{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T00:56:47Z","timestamp":1775609807403,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2014,10,9]],"date-time":"2014-10-09T00:00:00Z","timestamp":1412812800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Science Foundation of China","award":["61304234"],"award-info":[{"award-number":["61304234"]}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["HEUCFX041403"],"award-info":[{"award-number":["HEUCFX041403"]}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["HEUCFR1114"],"award-info":[{"award-number":["HEUCFR1114"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To overcome the effect of temperature on laser gyro zero bias and to stabilize the laser gyro output, this study proposes a modified radial basis function neural network (RBFNN) based on a Kohonen network and an orthogonal least squares (OLS) algorithm. The modified method, which combines the pattern classification capability of the Kohonen network and the optimal choice capacity of OLS, avoids the random selection of RBFNN centers and improves the compensation accuracy of the RBFNN. It can quickly and accurately identify the effect of temperature on laser gyro zero bias. A number of comparable identification and compensation tests on a variety of temperature-changing situations are completed using the multiple linear regression (MLR), RBFNN and modified RBFNN methods. The test results based on several sets of gyro output in constant and changing temperature conditions demonstrate that the proposed method is able to overcome the effect of randomly selected RBFNN centers. The running time of the method is about 60 s shorter than that of traditional RBFNN under the same test conditions, which suggests that the calculations are reduced. Meanwhile, the compensated gyro output accuracy using the modified method is about 7.0 \u00d7 10\u22124 \u00b0\/h; comparatively, the traditional RBFNN is about 9.0 \u00d7 10\u22124 \u00b0\/h and the MLR is about 1.4 \u00d7 10\u22123 \u00b0\/h.<\/jats:p>","DOI":"10.3390\/s141018711","type":"journal-article","created":{"date-parts":[[2014,10,9]],"date-time":"2014-10-09T10:20:20Z","timestamp":1412850020000},"page":"18711-18727","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Laser Gyro Temperature Compensation Using Modified RBFNN"],"prefix":"10.3390","volume":"14","author":[{"given":"Jicheng","family":"Ding","sequence":"first","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiquan","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuai","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,10,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"115501","DOI":"10.1088\/2040-8978\/12\/11\/115501","article-title":"New random walk reduction algorithm in ring laser gyroscopes","volume":"12","author":"Song","year":"2010","journal-title":"J. Opt."},{"key":"ref_2","unstructured":"Cheng, J.C., and Fang, J.C. (2012). Instrumentation and Control Technology, IEEE."},{"key":"ref_3","unstructured":"Hong, W.S., Lee, K.S., Paik, B.S., Han, J.Y., and Son, S.H. (2008, January 9\u201313). The compensation method for thermal bias of ring laser gyro. Acapulco, Mexico."},{"key":"ref_4","unstructured":"Yang, J.Q., Liao, D., Jin, X., and Jia, X.Q. (2010, January 27\u201329). The compensation methods of the start-up drift of four frequency differential laser gyro. Shenyang, China."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1898","DOI":"10.1016\/j.measurement.2011.08.032","article-title":"Application of Least Squares-Support Vector Machine in system-level temperature compensation of ring laser gyroscope","volume":"44","author":"Guo","year":"2011","journal-title":"Measurement"},{"key":"ref_6","unstructured":"Guo, Y.W., and Qi, T.G. Thermal Characteristics and Thermal Compensation of Four Frequency Ring Laser Gyro. Palm Springs, CA, USA."},{"key":"ref_7","first-page":"1509","article-title":"Dynamic modeling and compensation for thermal error of three-axis ring laser gyro","volume":"15","author":"Ge","year":"2007","journal-title":"Opt. Precis. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.3788\/OPE.20132105.1272","article-title":"Design and experiment of micro machined vibratory gyroscope","volume":"21","author":"Jia","year":"2013","journal-title":"Opt. Precis. Eng."},{"key":"ref_9","first-page":"738","article-title":"Analysis on temperature characteristic of mechanically dithered RLG's bias with a method of stepwise regression","volume":"32","author":"Zhang","year":"2006","journal-title":"Opt. Tech."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1251","DOI":"10.1109\/72.883412","article-title":"A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints","volume":"11","author":"Xue","year":"2000","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_11","first-page":"1912","article-title":"Temperature errors modeling for fiber optic gyro using Multiple Linear Regression models","volume":"29","author":"Jin","year":"2008","journal-title":"J. Astronaut."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Yang, P.X., Qin, Y.Y., and You, J.C. (2010). Temperature compensation for RLG based on neural network. Proc. SPIE, 7544.","DOI":"10.1117\/12.885310"},{"key":"ref_13","first-page":"81","article-title":"Study of temperature compensation for laser gyro SINS of land-based missile","volume":"4","author":"Han","year":"2013","journal-title":"Tactical Missile Technol."},{"key":"ref_14","first-page":"235","article-title":"Temperature error compensation for digital closed-loop fiber optic gyroscope based on RBF neural network","volume":"16","author":"Jin","year":"2008","journal-title":"Opt. Precis. Eng."},{"key":"ref_15","first-page":"119","article-title":"Application and compensation for startup phase of FOG based on RBF neural network","volume":"42","author":"Shen","year":"2013","journal-title":"Infrared Laser Eng."},{"key":"ref_16","first-page":"48","article-title":"Application of radial Basis function network for identification of axial RLG drifts in single-axis rotation inertial navigation system","volume":"34","author":"Yu","year":"2012","journal-title":"J. Natl. Univ. Def. Technol."},{"key":"ref_17","first-page":"695","article-title":"Temperature compensation model of fluxgate magnetometers based on RBF neural network","volume":"33","author":"Pang","year":"2012","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Jeatrakul, P., and Wong, K.W. (2009, January 20\u201322). Comparing the performance of different neural networks for binary classification problems. Bangkok, Thailand.","DOI":"10.1109\/SNLP.2009.5340935"},{"key":"ref_19","first-page":"8","article-title":"Research on temperature characteristic of angle sensor","volume":"35","author":"Wu","year":"2012","journal-title":"Electron. Meas. Technol."},{"key":"ref_20","first-page":"9","article-title":"Data mining using rule extraction from Kohonen self-organizing maps","volume":"15","author":"James","year":"2005","journal-title":"Neural Comput. Appl."},{"key":"ref_21","unstructured":"Liu, H.Y., and He, J. (2009, January 14\u201317). The application of dynamic K-means clustering algorithm in the Center selection of RBF Neural Networks. Guilin, China."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1786","DOI":"10.1109\/TIM.2007.895674","article-title":"A neural network parallel adaptive controller for dynamic system control","volume":"56","author":"Kamalasadan","year":"2007","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_23","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":"Deepak","year":"2012","journal-title":"Sensors"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1109\/JSEN.2009.2030072","article-title":"A radial basis function neural network classifier for the discrimination of individual odor using responses of thick-film tin-oxide sensors","volume":"9","author":"Kumar","year":"2009","journal-title":"IEEE Sens. J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1109\/JSEN.2010.2066559","article-title":"Wavelet coefficient trained neural network classifier for improvement in qualitative classification performance of oxygen-plasma treated thick film tin oxide sensor array exposed to different odors\/gases","volume":"11","author":"Kumar","year":"2011","journal-title":"IEEE Sens. J."},{"key":"ref_26","unstructured":"Gokhan, A.A., and Cansever, G. (2006, January 7\u20139). Adaptive neural network based fuzzy sliding mode control of robot manipulator. Bangkok, Thailand."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1300","DOI":"10.1109\/TBME.2006.889770","article-title":"Evaluation and Application of a RBF Neural Network for Online Single-Sweep Extraction of SEPs during Scoliosis Surgery","volume":"54","author":"Merzagora","year":"2007","journal-title":"IEEE Trans.Biomed. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/TNNLS.2011.2178323","article-title":"Visualized analysis of mixed numeric and categorical data via extended self-organizing map","volume":"23","author":"Hsu","year":"2012","journal-title":"IEEE Trans.Neural Netw. Learn. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1109\/TNN.2011.2169809","article-title":"Parallel programmable asynchronous neighborhood mechanism for kohonen SOM implemented in CMOS technology","volume":"22","author":"Dlugosz","year":"2011","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_30","first-page":"1271","article-title":"Reducing the number of neurons in radial basis function networks with dynamic decay adjustment","volume":"31","author":"Paetz","year":"2007","journal-title":"Appl. Math. Model."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1023\/A:1026289910256","article-title":"On the kernel widths in radial-basis function networks","volume":"18","author":"Benoudjit","year":"2003","journal-title":"Neural Proc. Lett."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/14\/10\/18711\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:16:44Z","timestamp":1760217404000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/14\/10\/18711"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,9]]},"references-count":31,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2014,10]]}},"alternative-id":["s141018711"],"URL":"https:\/\/doi.org\/10.3390\/s141018711","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,9]]}}}