{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T17:54:25Z","timestamp":1777658065407,"version":"3.51.4"},"reference-count":42,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,15]],"date-time":"2018-10-15T00:00:00Z","timestamp":1539561600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2015M580434"],"award-info":[{"award-number":["2015M580434"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Microelectromechanical Systems (MEMS) Inertial Measurement Unit (IMU) containing a three-orthogonal gyroscope and three-orthogonal accelerometer has been widely utilized in position and navigation, due to gradually improved accuracy and its small size and low cost. However, the errors of a MEMS IMU based standalone Inertial Navigation System (INS) will diverge over time dramatically, since there are various and nonlinear errors contained in the MEMS IMU measurements. Therefore, MEMS INS is usually integrated with a Global Positioning System (GPS) for providing reliable navigation solutions. The GPS receiver is able to generate stable and precise position and time information in open sky environment. However, under signal challenging conditions, for instance dense forests, city canyons, or mountain valleys, if the GPS signal is weak and even is blocked, the GPS receiver will fail to output reliable positioning information, and the integration system will fade to an INS standalone system. A number of effects have been devoted to improving the accuracy of INS, and de-nosing or modelling the random errors contained in the MEMS IMU have been demonstrated to be an effective way of improving MEMS INS performance. In this paper, an Artificial Intelligence (AI) method was proposed to de-noise the MEMS IMU output signals, specifically, a popular variant of Recurrent Neural Network (RNN) Long Short Term Memory (LSTM) RNN was employed to filter the MEMS gyroscope outputs, in which the signals were treated as time series. A MEMS IMU (MSI3200, manufactured by MT Microsystems Company, Shijiazhuang, China) was employed to test the proposed method, a 2 min raw gyroscope data with 400 Hz sampling rate was collected and employed in this testing. The results show that the standard deviation (STD) of the gyroscope data decreased by 60.3%, 37%, and 44.6% respectively compared with raw signals, and on the other way, the three-axis attitude errors decreased by 15.8%, 18.3% and 51.3% individually. Further, compared with an Auto Regressive and Moving Average (ARMA) model with fixed parameters, the STD of the three-axis gyroscope outputs decreased by 42.4%, 21.4% and 21.4%, and the attitude errors decreased by 47.6%, 42.3% and 52.0%. The results indicated that the de-noising scheme was effective for improving MEMS INS accuracy, and the proposed LSTM-RNN method was more preferable in this application.<\/jats:p>","DOI":"10.3390\/s18103470","type":"journal-article","created":{"date-parts":[[2018,10,16]],"date-time":"2018-10-16T02:52:53Z","timestamp":1539658373000},"page":"3470","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":113,"title":["A MEMS IMU De-Noising Method Using Long Short Term Memory Recurrent Neural Networks (LSTM-RNN)"],"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuai","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Boya","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Photogrammetry and Remote Sensing, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuming","family":"Bo","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,15]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1109\/TVT.2008.926076","article-title":"Performance enhancement of MEMS-based INS\/GPS integration for low-cost navigation applications","volume":"58","author":"Noureldin","year":"2009","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Chen, Y., Tang, J., Jiang, C., Zhu, L., Lehtom\u00e4ki, M., Kaartinen, H., Kaijaluoto, R., Wang, Y., Hyypp\u00e4, J., and Hyypp\u00e4, H. (2018). The accuracy comparison of three simultaneous localization and mapping (SLAM)-Based indoor mapping technologies. Sensors, 18.","DOI":"10.3390\/s18103228"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1007\/s10291-017-0601-1","article-title":"New optimal smoothing scheme for improving relative and absolute accuracy of tightly coupled GNSS\/SINS integration","volume":"21","author":"Zhang","year":"2017","journal-title":"GPS Solut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5311","DOI":"10.3390\/s150305311","article-title":"Fast fingerprint database maintenance for indoor positioning based on UGV SLAM","volume":"15","author":"Tang","year":"2015","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"20170121","DOI":"10.1587\/elex.14.20170121","article-title":"Implementation and performance evaluation of a fast relocation method in a GPS\/SINS\/CSAC integrated navigation system hardware prototype","volume":"14","author":"Jiang","year":"2017","journal-title":"IEICE Electron. Express"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ma, L., You, Z., Liu, T., and Shi, S. (2016). Coupled integration of CSAC, MIMU, and GNSS for improved PNT performance. Sensors, 16.","DOI":"10.3390\/s16050682"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Petritoli, E., and Leccese, F. (2015, January 4\u20135). Improvement of altitude precision in indoor and urban canyon navigation for small flying vehicles. Proceedings of the 2015 IEEE Metrology for Aerospace (MetroAeroSpace), Benevento, Italy.","DOI":"10.1109\/MetroAeroSpace.2015.7180626"},{"key":"ref_9","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_10","doi-asserted-by":"crossref","unstructured":"Fern\u00e1ndez, E., Calero, D., and Par\u00e9s, M.E. (2017). CSAC Characterization and Its Impact on GNSS Clock Augmentation Performance. Sensors, 17.","DOI":"10.3390\/s17020370"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/S1068-5200(02)00527-8","article-title":"Review of the present status of optical fiber sensors","volume":"9","author":"Lee","year":"2003","journal-title":"Opt. Fiber Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3711","DOI":"10.1109\/JSEN.2016.2535396","article-title":"Fiber-optic gyroscope signal denoising using an adaptive robust Kalman filter","volume":"16","author":"Narasimhappa","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.sna.2016.09.036","article-title":"ARMA model based adaptive unscented fading Kalman filter for reducing drift of fiber optic gyroscope","volume":"251","author":"Narasimhappa","year":"2016","journal-title":"Sens. Actuators A Phys."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Jiang, C., Chen, S., Chen, Y., and Bo, Y. (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_15","doi-asserted-by":"crossref","first-page":"26212","DOI":"10.3390\/s151026212","article-title":"Real-time single-frequency GPS\/MEMS-IMU attitude determination of lightweight UAVs","volume":"15","author":"Eling","year":"2015","journal-title":"Sensors"},{"key":"ref_16","first-page":"253","article-title":"Research of fast relocation technology assisted by IMU in the GPS\/SINS ultra-tightly coupled navigation system","volume":"48","author":"Jiang","year":"2016","journal-title":"J. Aeronaut. Astronaut. Aviat."},{"key":"ref_17","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_18","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_19","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_20","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_21","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_22","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_23","doi-asserted-by":"crossref","first-page":"371","DOI":"10.5139\/IJASS.2011.12.4.371","article-title":"Improvement of a low cost MEMS inertial-GPS integrated system using wavelet denoising techniques","volume":"12","author":"Kang","year":"2011","journal-title":"Int. J. Aeronaut. Space Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00542-010-1169-7","article-title":"Application of wavelet neural network in signal processing of MEMS accelerometers","volume":"17","author":"Chen","year":"2011","journal-title":"Microsyst. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"25277","DOI":"10.3390\/s151025277","article-title":"Auto regressive moving average (ARMA) modeling method for Gyro random noise using a robust Kalman filter","volume":"15","author":"Huang","year":"2015","journal-title":"Sensors"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"47911","DOI":"10.1109\/ACCESS.2018.2867632","article-title":"Novel time series modeling methods for gyro random noise used in Internet of Things","volume":"6","author":"Huang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"105103","DOI":"10.1088\/0957-0233\/27\/10\/105103","article-title":"Real-time modeling and online filtering of the stochastic error in a fiber optic current transducer","volume":"27","author":"Wang","year":"2016","journal-title":"Meas. Sci. Technol."},{"key":"ref_28","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_29","doi-asserted-by":"crossref","first-page":"6239","DOI":"10.1109\/JSEN.2016.2581200","article-title":"Systematic error elimination using additive measurements and combination of two low cost IMSs","volume":"16","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Yang, H., Li, W., Luo, T., Liang, H., Zhang, H., Gu, Y., and Luo, C. (2017). Research on the Strategy of Motion Constraint-Aided ZUPT for the SINS Positioning System of a Shearer. Micromachines, 8.","DOI":"10.3390\/mi8110340"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Ning, Y., Wang, J., Han, H., Tan, X., and Liu, T. (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_32","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.measurement.2017.09.012","article-title":"Bridging the gap between sensor noise modeling and sensor characterization","volume":"116","author":"Jerath","year":"2018","journal-title":"Measurement"},{"key":"ref_33","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_34","doi-asserted-by":"crossref","unstructured":"Chu, Y., and Fei, J. (2015). Adaptive global sliding mode control for MEMS gyroscope using RBF neural network. Math. Probl. Eng.","DOI":"10.1155\/2015\/403180"},{"key":"ref_35","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_36","doi-asserted-by":"crossref","unstructured":"Xing, H., Hou, B., Lin, Z., and Guo, M. (2017). Modeling and Compensation of Random Drift of MEMS Gyroscopes Based on Least Squares Support Vector Machine Optimized by Chaotic Particle Swarm Optimization. Sensors, 17.","DOI":"10.3390\/s17102335"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_38","unstructured":"Gallicchio, C. (arXiv, 2018). Short-term memory of deep rnn, arXiv."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Li, X., and Wu, X. (2015, January 19\u201324). Constructing long short-term memory based deep recurrent neural networks for large vocabulary speech recognition. Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), South Brisbane, Australia.","DOI":"10.1109\/ICASSP.2015.7178826"},{"key":"ref_40","unstructured":"(2015, August 27). Understanding LSTM Networks. Available online: https:\/\/colah.github.io\/posts\/2015-08-Understanding-LSTMs."},{"key":"ref_41","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_42","unstructured":"(2018, September 30). MT Microsystems. Available online: http:\/\/www.mtmems.com\/product_view.asp?id=28."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3470\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:25:46Z","timestamp":1760196346000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3470"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,15]]},"references-count":42,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["s18103470"],"URL":"https:\/\/doi.org\/10.3390\/s18103470","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,15]]}}}