{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T22:25:03Z","timestamp":1777501503943,"version":"3.51.4"},"reference-count":26,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T00:00:00Z","timestamp":1655424000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["61973280"],"award-info":[{"award-number":["61973280"]}]},{"name":"National Natural Science Foundation of China","award":["202003D111007"],"award-info":[{"award-number":["202003D111007"]}]},{"name":"Shanxi Province Key R&amp;D Program","award":["61973280"],"award-info":[{"award-number":["61973280"]}]},{"name":"Shanxi Province Key R&amp;D Program","award":["202003D111007"],"award-info":[{"award-number":["202003D111007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Single-axis rotation modulation (SRM) still accumulates errors in the roll axis direction, which leads to the navigation accuracy not meeting the requirements of guided missiles. Compound rotation modulation (CRM) superimposes one-dimensional rotation on the basis of SRM, so that the error of the projectile in the direction of the roll axis is also modulated. However, the error suppression effect of CRM is not only affected by the error of the IMU itself, but also related to the modulation angular velocity. In order to improve the accuracy of rotary semi-strapdown inertial navigation system (RSSINS), this paper proposes an optimal rotation angular velocity determination method. Firstly, the residual error in CRM scheme is analyzed; then, the relationship between the incomplete modulation error and the modulation angular velocity in CRM is discussed; finally, a method for determining the optimal modulation angular velocity is proposed (K-value method). The analysis of the results shows that the navigation accuracy of the guided projectile is effectively improved with the rotation scheme set at the modulation angular velocity determined by the K-value method.<\/jats:p>","DOI":"10.3390\/s22124583","type":"journal-article","created":{"date-parts":[[2022,6,19]],"date-time":"2022-06-19T21:19:26Z","timestamp":1655673566000},"page":"4583","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Optimal Rotational Angular Velocity Determination Method Based on Compound Rotary Semi-Strapdown Inertial Navigation System"],"prefix":"10.3390","volume":"22","author":[{"given":"Chenming","family":"Zhang","sequence":"first","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Li","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoqiao","family":"Yuan","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xi","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electrical Control Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaokai","family":"Wei","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kaiqiang","family":"Feng","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chenjun","family":"Hu","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Debiao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronic Information Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yubing","family":"Jiao","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wu, Z., Wang, Y., Zhu, L., and Yang, F. (2020). Design of a Projectile-Borne Data Recorder Triggered by Overload. Electronics, 9.","DOI":"10.3390\/electronics9050860"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Xu, Y., and Zhou, T. (2019). Research on In-Flight Alignment for Micro Inertial Navigation System Based on Changing Acceleration using Exponential Function. Micromachines, 10.","DOI":"10.3390\/mi10010024"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"80772","DOI":"10.1109\/ACCESS.2021.3083963","article-title":"Robust Central Difference Kalman Filter with Mixture Correntropy: A Case Study for Integrated Navigation","volume":"9","author":"Feng","year":"2021","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5810174","DOI":"10.1155\/2019\/5810174","article-title":"Application of Elman Neural Network Based on Genetic Algorithm in Initial Alignment of SINS for Guided Projectile","volume":"2019","author":"Sun","year":"2019","journal-title":"Math. Probl. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"105102","DOI":"10.1088\/0957-0233\/27\/10\/105102","article-title":"A novel redundant INS based on triple rotary inertial measurement units","volume":"27","author":"Chen","year":"2016","journal-title":"Meas. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1550147717746351","DOI":"10.1177\/1550147717746351","article-title":"A micro-electro-mechanical-system-based inertial system with rotating accelerometers and gyroscopes for land vehicle navigation","volume":"13","author":"Du","year":"2017","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Mi, J., Li, J., Zhang, X., Feng, K., Hu, C., Wei, X., and Yuan, X. (2020). Roll Angular Rate Measurement for High Spinning Projectiles Based on Redundant Gyroscope System. Micromachines, 11.","DOI":"10.3390\/mi11100940"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ge, B.S., Zhang, H., Fu, W.X., and Yang, J.B. (2020). Enhanced Redundant Measurement-Based Kalman Filter for Measurement Noise Covariance Estimation in INS\/GNSS Integration. Remote Sens., 12.","DOI":"10.3390\/rs12213500"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3841","DOI":"10.1109\/TVT.2020.2976975","article-title":"MEMS Gyro Bias Estimation in Accelerated Motions Using Sensor Fusion of Camera and Angular-Rate Gyroscope","volume":"69","author":"Nazemipour","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.ast.2018.02.040","article-title":"Hybridized attitude determination techniques to improve ballistic projectile navigation, guidance and control","volume":"77","author":"Cadarso","year":"2018","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"116207","DOI":"10.1109\/ACCESS.2021.3105412","article-title":"Stabilized Inertial Guidance Solution for Rolling Projectile Based on Partial Strapdown Platform","volume":"9","author":"Duan","year":"2021","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4176","DOI":"10.1177\/0954410018817424","article-title":"Guidance law for mimicking short-range ballistic trajectories","volume":"233","author":"Sharma","year":"2019","journal-title":"Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Bai, S.Y., Lai, J.Z., Lyu, P., Xu, X.W., Liu, M., and Huang, K. (2019). A System-Level Self-Calibration Method for Installation Errors in A Dual-Axis Rotational Inertial Navigation System. Sensors, 19.","DOI":"10.3390\/s19184005"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Du, S., Sun, W., and Gao, Y. (2016). MEMS IMU Error Mitigation Using Rotation Modulation Technique. Sensors, 16.","DOI":"10.3390\/s16122017"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1016\/j.measurement.2018.07.065","article-title":"Online self-calibration research of single-axis rotational inertial navigation system","volume":"129","author":"Li","year":"2018","journal-title":"Measurement"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wang, S.Q., Zheng, W., and Li, Z.W. (2021). Optimizing Matching Area for Underwater Gravity-Aided Inertial Navigation Based on the Convolution Slop Parameter-Support Vector Machine Combined Method. Remote Sens., 13.","DOI":"10.3390\/rs13193940"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.1109\/TIM.2018.2800878","article-title":"Online Calibration of the Geographic-Frame-Equivalent Gyro Bias in Dual-Axis RINS","volume":"67","author":"Cai","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_18","first-page":"1","article-title":"Self-Calibration of Tri-Axis Rotational Inertial Navigation System Based on Virtual Platform","volume":"70","author":"Hu","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"13072","DOI":"10.1364\/OE.26.013072","article-title":"Improved motor control method with measurements of fiber optics gyro (FOG) for dual-axis rotational inertial navigation system (RINS)","volume":"26","author":"Song","year":"2018","journal-title":"Opt. Express"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1166\/sl.2012.2464","article-title":"Error Modulation Scheme Analyzing for Dual-Axis Rotating Fiber-Optic Gyro Inertial Navigation System","volume":"10","author":"Yin","year":"2012","journal-title":"Sens. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"076106","DOI":"10.1117\/1.OE.52.7.076106","article-title":"Fiber-based rotary strapdown inertial navigation system","volume":"52","author":"Sun","year":"2013","journal-title":"Opt. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yuan, X., Li, J., Zhang, X., Feng, K., Wei, X., Zhang, D., and Mi, J. (2021). A Low-Cost MEMS Missile-Borne Compound Rotation Modulation Scheme. Sensors, 21.","DOI":"10.3390\/s21144910"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"16519","DOI":"10.1109\/JSEN.2021.3079582","article-title":"A High-Accuracy Method for Calibration of Nonorthogonal Angles in Dual-Axis Rotational Inertial Navigation System","volume":"21","author":"Lin","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1017\/S037346331500051X","article-title":"Compensation for Stochastic Error of Gyros in a Dual-axis Rotational Inertial Navigation System","volume":"69","author":"Zheng","year":"2016","journal-title":"J. Navig."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Liu, F., Li, X., Wang, J., and Zhang, J.X. (2019). An Adaptive UWB\/MEMS-IMU Complementary Kalman Filter for Indoor Location in NLOS Environment. Remote Sens., 11.","DOI":"10.3390\/rs11222628"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, J., Li, J., Che, X., Zhang, X., Hu, C., Feng, K., and Xu, T. (2019). The Optimal Design of Modulation Angular Rate for MEMS-Based Rotary Semi-SINS. Micromachines, 10.","DOI":"10.3390\/mi10020111"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/12\/4583\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:34:02Z","timestamp":1760139242000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/12\/4583"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,17]]},"references-count":26,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["s22124583"],"URL":"https:\/\/doi.org\/10.3390\/s22124583","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,17]]}}}