{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T04:49:25Z","timestamp":1768279765233,"version":"3.49.0"},"reference-count":34,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T00:00:00Z","timestamp":1626652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51575500"],"award-info":[{"award-number":["51575500"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51705477"],"award-info":[{"award-number":["51705477"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61973280"],"award-info":[{"award-number":["61973280"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Postgraduate Innovation Project of Shanxi Province","award":["2020SY377"],"award-info":[{"award-number":["2020SY377"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Rotation modulation (RM) has been widely used in navigation systems to significantly improve the navigation accuracy of inertial navigation systems (INSs). However, the traditional single-axis rotation modulation cannot achieve the modulation of all the constant errors in the three directions; thus, it is not suitable for application in highly dynamic environments due to requirements for high precision in missiles. Aiming at the problems of error accumulation and divergence in the direction of rotation axis existing in the traditional single-axis rotation modulation, a novel rotation scheme is proposed. Firstly, the error propagation principle of the new rotation modulation scheme is analyzed. Secondly, the condition of realizing the error modulation with constant error is discussed. Finally, the original rotation modulation navigation algorithm is optimized for the new rotation modulation scheme. The experiment and simulation results show that the new rotation scheme can effectively modulate the error divergence of roll angle and improve the accuracy of roll angle by two orders of magnitude.<\/jats:p>","DOI":"10.3390\/s21144910","type":"journal-article","created":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T10:07:37Z","timestamp":1626689257000},"page":"4910","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Low-Cost MEMS Missile-Borne Compound Rotation Modulation Scheme"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0619-1402","authenticated-orcid":false,"given":"Xiaoqiao","family":"Yuan","sequence":"first","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}]},{"given":"Jie","family":"Li","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}]},{"given":"Xi","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electrical Control Engineering, North University of China, Taiyuan 030051, China"}]},{"given":"Kaiqiang","family":"Feng","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}]},{"given":"Xiaokai","family":"Wei","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}]},{"given":"Debiao","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}]},{"given":"Jing","family":"Mi","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.ymssp.2015.10.021","article-title":"Development of a new integrated local trajectory planning and tracking control framework for autonomous ground vehicles","volume":"87","author":"Li","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1017\/S037346331600045X","article-title":"Strapdown Inertial Navigation Algorithms Based on Lie Group","volume":"70","author":"Mao","year":"2017","journal-title":"J. Navig."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1007\/s00006-012-0326-8","article-title":"Strapdown Inertial Navigation System Algorithms Based on Geometric Algebra","volume":"22","author":"Wu","year":"2012","journal-title":"Adv. Appl. Clifford Algebras"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"107565","DOI":"10.1016\/j.ymssp.2020.107565","article-title":"An improved integrated navigation method with enhanced robustness based on factor graph","volume":"155","author":"Wei","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wei, X., Li, J., Zhang, D., Feng, K., Zhang, J., Li, J., and Lu, Z. (2019). Optimization of a New High Rotary Missile-Borne Stabilization Platform. Sensors, 19.","DOI":"10.3390\/s19194143"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"18443","DOI":"10.3390\/s150818443","article-title":"An Accurate Calibration Method Based on Velocity in a Rotational Inertial Navigation System","volume":"15","author":"Zhang","year":"2015","journal-title":"Sensors"},{"key":"ref_7","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"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2585","DOI":"10.1016\/j.measurement.2013.04.035","article-title":"MEMS-based rotary strapdown inertial navigation system","volume":"46","author":"Sun","year":"2013","journal-title":"Measurement"},{"key":"ref_9","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_10","first-page":"5423","article-title":"An improved rotation scheme for Tri-axis rotational inertial navigation system","volume":"23","author":"Liu","year":"2017","journal-title":"Microsyst. Technol. Micro Nanosyst. Inf. Storage Process. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4189","DOI":"10.1109\/JSEN.2017.2703604","article-title":"An Improved Rotation Scheme for Dual-Axis Rotational Inertial Navigation System","volume":"17","author":"Liu","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, Z., Cheng, X., and Du, J. (2020). Thermal Modeling and Calibration Method in Complex Temperature Field for Single-Axis Rotational Inertial Navigation System. Sensors, 20.","DOI":"10.3390\/s20020384"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"26221","DOI":"10.1109\/ACCESS.2021.3058284","article-title":"Research on the Update Method of Attitude Quaternion for Strapdown Inertial Navigation","volume":"9","author":"Zhang","year":"2021","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.sna.2014.08.011","article-title":"A multi-position self-calibration method for dual-axis rotational inertial navigation system","volume":"219","author":"Ren","year":"2014","journal-title":"Sens. Actuators A Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1017\/S0373463314000319","article-title":"The Compensation Effects of Gyros\u2019 Stochastic Errors in a Rotational Inertial Navigation System","volume":"67","author":"Lv","year":"2014","journal-title":"J. Navig."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"30956","DOI":"10.1364\/OE.25.030956","article-title":"Single-axis rotation\/azimuth-motion insulation inertial navigation control system with FOGs","volume":"25","author":"Wang","year":"2017","journal-title":"Opt. Express"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"14859","DOI":"10.1109\/ACCESS.2019.2893895","article-title":"Damping Rotating Grid SINS Based on a Kalman Filter for Shipborne Application","volume":"7","author":"Fang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Du, S., Sun, W., and Gao, Y. (2017). Improving Observability of an Inertial System by Rotary Motions of an IMU. Sensors, 17.","DOI":"10.3390\/s17040698"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1177\/0954406218756940","article-title":"Error analysis and compensation for dual-axis inertial navigation system with horizontal rotation modulation","volume":"233","author":"Zhang","year":"2019","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.ymssp.2018.10.005","article-title":"An inertial device biases on-line monitoring method in the applications of two rotational inertial navigation systems redundant configuration","volume":"120","author":"Wu","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1017\/S0373463313000246","article-title":"Analysis and Verification of Rotation Modulation Effects on Inertial Navigation System based on MEMS Sensors","volume":"66","author":"Wang","year":"2013","journal-title":"J. Navig."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2023","DOI":"10.1109\/JSEN.2018.2789884","article-title":"Error Analysis and Compensation of MEMS Rotation Modulation Inertial Navigation System","volume":"18","author":"Jia","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_23","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_24","doi-asserted-by":"crossref","first-page":"47875","DOI":"10.1109\/ACCESS.2021.3068744","article-title":"A Mixed Optimization Method Based on Adaptive Kalman Filter and Wavelet Neural Network for INS\/GPS During GPS Outages","volume":"9","author":"Wei","year":"2021","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Jing, Z., Li, J., Zhang, X., Feng, K., and Zheng, T. (2019). A Novel Rotation Scheme for MEMS IMU Error Mitigation Based on a Missile-Borne Rotation Semi-Strapdown Inertial Navigation System. Sensors, 19.","DOI":"10.3390\/s19071683"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, J., Li, J., Zhang, X., Che, X., Huang, Y., and Feng, K. (2018). Analysis and Compensation of Modulation Angular Rate Error Based on Missile-Borne Rotation Semi-Strapdown Inertial Navigation System. Sensors, 18.","DOI":"10.3390\/s18051430"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.dsp.2016.09.011","article-title":"Cooperative parallel particle filters for online model selection and applications to urban mobility","volume":"60","author":"Martino","year":"2017","journal-title":"Digit. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1016\/j.dsp.2006.09.003","article-title":"Analysis of selection methods for cost-reference particle filtering with applications to maneuvering target tracking and dynamic optimization","volume":"17","author":"Miguez","year":"2007","journal-title":"Digit. Signal. Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3589","DOI":"10.1109\/TWC.2007.05912","article-title":"Mobility tracking in cellular networks using particle filtering","volume":"6","author":"Mihaylova","year":"2007","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_30","first-page":"3301","article-title":"Calibration and data processing technology of gyroscope in dual axis rotational inertial navigation system","volume":"23","author":"Chen","year":"2017","journal-title":"Microsyst. Technol. Micro Nanosyst. Inf. Storage Process. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"74","DOI":"10.5772\/58579","article-title":"Decrease in Accuracy of a Rotational SINS Caused by its Rotary Table\u2019s Errors","volume":"11","author":"Lv","year":"2014","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_32","first-page":"189","article-title":"The Six-Position Calibration Technique of Gyro Bias for Rotational Inertial Navigation System Based on Ring Laser Gyroscope","volume":"22","author":"Yu","year":"2019","journal-title":"J. Korea Inst. Mil. Sci. Technol."},{"key":"ref_33","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_34","doi-asserted-by":"crossref","first-page":"1757","DOI":"10.2514\/1.53584","article-title":"Guidance and Control of a Projectile with Reduced Sensor and Actuator Requirements","volume":"34","author":"Fresconi","year":"2011","journal-title":"J. Guid. Control. Dyn."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/14\/4910\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:31:51Z","timestamp":1760164311000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/14\/4910"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,19]]},"references-count":34,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["s21144910"],"URL":"https:\/\/doi.org\/10.3390\/s21144910","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,19]]}}}