynamic Performance of a Kalman Filter for Combining Multiple MEMS Gyroscopes"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0044-4598","authenticated-orcid":false,"given":"Liang","family":"Xue","sequence":"first","affiliation":[{"name":"Xi'an Research Inst. of Hi-Tech, Hongqing Town, Xi'an 710025, China"}]},{"given":"Lixin","family":"Wang","sequence":"additional","affiliation":[{"name":"Xi'an Research Inst. of Hi-Tech, Hongqing Town, Xi'an 710025, China"}]},{"given":"Tao","family":"Xiong","sequence":"additional","affiliation":[{"name":"Xi'an Research Inst. of Hi-Tech, Hongqing Town, Xi'an 710025, China"}]},{"given":"Chengyu","family":"Jiang","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Micro and Nano Systems for Aerospace, Northwestern Polytechnical University, 127 Youyi West Road, Xi'an 710072, China"}]},{"given":"Weizheng","family":"Yuan","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Micro and Nano Systems for Aerospace, Northwestern Polytechnical University, 127 Youyi West Road, Xi'an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2014,11,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Guo, Z.Y., Lin, L.T., Zhao, Q.C., Cui, J., Chi, X.Z., Yang, Z.C., and Yan, G.Z. (2009, January 25\u201329). An electrically decoupled lateral-axis tuning fork gyroscope operating at atmospheric pressure. Proceedings of the IEEE 22nd International Conference on Micro Electro Mechanical Systems, Sorrento, Italy.","DOI":"10.1109\/MEMSYS.2009.4805330"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1640","DOI":"10.1109\/5.704269","article-title":"Micromachined inertial sensors","volume":"86","author":"Yazdi","year":"1998","journal-title":"Proc. IEEE"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Nitzan, S., Ahn, C.H., Su, T.-H., Li, M., Ng, E.J., Wang, S., Yang, Z.M., O\u2019Brien, G., Boser, B.E., Kenny, T.W., and Horsley, D.A. (2013, January 20\u201324). Epitaxially-encapsulated polysilicon disk resonator gyroscope. Proceedings of the IEEE 26th International Conference on Micro Electro Mechanical Systems, Taipei, Taiwan.","DOI":"10.1109\/MEMSYS.2013.6474319"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2661","DOI":"10.1016\/j.measurement.2013.03.022","article-title":"A parametric study on design of a microrate-gyroscope with parametric resonance","volume":"46","author":"Pakniyat","year":"2013","journal-title":"Measurement"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4972","DOI":"10.3390\/s110504972","article-title":"Two-scale simulation of drop-induced failure of polysilicon MEMS sensors","volume":"11","author":"Mariani","year":"2011","journal-title":"Sensors"},{"key":"ref_6","unstructured":"Sonmezoglu, S., Alper, S.E., and Akin, T. (February, January 29). An automatically mode-matched MEMS gyroscope with 50 Hz bandwidth. Proceedings of the IEEE 25th International Conference on Micro Electro Mechanical Systems, Paris, France."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1651","DOI":"10.3390\/s130201651","article-title":"Design of a novel MEMS gyroscope array","volume":"13","author":"Wang","year":"2013","journal-title":"Sensors"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"595","DOI":"10.3938\/jkps.40.595","article-title":"A gyroscope array with capacitive detection","volume":"40","author":"Kim","year":"2002","journal-title":"J. Korean Phys. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Tanenhaus, M., Carhoun, D., Geis, T., Wan, E., and Holland, A. (2012, January 23\u201326). Miniature IMU\/INS with optimally fused low drift MEMS gyro and accelerometers for applications in GPS-denied environments. Proceedings of IEEE Symposium on Position, Location and Navigation, Myrtle Beach, SC, USA.","DOI":"10.1109\/PLANS.2012.6236890"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Al-Majed, M.I., and Alsuwaidan, B.N. (2009, January 14\u201317). A new testing platform for attitude determination and control subsystems: Design and applications. Proceedings of the IEEE\/ASME International Conference on Advanced Intelligent Mechatronics, Singapore, Singapore.","DOI":"10.1109\/AIM.2009.5229871"},{"key":"ref_11","unstructured":"Bayard, D.S., and Ploen, S.R. (2003). High accuracy inertial sensors from inexpensive components. (US20030187623A1), U.S. Patent."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2886","DOI":"10.3390\/s8042886","article-title":"An integrated MEMS gyroscope array with higher accuracy output","volume":"8","author":"Chang","year":"2008","journal-title":"Sensors"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1016\/j.measurement.2011.12.016","article-title":"A novel Kalman filter for combining outputs of MEMS gyroscope array","volume":"45","author":"Xue","year":"2012","journal-title":"Measurement"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3084","DOI":"10.1109\/TIM.2012.2200818","article-title":"Combining numerous uncorrelated MEMS gyroscopes for accuracy improvement based on an optimal Kalman filter","volume":"61","author":"Chang","year":"2012","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_15","unstructured":"Colomina, I., Gim\u00e9nez, M., Rosales, J.J., Wis, M., Gomez, A., and Miguelsanz, P. (2004, January 12\u201323). Redundant IMUs for precise trajectory determination. Proceedings of the 20th ISPRS Congress, Istanbul, Turkey."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"065201","DOI":"10.1088\/0957-0233\/21\/6\/065201","article-title":"Noise reduction and estimation in multiple micro-electro-mechanical inertial systems","volume":"21","author":"Waegli","year":"2010","journal-title":"Meas. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wis, M., and Colomina, I. (2010, January 8\u201310). Dynamic dependent IMU stochastic modeling for enhanced INS\/GNSS navigation. Proceedings of the 5th ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing, Noordwijk, The Netherlands.","DOI":"10.1109\/NAVITEC.2010.5708041"},{"key":"ref_18","first-page":"24193","article-title":"The generalized method of wavelet moments for inertial navigation filter design","volume":"2012","author":"Stebler","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1016\/j.isatra.2013.10.002","article-title":"Cascaded Kalman and particle filters for photogrammetry based gyroscope drift and robot attitude estimation","volume":"53","author":"Poshtan","year":"2014","journal-title":"ISA Trans."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1109\/TIM.2007.908635","article-title":"Analysis and modeling of inertial sensors using Allan variance","volume":"57","author":"Hou","year":"2008","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_21","unstructured":"Analog devices, ADXRS300. Available online:http:\/\/www.analog.com\/static\/imported-files\/data_sheets\/ADXRS300.pdf."},{"key":"ref_22","unstructured":"Texas Instrum, TMS320VC5416. Available online:http:\/\/focus.ti.com\/docs\/prod\/folders\/print\/tms320vc5416.html."},{"key":"ref_23","unstructured":"Burr-Brown Products from Texas Instruments, ADS7807. Available online:http:\/\/focus.ti.com\/lit\/ds\/symlink\/ads7807.pdf."},{"key":"ref_24","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."}],"container-title":["Micromachines"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-666X\/5\/4\/1034\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:09:06Z","timestamp":1760216946000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-666X\/5\/4\/1034"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,7]]},"references-count":24,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,12]]}},"alternative-id":["mi5041034"],"URL":"https:\/\/doi.org\/10.3390\/mi5041034","relation":{},"ISSN":["2072-666X"],"issn-type":[{"type":"electronic","value":"2072-666X"}],"subject":[],"published":{"date-parts":[[2014,11,7]]}}}