{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T04:12:40Z","timestamp":1772338360837,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,17]],"date-time":"2018-12-17T00:00:00Z","timestamp":1545004800000},"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>Microelectromechanical System (MEMS) Inertial Measurement Unit (IMU) is popular in the community for constructing a navigation system, due to its small size and low power consumption. However, limited by the manufacturing technology, MEMS IMU experiences more complicated noises and errors. Thus, noise modeling and suppression is important for improving accuracy of the navigation system based on MEMS IMU. Motivated by this problem, in this paper, a deep learning method was introduced to MEMS gyroscope de-noising. Specifically, a recently popular Recurrent Neural Networks (RNN) variant Simple Recurrent Unit (SRU-RNN) was employed in MEMS gyroscope raw signals de-noising. A MEMS IMU MSI3200 from MT Microsystem Company was employed in the experiments for evaluating the proposed method. Following two problems were furtherly discussed and investigated: (1) the employed SRU with different training data length were compared to explore whether there was trade-off between the training data length and prediction performance; (2) Allan Variance was the most popular MEMS gyroscope analyzing method, and five basic parameters were employed to describe the performance of different grade MEMS gyroscope; among them, quantization noise, angle random walk, and bias instability were the major factors influencing the MEMS gyroscope accuracy, the compensation results of the three parameters for gyroscope were presented and compared. The results supported the following conclusions: (1) considering the computation brought from training dataset, the values of 500, 3000, and 3000 were individually sufficient for the three-axis gyroscopes to obtain a reliable and stable prediction performance; (2) among the parameters, the quantization noise, angle random walk, and bias instability performed 0.6%, 6.8%, and 12.5% improvement for X-axis gyroscope, 60.5%, 17.3%, and 34.1% improvement for Y-axis gyroscope, 11.3%, 22.7%, and 35.7% improvement for Z-axis gyroscope, and the corresponding attitude errors decreased by 19.2%, 82.1%, and 69.4%. The results surely demonstrated the effectiveness of the employed SRU in this application.<\/jats:p>","DOI":"10.3390\/s18124471","type":"journal-article","created":{"date-parts":[[2018,12,18]],"date-time":"2018-12-18T02:15:59Z","timestamp":1545099359000},"page":"4471","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["Performance Analysis of a Deep Simple Recurrent Unit Recurrent Neural Network (SRU-RNN) in MEMS Gyroscope De-Noising"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4788-2464","authenticated-orcid":false,"given":"Changhui","family":"Jiang","sequence":"first","affiliation":[{"name":"School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China"},{"name":"Centre of Excellence in Laser Scanning Research, Finnish Geospatial Research Institute (FGI), Geodeetinrinne 2, FI-02431 Kirkkonummi, Finland"}]},{"given":"Shuai","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0148-3609","authenticated-orcid":false,"given":"Yuwei","family":"Chen","sequence":"additional","affiliation":[{"name":"Centre of Excellence in Laser Scanning Research, Finnish Geospatial Research Institute (FGI), Geodeetinrinne 2, FI-02431 Kirkkonummi, Finland"}]},{"given":"Yuming","family":"Bo","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Lin","family":"Han","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Jun","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Ziyi","family":"Feng","sequence":"additional","affiliation":[{"name":"Centre of Excellence in Laser Scanning Research, Finnish Geospatial Research Institute (FGI), Geodeetinrinne 2, FI-02431 Kirkkonummi, Finland"}]},{"given":"Hui","family":"Zhou","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Lutwak, R. (2014, January 25\u201326). Micro-technology for positioning, navigation, and timing towards PNT everywhere and always. Proceedings of the IEEE International Symposium on Inertial Sensors and Systems (ISISS), Laguna Beach, CA, USA.","DOI":"10.1109\/ISISS.2014.6782498"},{"key":"ref_2","first-page":"8","article-title":"The chip-scale combinatorial atomic navigator","volume":"24","author":"Shkel","year":"2013","journal-title":"GPS World"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Jiang, C.H., Chen, S., Chen, Y.W., and Bo, Y.M. (2018). Research on Chip Scale Atomic Clock Driven GNSS\/SINS Deeply Coupled Navigation System for Augmented Performance. IET Radar Sonar Navig.","DOI":"10.1049\/iet-rsn.2018.5152"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1007\/s00190-015-0802-8","article-title":"Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo","volume":"89","author":"Li","year":"2015","journal-title":"J. Geod."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1007\/s10291-015-0495-8","article-title":"Multi-GNSS precise point positioning with raw single-frequency and dual-frequency measurement models","volume":"20","author":"Lou","year":"2016","journal-title":"GPS Solut."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s10291-013-0339-3","article-title":"Performance assessment of single-and dual-frequency BeiDou\/GPS single-epoch kinematic positioning","volume":"18","author":"He","year":"2014","journal-title":"GPS Solut."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1017\/S0373463311000087","article-title":"Shadow matching: A new GNSS positioning technique for urban canyons","volume":"64","author":"Groves","year":"2011","journal-title":"J. Navig."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3847","DOI":"10.1016\/j.measurement.2013.07.016","article-title":"Novel hybrid of strong tracking Kalman filter and wavelet neural network for GPS\/INS during GPS outages","volume":"46","author":"Chen","year":"2013","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1109\/JSEE.2012.00033","article-title":"Accuracy improvement of GPS\/MEMS-INS integrated navigation system during GPS signal outage for land vehicle navigation","volume":"23","author":"Qin","year":"2012","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1016\/j.asoc.2007.05.010","article-title":"An intelligent navigator for seamless INS\/GPS integrated land vehicle navigation applications","volume":"8","author":"Chiang","year":"2008","journal-title":"Appl. Soft Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1109\/JSTSP.2009.2023341","article-title":"Performance analysis of vector tracking algorithms for weak GPS signals in high dynamics","volume":"3","author":"Lashley","year":"2009","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"S151","DOI":"10.1017\/S0373463311000440","article-title":"Implementation and performance assessment of a vector tracking method based on a software GPS receiver","volume":"64","author":"Zhao","year":"2001","journal-title":"J. Navig."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1017\/S0373463311000051","article-title":"Positional accuracy of assisted GPS data from high-sensitivity GPS-enabled mobile phones","volume":"64","author":"Paul","year":"2011","journal-title":"J. Navig."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1109\/TVT.2007.891492","article-title":"High-sensitivity GPS data classification based on signal degradation conditions","volume":"56","author":"Wang","year":"2007","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/s00779-006-0094-3","article-title":"Pedestrian navigation with high sensitivity GPS receivers and MEMS","volume":"11","author":"Lachapelle","year":"2007","journal-title":"Pers. Ubiquitous Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2583","DOI":"10.1109\/TAES.2017.2705338","article-title":"GNSS Multi-receiver Vector Tracking","volume":"53","author":"Yuting","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_17","first-page":"289","article-title":"Performance Analysis of GNSS Vector Tracking Loop Based GNSS\/CSAC Integrated Navigation System","volume":"49","author":"Jiang","year":"2017","journal-title":"J. Aeronaut. Astronaut. Aviat."},{"key":"ref_18","first-page":"271","article-title":"An Adaptive Tuning Method of GNSS Carrier Tracking Loop for High Dynamic Application","volume":"48","author":"Jiang","year":"2016","journal-title":"J. Aeronaut. Astronaut. Aviat."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1061\/(ASCE)0733-9453(2007)133:3(134)","article-title":"Land-vehicle INS\/GPS accurate positioning during GPS signal blockage periods","volume":"133","author":"Sameh","year":"2007","journal-title":"J. Surv. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1109\/TRA.2002.807557","article-title":"Autonomous vehicle positioning with GPS in urban canyon environments","volume":"19","author":"Cui","year":"2003","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2166","DOI":"10.1016\/j.eswa.2013.09.015","article-title":"A novel hybrid fusion algorithm to bridge the period of GPS outages using low-cost INS","volume":"41","author":"Bhatt","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yuting, N., and Gao, X.X. (2016, January 11\u201316). Joint GPS and vision direct position estimation. Proceedings of the IEEE\/ION Position, Location and Navigation Symposium (PLANS), Savannah, GA, USA.","DOI":"10.1109\/PLANS.2016.7479724"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1109\/MAES.2005.1514768","article-title":"GPS\/INS uses low-cost MEMS IMU","volume":"20","author":"Brown","year":"2005","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1323","DOI":"10.1109\/7.259535","article-title":"Multi-position alignment of strap-down inertial navigation system","volume":"29","author":"Lee","year":"1993","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1109\/TAES.2004.1310002","article-title":"Observability of an integrated GPS\/INS during maneuvers","volume":"40","author":"Rhee","year":"2004","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Jiang, C.H., Chen, S., Liu, Y.L., and Han, X. (2016, January 23\u201326). Implementation and performance evaluation of a distributed GNSS\/SINS ultra-tightly integrated navigation system. Proceedings of the IEEE International Instrumentation and Measurement Technology Conference Proceedings (I2MTC), Taipei, Taiwan.","DOI":"10.1109\/I2MTC.2016.7520490"},{"key":"ref_27","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":"Naser","year":"2008","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"9549","DOI":"10.3390\/s130809549","article-title":"A comparison between different error modeling of MEMS applied to GPS\/INS integrated systems","volume":"13","author":"Quinchia","year":"2013","journal-title":"Sensors"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1897","DOI":"10.1088\/0957-0233\/18\/7\/016","article-title":"A new multi-position calibration method for MEMS inertial navigation systems","volume":"18","author":"Syed","year":"2007","journal-title":"Meas. Sci. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1109\/TIM.2011.2171609","article-title":"Statistical modeling of rate gyros","volume":"61","author":"Vaccaro","year":"2012","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1017\/S0373463307004560","article-title":"A standard testing and calibration procedure for low cost MEMS inertial sensors and units","volume":"61","author":"Aggarwal","year":"2008","journal-title":"J. Navig."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1967","DOI":"10.1109\/TIM.2008.2006126","article-title":"Calibration of a novel MEMS inertial reference unit","volume":"58","author":"Bekkeng","year":"2009","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Ning, Y.P., Wang, J., Han, H.Z., Tan, X.L., and Liu, T.J. (2018). An Optimal Radial Basis Function Neural Network Enhanced Adaptive Robust Kalman Filter for GNSS\/INS Integrated Systems in Complex Urban Areas. Sensors, 18.","DOI":"10.3390\/s18093091"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"9448","DOI":"10.3390\/s120709448","article-title":"An enhanced mems error modeling approach based on nu-support vector regression","volume":"12","author":"Bhatt","year":"2012","journal-title":"Sensors"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"403180","DOI":"10.1155\/2015\/403180","article-title":"Adaptive global sliding mode control for MEMS gyroscope using RBF neural network","volume":"2015","author":"Chu","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1017\/S0373463304002875","article-title":"An efficient neural network model for de-noising of MEMS-based inertial data","volume":"57","year":"2004","journal-title":"J. Navig."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Hosseinyalamdary, S. (2018). Deep Kalman Filter: Simultaneous Multi-Sensor Integration and Modelling; A GNSS\/IMU Case Study. Sensors, 18.","DOI":"10.20944\/preprints201803.0121.v1"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Jiang, C.H., Chen, S., Chen, Y.W., Zhang, B.Y., Feng, Z.Y., Zhou, H., and Bo, Y.M. (2018). A MEMS IMU De-Noising Method Using Long Short Term Memory Recurrent Neural Networks (LSTM-RNN). Sensors, 18.","DOI":"10.3390\/s18103470"},{"key":"ref_39","unstructured":"Lei, T., Zhang, Y., Wang, S.I., Dai, W., and Artzi, Y. (November, January 31). Simple recurrent units for highly parallelizable recurrence. Proceedings of the Conference on Empirical Methods in Natural Language Processing, Brussels, Belgium."},{"key":"ref_40","unstructured":"(2017, September 01). SRU. Available online: https:\/\/www.zhihu.com\/question\/65244705."},{"key":"ref_41","unstructured":"(2017, December 01). MSI3200. Available online: http:\/\/www.mtmems.com\/product_view.asp?id=28."},{"key":"ref_42","unstructured":"Gro\u00dfekatth\u00f6fer, K., and Yoon, Z. (2012). Introduction into Quaternions for Spacecraft Attitude Representation."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/12\/4471\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:34:34Z","timestamp":1760196874000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/12\/4471"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,17]]},"references-count":42,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["s18124471"],"URL":"https:\/\/doi.org\/10.3390\/s18124471","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,17]]}}}