{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,13]],"date-time":"2026-09-13T03:13:12Z","timestamp":1789269192567,"version":"build-2803163510"},"reference-count":24,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:00:00Z","timestamp":1783468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"publisher","award":["2022YFA1604600"],"award-info":[{"award-number":["2022YFA1604600"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Open Fund of the Stable Support Project for Fundamental Military Research Institutes","award":["WDZC20230201"],"award-info":[{"award-number":["WDZC20230201"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The residual magnetic field of the magnetic shielding system is a key factor limiting the bias stability of high-precision atomic gyroscopes. Due to the temperature dependence of hysteresis in soft magnetic materials, variations in ambient temperature can cause drift in the residual magnetic field inside the shielding cavity, thereby introducing measurement errors. Existing studies mostly rely on time-consuming finite element methods (FEM), which struggle to efficiently characterize the temperature\u2013magnetic coupling effect. To address this issue, this paper develops a theoretical model for a fast solution. First, a static magnetic field analytical model for the multilayer cylindrical magnetic shielding system is established. Second, nonlinear magnetization theory is introduced to correct the calculation errors caused by the nonlinear variation in material permeability under weak fields. On this basis, an improved Jiles-Atherton (J-A) model incorporating a temperature correction factor is constructed to accurately characterize the magnetic field distribution inside the shielding system at different temperatures. The results demonstrate that the proposed analytical model can independently and rapidly predict the residual magnetic field distribution at different temperatures, without requiring any calibration or fitting based on FEM simulations. After accounting for hysteresis nonlinearity, the deviation of the shielding factor at the center point between the analytical model and FEM simulations is approximately 5%. The static residual magnetic field at the center point exhibits a negative correlation with temperature variation. Within the actual operating temperature range of the atomic gyroscope from \u221240 \u00b0C to 60 \u00b0C, the measured results agree with the model predictions regarding the temperature-dependent trend of the radial residual magnetic field. The relative deviation of the radial residual magnetic field ranges from 2.78% to 7.69%, and that of the axial residual magnetic field ranges from 7.94% to 14.47%, thereby verifying the accuracy of the theoretical model. This model effectively predicts the residual magnetic field drift law of the magnetic shielding system under varying temperature conditions and can provide theoretical support for the analysis and active compensation of thermally induced magnetic errors in atomic gyroscopes.<\/jats:p>","DOI":"10.3390\/s26144330","type":"journal-article","created":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T16:16:18Z","timestamp":1783527378000},"page":"4330","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Temperature Effect on Residual Magnetic Field of Atomic Gyroscope Magnetic Shielding System: A High-Precision Modeling Method"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-4794-0819","authenticated-orcid":false,"given":"Yitao","family":"Chen","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6041-8439","authenticated-orcid":false,"given":"Junzhong","family":"Li","sequence":"additional","affiliation":[{"name":"Laboratory for Space Environment and Physical Sciences, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1537-4035","authenticated-orcid":false,"given":"Shengxin","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yicheng","family":"Deng","sequence":"additional","affiliation":[{"name":"Quantum Engineering Research Center of CASC, Beijing 100094, China"},{"name":"Beijing Institute of Aerospace Control Devices, Beiing 100854, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianshun","family":"Wang","sequence":"additional","affiliation":[{"name":"Quantum Engineering Research Center of CASC, Beijing 100094, China"},{"name":"Beijing Institute of Aerospace Control Devices, Beiing 100854, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7403-1542","authenticated-orcid":false,"given":"Donghua","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Zhengzhou Research Institute, Harbin Institute of Technology, Zhengzhou 450003, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"148176","DOI":"10.1109\/ACCESS.2019.2946379","article-title":"Investigation on Rotation Response of Spin-Exchange Relaxation-Free Atomic Spin Gyroscope","volume":"7","author":"Yang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1433","DOI":"10.1109\/JSEN.2020.3015852","article-title":"Reanalyzing Atomic Beam Interferometric Gyroscopes: Dependence of Sensitivity on Experimental Parameters","volume":"21","author":"Luo","year":"2021","journal-title":"IEEE Sens. 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