{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T15:17:52Z","timestamp":1777475872454,"version":"3.51.4"},"reference-count":23,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2016,5,31]],"date-time":"2016-05-31T00:00:00Z","timestamp":1464652800000},"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>The different noise components in a dual-mass micro-electromechanical system (MEMS) gyroscope structure is analyzed in this paper, including mechanical-thermal noise (MTN), electronic-thermal noise (ETN), flicker noise (FN) and Coriolis signal in-phase noise (IPN). The structure equivalent electronic model is established, and an improved white Gaussian noise reduction method for dual-mass MEMS gyroscopes is proposed which is based on sample entropy empirical mode decomposition (SEEMD) and time-frequency peak filtering (TFPF). There is a contradiction in TFPS, i.e., selecting a short window length may lead to good preservation of signal amplitude but bad random noise reduction, whereas selecting a long window length may lead to serious attenuation of the signal amplitude but effective random noise reduction. In order to achieve a good tradeoff between valid signal amplitude preservation and random noise reduction, SEEMD is adopted to improve TFPF. Firstly, the original signal is decomposed into intrinsic mode functions (IMFs) by EMD, and the SE of each IMF is calculated in order to classify the numerous IMFs into three different components; then short window TFPF is employed for low frequency component of IMFs, and long window TFPF is employed for high frequency component of IMFs, and the noise component of IMFs is wiped off directly; at last the final signal is obtained after reconstruction. Rotation experimental and temperature experimental are carried out to verify the proposed SEEMD-TFPF algorithm, the verification and comparison results show that the de-noising performance of SEEMD-TFPF is better than that achievable with the traditional wavelet, Kalman filter and fixed window length TFPF methods.<\/jats:p>","DOI":"10.3390\/s16060796","type":"journal-article","created":{"date-parts":[[2016,5,31]],"date-time":"2016-05-31T10:40:18Z","timestamp":1464691218000},"page":"796","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["A Noise Reduction Method for Dual-Mass Micro-Electromechanical Gyroscopes Based on Sample Entropy Empirical Mode Decomposition and Time-Frequency Peak Filtering"],"prefix":"10.3390","volume":"16","author":[{"given":"Chong","family":"Shen","sequence":"first","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, Key Laboratory of Instrumentation Science &amp; Dynamic Measurement, Ministry of Education, School of Instrument and Electronics, North University of China, Taiyuan 030051, China"}]},{"given":"Jie","family":"Li","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, Key Laboratory of Instrumentation Science &amp; Dynamic Measurement, Ministry of Education, School of Instrument and Electronics, North University of China, Taiyuan 030051, China"}]},{"given":"Xiaoming","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, Key Laboratory of Instrumentation Science &amp; Dynamic Measurement, Ministry of Education, School of Instrument and Electronics, North University of China, Taiyuan 030051, China"}]},{"given":"Yunbo","family":"Shi","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, Key Laboratory of Instrumentation Science &amp; Dynamic Measurement, Ministry of Education, School of Instrument and Electronics, North University of China, Taiyuan 030051, China"}]},{"given":"Jun","family":"Tang","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, Key Laboratory of Instrumentation Science &amp; Dynamic Measurement, Ministry of Education, School of Instrument and Electronics, North University of China, Taiyuan 030051, China"}]},{"given":"Huiliang","family":"Cao","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, Key Laboratory of Instrumentation Science &amp; Dynamic Measurement, Ministry of Education, School of Instrument and Electronics, North University of China, Taiyuan 030051, China"}]},{"given":"Jun","family":"Liu","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, Key Laboratory of Instrumentation Science &amp; Dynamic Measurement, Ministry of Education, School of Instrument and Electronics, North University of China, Taiyuan 030051, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,5,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"23041","DOI":"10.3390\/s141223041","article-title":"Study of the algorithm of backtracking decoupling and adaptive extended Kalman filter based on the quaternion expanded to the state variable for under glider navigation","volume":"14","author":"Huang","year":"2014","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1109\/JSEN.2015.2477444","article-title":"Tightly-coupled integration of WiFi and MEMS sensors on handheld devices for indoor pedestrian navigation","volume":"16","author":"Zhuang","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"71","DOI":"10.3390\/s16010071","article-title":"Optimization and experimentation of dual-mass MEMS gyroscope Quadrature error correction methods","volume":"16","author":"Cao","year":"2016","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"033003","DOI":"10.1117\/1.JMM.13.3.033003","article-title":"Electrostatic stiffness correction for quadrature error in decoupled dual-mass MEMS gyroscope","volume":"13","author":"Li","year":"2014","journal-title":"J. Micro Nanolithogr. MEMS MOEMS"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1788","DOI":"10.1016\/j.mee.2007.01.168","article-title":"Low frequency noise measurement and analysis of capacitive micro-accelerometers","volume":"84","author":"Nagel","year":"2007","journal-title":"Microelectron. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/S0038-1101(02)00220-4","article-title":"Measurement of noise characteristics of MEMS accelerometers","volume":"47","author":"Korman","year":"2003","journal-title":"Solid State Electron."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1016\/j.mee.2008.12.045","article-title":"Noise and reliability measurement of a three-axis micro-accelerometer","volume":"86","author":"Zaiyadi","year":"2009","journal-title":"Microelectron. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.1016\/j.ymssp.2015.08.002","article-title":"An improved interface and noise analysis of a turning fork microgyroscope structure","volume":"70\u201371","author":"Cao","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"266","DOI":"10.3390\/mi6020266","article-title":"Noise reduction of MEMS gyroscope based on direct modeling for an angular rate signal","volume":"6","author":"Xue","year":"2015","journal-title":"Micromachines"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/s12200-015-0474-2","article-title":"An improved noise reduction algorithm based on wavelet transformation for MEMS gyroscope","volume":"8","author":"Yuan","year":"2015","journal-title":"Front. Optoelectron."},{"key":"ref_11","first-page":"4633","article-title":"The silicon micro-gyroscope signal processing method based on morphological wavelet filter","volume":"15","author":"Zhao","year":"2012","journal-title":"Inf. Int. Interdiscip. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.measurement.2013.12.025","article-title":"Digital signal processing for a micromachined vibratory gyroscope based on a three dimensional adaptive filter demodulator","volume":"50","author":"Liu","year":"2014","journal-title":"Measurement"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4025","DOI":"10.1109\/TGRS.2013.2278981","article-title":"Random-noise attenuation for seismic data by local parallel radial-trace TFPF","volume":"52","author":"Xiong","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6449","DOI":"10.1109\/TGRS.2013.2296603","article-title":"Variable-eccentricity hyperbolic-trace TFPF for seismic random noise attenuation","volume":"52","author":"Tian","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1109\/LGRS.2011.2129552","article-title":"Noise attenuation for 2-D seismic data by radial-trace time frequency peak filtering","volume":"8","author":"Wu","year":"2011","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1093\/gji\/ggv340","article-title":"Signal preserving and seismic random noise attenuation by Hurst exponent based time-frequency peak filter","volume":"203","author":"Zhang","year":"2015","journal-title":"Geophys. J. Int."},{"key":"ref_17","first-page":"4559","article-title":"Elimination of seismic random noise based on the SW statistic adaptive TFPF","volume":"58","author":"Lin","year":"2015","journal-title":"Chin. J. Geophys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2252","DOI":"10.1109\/LGRS.2015.2464233","article-title":"Curvature-varying Hyperbolic trace TFPF for seismic random noise attenuation","volume":"12","author":"Zhuang","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"495","DOI":"10.3233\/JAE-131668","article-title":"Investigation of a vacuum packaged MEMS gyroscope architecture\u2019s temperature robustness","volume":"41","author":"Cao","year":"2013","journal-title":"Int. J. Appl. Electromagn. Mech."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"15022","DOI":"10.3390\/s140815022","article-title":"Fault detection of a roller-bearing system through the EMD of a wavelet denoised signal","volume":"14","author":"Ahn","year":"2014","journal-title":"Sensors"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2338","DOI":"10.1016\/j.ijleo.2015.05.145","article-title":"Applying empirical mode decomposition (EMD) and entropy to diagnose circuit breaker faults","volume":"126","author":"Liu","year":"2015","journal-title":"Optik"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.cnsns.2015.10.023","article-title":"Modified generalized sample entropy and surrogate data analysis for stock markets","volume":"35","author":"Xu","year":"2016","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.sna.2015.04.021","article-title":"Improved hybrid filter for fiber optic gyroscope signal denoising based on EMD and forward linear prediction","volume":"230","author":"Cui","year":"2015","journal-title":"Sens. Actuators A Phys."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/6\/796\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:24:47Z","timestamp":1760210687000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/6\/796"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,31]]},"references-count":23,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2016,6]]}},"alternative-id":["s16060796"],"URL":"https:\/\/doi.org\/10.3390\/s16060796","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5,31]]}}}