{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:33:00Z","timestamp":1760239980435,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T00:00:00Z","timestamp":1547164800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["grant no. 61705052"],"award-info":[{"award-number":["grant no. 61705052"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>As an important angle sensor of the opto-electric platform, gyro output accuracy plays a vital role in the stabilization and track accuracy of the whole system. It is known that the generally used fixed-bandwidth filters, single neural network models, or linear models cannot compensate for gyro error well, and so they cannot meet engineering needs satisfactorily. In this paper, a novel hybrid ARIMA-Elman model is proposed. For the reason that it can fully combine the strong linear approximation capability of the ARIMA model and the superior nonlinear compensation capability of a neural network, the proposed model is suitable for handling gyro error, especially for its non-stationary random component. Then, to solve the problem that the parameters of ARIMA model and the initial weights of the Elman neural network are difficult to determine, a differential algorithm is initially utilized for parameter selection. Compared with other commonly used optimization algorithms (e.g., the traditional least-squares identification method and the genetic algorithm method), the intelligence differential algorithm can overcome the shortcomings of premature convergence and has higher optimization speed and accuracy. In addition, the drift error is obtained based on the technique of lift-wavelet separation and reconstruction, and, in order to weaken the randomness of the data sequence, an ashing operation and Jarque-Bear test have been added to the handle process. In this study, actual gyro data is collected and the experimental results show that the proposed method has higher compensation accuracy and faster network convergence, when compared with other commonly used error-compensation methods. Finally, the hybrid method is used to compensate for gyro error collected in other states. The test results illustrate that the proposed algorithm can effectively improve error compensation accuracy, and has good generalization performance.<\/jats:p>","DOI":"10.3390\/a12010022","type":"journal-article","created":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T04:10:16Z","timestamp":1547179816000},"page":"22","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Gyro Error Compensation in Optoelectronic Platform Based on a Hybrid ARIMA-Elman Model"],"prefix":"10.3390","volume":"12","author":[{"given":"Xingkui","family":"Xu","sequence":"first","affiliation":[{"name":"Research Center for Space Optical Engineering, Harbin Institute of Technology, Harbin 150001, China"}]},{"given":"Chunfeng","family":"Wu","sequence":"additional","affiliation":[{"name":"Research Center for Space Optical Engineering, Harbin Institute of Technology, Harbin 150001, China"},{"name":"China Space Sanjiang Group Corporation Limited, Wuhan 430023, China"}]},{"given":"Qingyu","family":"Hou","sequence":"additional","affiliation":[{"name":"Research Center for Space Optical Engineering, Harbin Institute of Technology, Harbin 150001, China"}]},{"given":"Zhigang","family":"Fan","sequence":"additional","affiliation":[{"name":"Research Center for Space Optical Engineering, Harbin Institute of Technology, Harbin 150001, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1117\/12.258208","article-title":"Fiber Optic Gyros for Space, Marine, and Aviation Application","volume":"2837","author":"Sander","year":"1996","journal-title":"Proc. SPIE"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1364\/OL.5.000173","article-title":"Fiber-optic Rotation Sensing with Low Drift","volume":"5","author":"Ulrich","year":"1980","journal-title":"Opt. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1088\/1009-1963\/16\/3\/029","article-title":"Phenomena of Optic-bound Effect on Fiber Optic Gyro","volume":"16","author":"Fang","year":"2007","journal-title":"Chin. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1109\/PROC.1966.4634","article-title":"Statistics of Atomic Frequency Standards","volume":"54","author":"Allan","year":"1966","journal-title":"Proc. IEEE"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1109\/JLT.2006.889658","article-title":"Reduced thermal sensitivity of a fiber-optic gyroscope using an air-core photonic-band gap fiber","volume":"25","author":"Blin","year":"2007","journal-title":"J. Light Wave Technol."},{"key":"ref_6","first-page":"273","article-title":"Application of artificial neural network and genetic algorithm in modeling of fiber optic gyroscope temperature drift","volume":"22","author":"Long","year":"2006","journal-title":"Artif. Intell."},{"key":"ref_7","first-page":"221","article-title":"Identification of temperature drift for FOG using RBF neural networks","volume":"32","author":"Zhu","year":"2000","journal-title":"J. Shang Hai Jiao Tong Univ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.actaastro.2017.11.020","article-title":"Experimental study on line-of-sight (LOS) attitude control using control moment gyros under micro-gravity environment","volume":"143","author":"Kojima","year":"2018","journal-title":"Acta Astronaut."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1382","DOI":"10.1016\/j.asr.2014.06.038","article-title":"Adaptive neural control of spacecraft using control moment gyros","volume":"55","author":"Leeghim","year":"2015","journal-title":"Adv. Space Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2529","DOI":"10.1016\/j.ijleo.2015.06.044","article-title":"Allan variance method for gyro noise analysis using weighted least square algorithm","volume":"126","author":"Lv","year":"2015","journal-title":"Optik"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.cor.2018.04.009","article-title":"A multi-objective differential evolution algorithm for parallel batch processing machine scheduling considering electricity consumption cost","volume":"96","author":"Zhou","year":"2018","journal-title":"Comput. Oper. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1016\/j.sna.2018.04.008","article-title":"MEMS gyros temperature calibration through artificial neural networks","volume":"279","author":"Fontanellaa","year":"2018","journal-title":"Sens. Actuators A Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.specom.2017.08.003","article-title":"Deep Elman recurrent neural networks for statistical parametric speech synthesis","volume":"93","author":"Achanta","year":"2017","journal-title":"Speech Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1016\/j.eswa.2017.09.059","article-title":"Energy consumption forecasting based on Elman neural networks with evolutive optimization","volume":"92","author":"Ruiz","year":"2018","journal-title":"Expert Syst. Appl."},{"key":"ref_15","first-page":"264","article-title":"Adaptive backstepping Elman-based neural control for unknown nonlinear systems","volume":"130","author":"Hsu","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1016\/j.asoc.2010.01.006","article-title":"A differential evolution based neural network approach to nonlinear system identification","volume":"11","author":"Subudhi","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_17","first-page":"92","article-title":"Differential evolution strategy for structural system identification","volume":"26","author":"Tang","year":"2011","journal-title":"Comput. Aided Civ. Infrastruct. Eng."},{"key":"ref_18","first-page":"53","article-title":"A simple and global optimization algorithm for engineering problems: differential evolution algorithm","volume":"12","author":"Karaboga","year":"2004","journal-title":"Turk. J. Electr. Eng. Comput. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.knosys.2017.07.005","article-title":"An efficient intrusion detection system based on hyper graph - Genetic algorithm for parameter optimization and feature selection in support vector machine","volume":"134","author":"Raman","year":"2017","journal-title":"Knowl.-Based Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.knosys.2016.01.046","article-title":"Hybrid kernel density estimation for discriminant analysis with information complexity and genetic algorithm","volume":"99","author":"Baek","year":"2016","journal-title":"Knowl.-Based Syst."},{"key":"ref_21","unstructured":"Chettah, A.K., and Talbi, H. (2018). A Compound Sinusoidal Differential Evolution algorithm for continuous optimization. Swarm and Evolutionary Computation. Swarm Evol. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1016\/j.ejor.2017.10.013","article-title":"Auto-selection mechanism of differential evolution algorithm variants and its application","volume":"270","author":"Qin","year":"2018","journal-title":"Eur. J. Oper. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.aeue.2017.04.020","article-title":"Optimization of weighted myriad filters with differential evolution algorithm","volume":"77","author":"Zorlu","year":"2017","journal-title":"AEU-Int. J. Electron. Commun."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/1\/22\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:25:10Z","timestamp":1760185510000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/1\/22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,11]]},"references-count":23,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["a12010022"],"URL":"https:\/\/doi.org\/10.3390\/a12010022","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2019,1,11]]}}}