{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:44:48Z","timestamp":1760240688830,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2019,8,24]],"date-time":"2019-08-24T00:00:00Z","timestamp":1566604800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"undefined  &lt;span style=&quot;color:gray;font-size:10px;&quot;&gt;undefined&lt;\/span&gt;","award":["61603398"],"award-info":[{"award-number":["61603398"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61603398","61603398"],"award-info":[{"award-number":["61603398","61603398"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To realize the error parameter estimation of strap-down inertial navigation system (SINS) and improve the navigation accuracy for aircraft, a hybrid improved restricted Boltzmann machine BP neural network (IRBM-BPNN) approach, which combines restricted Boltzmann machine (RBM) and BP neural network (BPNN), is proposed to forecast the inertial measurement unit (IMU) instrument errors and initial alignment errors of SINS. Firstly, the error generation mechanism of SINS is analyzed, and initial alignment error model and IMU instrument error model are established. Secondly, an unsupervised RBM method is introduced to initialize BPNN to improve the forecast performance of the neural network. The RBM-BPNN model is constructed through the information fusion of SINS\/GPS\/CNS integrated navigation system by using the sum of position deviation, the sum of velocity deviation and the sum of attitude deviation as the inputs and by using the error parameters of SINS as the outputs. The RBM-BPNN structure is improved to enhance its forecast accuracy, and the pulse signal is increased as the input of the neural network. Finally, we conduct simulation experiments to forecast and compensate the error parameters of the proposed IRBM-BPNN method. Simulation results show that the artificial neural network method is feasible and effective in forecasting SINS error parameters, and the forecast accuracy of SINS error parameters can be effectively improved by combining RBM and BPNN methods and improving the neural network structure. The proposed IRBM-BPNN method has the optimal forecast accuracy of SINS error parameters and navigation accuracy of aircraft compared with the radial basis function neural network method and BPNN method.<\/jats:p>","DOI":"10.3390\/s19173682","type":"journal-article","created":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T04:38:23Z","timestamp":1566794303000},"page":"3682","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Hybrid IRBM-BPNN Approach for Error Parameter Estimation of SINS on Aircraft"],"prefix":"10.3390","volume":"19","author":[{"given":"Weilin","family":"Guo","sequence":"first","affiliation":[{"name":"Xi\u2019an Research Institute of High Technology, Xi\u2019an 710025, China"}]},{"given":"Yong","family":"Xian","sequence":"additional","affiliation":[{"name":"Xi\u2019an Research Institute of High Technology, Xi\u2019an 710025, China"}]},{"given":"Daqiao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Xi\u2019an Research Institute of High Technology, Xi\u2019an 710025, China"}]},{"given":"Bing","family":"Li","sequence":"additional","affiliation":[{"name":"Xi\u2019an Research Institute of High Technology, Xi\u2019an 710025, China"}]},{"given":"Leliang","family":"Ren","sequence":"additional","affiliation":[{"name":"Xi\u2019an Research Institute of High Technology, Xi\u2019an 710025, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.actaastro.2014.09.007","article-title":"Cubature Kalman filtering for relative spacecraft attitude and position estimation","volume":"105","author":"Zhang","year":"2014","journal-title":"Acta Astronaut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1016\/j.ast.2016.09.023","article-title":"A robust filtering algorithm for integrated navigation system of aerospace vehicle in launch inertial coordinate","volume":"58","author":"Zhao","year":"2016","journal-title":"Aerosp. 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