{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T20:57:32Z","timestamp":1771102652481,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T00:00:00Z","timestamp":1743638400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52205043"],"award-info":[{"award-number":["52205043"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Aiming at the problem of nonlinear coupling error in the measurement of parallel six-axis accelerometers, this study improves the back propagation (BP) neural network and proposes an improved BP neural network decoupling model that introduces the gradient descent with momentum and the Levenberg\u2013Marquardt (LM) algorithm. By introducing the momentum factor in the model updating stage, the LM algorithm is used in the local learning stage to improve the convergence speed and shock resistance of the network, and to enhance the accuracy of the algorithm. Based on the mid-frequency standard vibration device APS 129 ELECTRO-SEIS (SPEKTRA, Stuttgart, Baden-W\u00fcrttemberg, Germany), the calibration data are obtained and the improved BP neural network decoupling model is trained to complete the nonlinear decoupling of the test set. Compared with the linear decoupling method, the decoupled six-axis accelerometers with the improved BP neural network model have acceleration measurement accuracies of 0.035%, 0.018% and 0.039% along the x, y and z axes, respectively, which indicates that the model has high decoupling accuracy, and it can significantly improve the measurement accuracy of the sensors. The research results can provide theoretical support for high-precision inertial navigation.<\/jats:p>","DOI":"10.3390\/s25072280","type":"journal-article","created":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T03:36:45Z","timestamp":1743737805000},"page":"2280","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Nonlinear Decoupling Study of Six-Axis Acceleration Sensor Based on Improved BP Neural Network"],"prefix":"10.3390","volume":"25","author":[{"given":"Jialin","family":"Zhang","sequence":"first","affiliation":[{"name":"The School of Technology, Beijing Forestry University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunzhan","family":"Yu","sequence":"additional","affiliation":[{"name":"The School of Technology, Beijing Forestry University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengxin","family":"Du","sequence":"additional","affiliation":[{"name":"The School of Technology, Beijing Forestry University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhe","family":"Hao","sequence":"additional","affiliation":[{"name":"The School of Technology, Beijing Forestry University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhibo","family":"Sun","sequence":"additional","affiliation":[{"name":"Beihang School, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zheng, R., Sun, G., and Li, F.D. 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