{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T18:52:16Z","timestamp":1780512736963,"version":"3.54.1"},"reference-count":19,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2014,8,28]],"date-time":"2014-08-28T00:00:00Z","timestamp":1409184000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Gyroscopes based on micro-electromechanical system (MEMS) technology suffer in high-dynamic applications due to obvious g-sensitivity errors. These errors can induce large biases in the gyroscope, which can directly affect the accuracy of attitude estimation in the integration of the inertial navigation system (INS) and the Global Positioning System (GPS). The observability determines the existence of solutions for compensating them. In this paper, we investigate the observability of the INS\/GPS system with consideration of the g-sensitivity errors. In terms of two types of g-sensitivity coefficients matrix, we add them as estimated states to the Kalman filter and analyze the observability of three or nine elements of the coefficient matrix respectively. A global observable condition of the system is presented and validated. Experimental results indicate that all the estimated states, which include position, velocity, attitude, gyro and accelerometer bias, and g-sensitivity coefficients, could be made observable by maneuvering based on the conditions. Compared with the integration system without compensation for the g-sensitivity errors, the attitude accuracy is raised obviously.<\/jats:p>","DOI":"10.3390\/s140916003","type":"journal-article","created":{"date-parts":[[2014,8,28]],"date-time":"2014-08-28T10:37:35Z","timestamp":1409222255000},"page":"16003-16016","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Observability Analysis of a MEMS INS\/GPS Integration System with Gyroscope G-Sensitivity Errors"],"prefix":"10.3390","volume":"14","author":[{"given":"Chen","family":"Fan","sequence":"first","affiliation":[{"name":"College of Mechatronics and Automation, National University of Defense Technology,  Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoping","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Automation, National University of Defense Technology,  Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaofeng","family":"He","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Automation, National University of Defense Technology,  Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kanghua","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Automation, National University of Defense Technology,  Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bing","family":"Luo","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Automation, National University of Defense Technology,  Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2014,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.1016\/j.conengprac.2008.04.011","article-title":"Kalman filter configurations for a low-cost loosely integrated inertial navigation system on an airship","volume":"16","author":"Bijker","year":"2008","journal-title":"Control Eng. Pract."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9549","DOI":"10.3390\/s130809549","article-title":"A comparison between different error modeling of MEMS applied to GPS\/INS integrated systems","volume":"13","author":"Quinchia","year":"2013","journal-title":"Sensors"},{"key":"ref_3","unstructured":"Shin, E.-H. (2005). Estimation Techniques for Low-Cost Inertial Navigation, University of Calgary. UCGE report."},{"key":"ref_4","unstructured":"Groves, P.D. (2013). Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Artech House."},{"key":"ref_5","unstructured":"Weinberg, H. (2011). Gyro Mechanical Performance: The Most Important Parameter, Analog Devices Inc.. Technical Article MS-2158."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Bancroft, J.B., and Lachapelle, G. (2012, January 3\u20134). Estimating mems gyroscope g-sensitivity errors in foot mounted navigation. Helsinki, Finland.","DOI":"10.1109\/UPINLBS.2012.6409753"},{"key":"ref_7","unstructured":"Savage, P.G. (2000). Strapdown Analytics Part I, Strapdown Associates Inc."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Titterton, D., and Weston, J. (2004). Strapdown Inertial Navigation Technology, The Institution of Electronical Engineers (IET). [2nd].","DOI":"10.1049\/PBRA017E"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Grewal, M.S., Weill, L.R., and Andrews, A.P. (2007). Global Positioning Systems, Inertial Navigation, and Integration, John Wiley & Sons.","DOI":"10.1002\/0470099720"},{"key":"ref_10","unstructured":"Iozan, L., Collin, J., Pekkalin, O., Hautam\u00e4ki, J., Takala, J., and Rusu, C. (2010, January 21\u201322). Measuring the earth's rotation rate using a low-cost MEMS gyroscope. Karlsruhe, Germany."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1109\/TVT.2008.926213","article-title":"INS\/GPS integration: Global observability analysis","volume":"58","author":"Tang","year":"2009","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wijesoma, S., Lee, K.W., and Guzman, J.I. (2006, January 17\u201320). On the observability of path constrained vehicle localisation. Toronto, ON, Canada.","DOI":"10.1109\/ITSC.2006.1707438"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"728","DOI":"10.1109\/TAC.1977.1101601","article-title":"Nonlinear controllability and observability","volume":"22","author":"Hermann","year":"1977","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1109\/TAES.2004.1310002","article-title":"Observability of an integrated GPS\/INS during maneuvers","volume":"40","author":"Rhee","year":"2004","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1002\/j.2161-4296.1990.tb01544.x","article-title":"A strapdown inertial algorithm using an earth-fixed cartesian frame","volume":"37","author":"Wei","year":"1990","journal-title":"Navigation"},{"key":"ref_16","unstructured":"Chen, C.-T. (1995). Linear System Theory and Design, Oxford University Press, Inc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.2514\/3.2555","article-title":"A passive system for determining the attitude of a satellite","volume":"2","author":"Black","year":"1964","journal-title":"AIAA J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1109\/7.165367","article-title":"Observability analysis of piece-wise constant systems. I. Theory","volume":"28","year":"1992","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1109\/TVT.2004.841540","article-title":"Observability of error states in GPS\/INS integration","volume":"54","author":"Hong","year":"2005","journal-title":"IEEE Trans. Veh. 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