{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T18:17:12Z","timestamp":1784917032485,"version":"3.55.0"},"reference-count":82,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,2,23]],"date-time":"2017-02-23T00:00:00Z","timestamp":1487808000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Brazilian Funding Authority for Studies and Projects (FINEP)","award":["01.06.1177"],"award-info":[{"award-number":["01.06.1177"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents the second part of a study aiming at the error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and the number of unobservable modes is established. Through the analytical manipulation of the full SINS error model, the unobservable modes of the system are determined, and the SSAC error states (except the velocity errors) are proven to be individually unobservable. The estimability of the system is determined through the examination of the major diagonal terms of the covariance matrix and their eigenvalues\/eigenvectors. Filter order reduction based on observability analysis is shown to be inadequate, and several misconceptions regarding SSAC observability and estimability deficiencies are removed. As the main contributions of this paper, we demonstrate that, except for the position errors, all error states can be minimally estimated in the SSAC problem and, hence, should not be removed from the filter. Corroborating the conclusions of the first part of this study, a 12-state Kalman filter is found to be the optimal error state selection for SSAC purposes. Results from simulated and experimental tests support the outlined conclusions.<\/jats:p>","DOI":"10.3390\/s17030439","type":"journal-article","created":{"date-parts":[[2017,2,23]],"date-time":"2017-02-23T11:45:01Z","timestamp":1487850301000},"page":"439","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters\u2014Part II: Observability\/Estimability Analysis"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3715-7023","authenticated-orcid":false,"given":"Felipe","family":"Silva","sequence":"first","affiliation":[{"name":"Department of Engineering, Federal University of Lavras, Lavras 37200-000, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elder","family":"Hemerly","sequence":"additional","affiliation":[{"name":"Aeronautics Institute of Technology, Division of Electronic Engineering, S\u00e3o Jos\u00e9 dos Campos 12228-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8364-866X","authenticated-orcid":false,"given":"Waldemar","family":"Leite Filho","sequence":"additional","affiliation":[{"name":"National Institute for Space Research, Division of Space Mechanics and Control, S\u00e3o Jos\u00e9 dos Campos 12227-010, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,23]]},"reference":[{"key":"ref_1","unstructured":"Rogers, R.M. (2007). Applied Mathematics in Integrated Navigation Systems, American Institute of Aeronautics and Astronautics."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Titterton, D.H., and Weston, J.L. (2004). Strapdown Inertial Navigation Technology, Institution of Electrical Engineers.","DOI":"10.1049\/PBRA017E"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Jekeli, C. (2001). Inertial Navigation Systems with Geodetic Applications, Walter de Gruyter GmbH & Co.","DOI":"10.1515\/9783110800234"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Chatfield, A.B. (1997). Fundamentals of High Accuracy Inertial Navigation, American Institute of Aeronautics and Astronautics.","DOI":"10.2514\/4.866463"},{"key":"ref_5","unstructured":"Farrel, J., and Barth, M. (1999). The Global Positioning System & Inertial Navigation, McGraw-Hill Companies."},{"key":"ref_6","unstructured":"Britting, K.R. (1971). Inertial Navigation Systems Analysis, John Wiley & Sons Canada, Limited."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1777","DOI":"10.1109\/TAES.2016.7738355","article-title":"Error Analysis of Analytical Coarse Alignment Formulation for Stationary SINS","volume":"52","author":"Silva","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_8","unstructured":"Groves, P.D. (2008). Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Artech House Remote Sensing Library."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"237","DOI":"10.2514\/3.20299","article-title":"Control theoretic approach to inertial navigation systems","volume":"11","author":"Berman","year":"1988","journal-title":"J. Guid. Control"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/7.135435","article-title":"Error estimation of INS ground alignment through observability analysis","volume":"28","author":"Jiang","year":"1992","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1109\/TITS.2011.2168818","article-title":"Inertial navigation aiding with stationary updates","volume":"13","author":"Ramanandan","year":"2012","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_12","first-page":"516","article-title":"Kalman filter mechanization for INS airstart","volume":"1","author":"Pham","year":"1992","journal-title":"IEEE AES Syst. Mag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"8103","DOI":"10.3390\/s130708103","article-title":"A Robust Self-Alignment Method for Ship\u2019s Strapdown INS under Mooring Conditions","volume":"13","author":"Sun","year":"2013","journal-title":"Sensors"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1109\/TAES.2012.6129622","article-title":"Observability of Strapdown Alignment: A Global Perspective","volume":"48","author":"Wu","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2644","DOI":"10.1016\/j.proeng.2012.01.365","article-title":"Study on the Low Accuracy IMU\u2019s Initial Alignment Technique in the Pipeline\u2019s Geographical Coordinate Measuring System","volume":"29","author":"Yang","year":"2012","journal-title":"Procedia Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2887","DOI":"10.1109\/TAES.2011.6034671","article-title":"Rapid Fine Strapdown INS Alignment Method under Marine Mooring Condition","volume":"47","author":"Gao","year":"2011","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1378","DOI":"10.1109\/TIM.2010.2084710","article-title":"Study on innovation adaptive EKF for in-flight alignment of airborne POS","volume":"60","author":"Jiancheng","year":"2011","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1080","DOI":"10.1109\/TIM.2010.2064631","article-title":"Experimental Feasibility of the In-Drilling Alignment Method for Inertial Navigation in Measurement-While-Drilling","volume":"60","author":"Jurkov","year":"2011","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1016\/S1000-9361(11)60055-1","article-title":"Multiple fading factors Kalman filter for SINS static alignment application","volume":"24","author":"Gao","year":"2011","journal-title":"Chin. J. Aeronaut."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Goshen-Meskin, D., and Bar-Itzhack, I.Y. (1989, January 14\u201316). Observability Studies of Inertial Navigation Systems. Proceedings of the Guidance, Navigation and Control Conference, AIAA, Boston, MA, USA.","DOI":"10.2514\/6.1989-3580"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1049\/iet-smt.2012.0071","article-title":"Strapdown inertial navigation system alignment based on marginalized unscented Kalman filter","volume":"7","author":"Chang","year":"2013","journal-title":"IET Sci. Meas. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1016\/j.scient.2012.01.002","article-title":"Processing algorithm for a strapdown gyrocompass","volume":"19","author":"Hemmati","year":"2012","journal-title":"Sci. Iran."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.ast.2010.06.007","article-title":"Improved self-alignment scheme for SINS using augmented measurement","volume":"15","author":"Acharya","year":"2011","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1016\/j.jfranklin.2009.09.003","article-title":"New techniques for initial alignment of strapdown inertial navigation system","volume":"346","author":"Xie","year":"2009","journal-title":"J. Frankl. Inst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1935","DOI":"10.1109\/TIM.2007.904485","article-title":"Observability Analysis for INS Alignment in Horizontal Drilling","volume":"56","author":"Petch","year":"2007","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s11768-005-0007-4","article-title":"A fast and accurate initial alignment method for strapdown inertial navigation system on stationary base","volume":"2","author":"Wang","year":"2005","journal-title":"J. Control Theory Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1088\/0957-0233\/15\/4\/021","article-title":"A novel method improving the alignment accuracy of a strapdown inertial navigation system on a stationary base","volume":"15","author":"Chuanbin","year":"2004","journal-title":"Meas. Sci. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.1109\/7.543871","article-title":"A Fast Initial Alignment Method for Strapdown Inertial Navigation System on Stationary Base","volume":"32","author":"Fang","year":"1996","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1109\/7.366314","article-title":"Covariance Analysis of Strapdown INS Considering Gyrocompass Characteristics","volume":"31","author":"Park","year":"1995","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1323","DOI":"10.1109\/7.259535","article-title":"Multiposition Alignment of Strapdown Inertial Navigation System","volume":"29","author":"Lee","year":"1993","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Jiang, Y.F., and Lin, Y.P. (1993, January 9\u201311). Error Estimation of Ground Alignment to Arbitrary Azimuth. Proceedings of the Guidance, Navigation and Control Conference, AIAA, Monterey, CA, USA.","DOI":"10.2514\/6.1993-3823"},{"key":"ref_32","first-page":"1","article-title":"Observability and Estimation Error Analysis of the Initial Fine Alignment Filter for Nonleveling Strapdown Inertial Navigation System","volume":"135","author":"Cho","year":"2013","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.ast.2009.04.002","article-title":"Fast alignment and calibration algorithms for inertial navigation system","volume":"13","author":"Xinlong","year":"2009","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"595","DOI":"10.5302\/J.ICROS.2008.14.6.595","article-title":"Error Analysis of Initial Alignment for Non-leveling INS","volume":"14","author":"Cho","year":"2008","journal-title":"J. Inst. Control Robot. Syst."},{"key":"ref_35","first-page":"1","article-title":"Design and Analysis of Low-Order Filters Applied to the Alignment of Inertial Platforms","volume":"Volume 82","year":"1976","journal-title":"Practical Aspects of Kalman Filtering Implementation"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.ast.2016.11.019","article-title":"On the error state selection for stationary SINS alignment and calibration Kalman filters\u2014Part I: Estimation Algorithms","volume":"61","author":"Silva","year":"2017","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"280","DOI":"10.2514\/3.55985","article-title":"Reduced-Order Kalman Filtering with Incomplete Observability","volume":"3","author":"Yonezawa","year":"1980","journal-title":"J. Guid. Control"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1946","DOI":"10.1109\/TIM.2007.903641","article-title":"Modeling of Observability During in-Drilling Alignment for Horizontal Directional Drilling","volume":"56","author":"Petch","year":"2007","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1109\/TAES.1983.309446","article-title":"Observability, Eigenvalues, and Kalman Filtering","volume":"19","author":"Ham","year":"1983","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_40","unstructured":"Brown, R.G. (1966, January 3\u20135). Not Just Observable, But How Observable?. Proceedings of the National Electronic Conference, Chicago, IL, USA."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2181","DOI":"10.1109\/TAES.2015.130674","article-title":"Stochastic observability-based analytic optimization of SINS multiposition alignment","volume":"51","author":"Yu","year":"2015","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1356","DOI":"10.2514\/1.38128","article-title":"A Stochastic Observability Test for Discrete-Time Kalman Filters","volume":"32","author":"Bageshwar","year":"2009","journal-title":"J. Guid. Control Dyn."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1109\/9.14433","article-title":"Estimability and Regulability of Linear Systems","volume":"33","author":"Baram","year":"1988","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_44","first-page":"731","article-title":"Observability of Error States in GPS\/INS Integration","volume":"54","author":"Hong","year":"2005","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1109\/7.165368","article-title":"Observability Analysis of Piece-Wise Constant Systems-Part II: Application to Inertial Navigation in-Flight Alignment","volume":"28","year":"1992","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_46","first-page":"28","article-title":"Observability Analysis Techniques on Inertial Navigation Systems","volume":"6","author":"Lee","year":"2012","journal-title":"J. Syst. Des. Dyn."},{"key":"ref_47","first-page":"1080","article-title":"Initial alignment for SINS based on low-cost IMU","volume":"6","author":"Jiong","year":"2011","journal-title":"J. Comput."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1109\/TVT.2007.905610","article-title":"Observability measures and their application to GPS\/INS","volume":"57","author":"Hong","year":"2008","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1007\/s12206-008-0206-2","article-title":"Estimability measures and their application to GPS\/INS","volume":"22","author":"Moon","year":"2008","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.1007\/BF02984046","article-title":"Observability analysis of alignment errors in GPS\/INS","volume":"19","author":"Lee","year":"2005","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1109\/41.107106","article-title":"Local observability and its application to multiple measurement estimation","volume":"38","author":"Chen","year":"1991","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1109\/TAC.1959.1104873","article-title":"On the general theory of control systems","volume":"1","author":"Kalman","year":"1959","journal-title":"IRE Trans. Autom. Control"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Feng, S., Qian, S., Yueyang, B., Ya, Z., and Gao, W. (2012, January 23\u201326). A New Method of Initial Alignment and Self-Calibration Based on Dual-Axis Rotating Strapdown Inertial Navigation System. Proceedings of the Position, Location and Navigation Symposium, IEEE\/ION, Myrtle Beach, SC, USA.","DOI":"10.1109\/PLANS.2012.6236959"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Fang, Q., Zhu, H.Y., Zhang, D.B., and Huang, X.S. (2015, January 8\u201310). Observable Degree Analysis for Inertial Navigation in-Flight Alignment Based on Information Theory. Proceedings of the International Conference on Information and Automation, Lijiang, China.","DOI":"10.1109\/ICInfA.2015.7279473"},{"key":"ref_55","unstructured":"Guo, Z.W., Miao, L.J., and Shen, J. (2011, January 9\u201311). A Novel Initial Alignment Algorithm of SINS\/GPS on Stationary Base with Attitude Measurement. Proceedings of the International Conference on Electronics, Communications and Control, Ningbo, China."},{"key":"ref_56","unstructured":"Guo, Z., Miao, L., and Shen, J. (2010, January 28\u201331). The Application of Observability Analysis on Stationary Base. Proceedings of the 29th Chinese Control Conference, Beijing, China."},{"key":"ref_57","unstructured":"Long, R., Qin, Y.Y., and Jia, J.C. (2008, January 21\u201322). Observable Degree Analysis of SINS Initial Alignment Based on Singular Value Decomposition. Proceedings of the International Symposium on Knowledge Acquisition and Modeling Workshop, Wuhan, China."},{"key":"ref_58","unstructured":"Zhang, T., Wang, B., Han, Z., and Li, J. (2004, January 15\u201319). Analysis on Observability on SINS\/GPS. Proceedings of the 5th World Congress on Intelligent Control and Automation, Hangzhou, China."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Krener, A.J., and Ide, K. (2009, January 16\u201318). Measures of Unobservability. Proceedings of the 48th Conference on Decision and Control, Shanghai, China.","DOI":"10.1109\/CDC.2009.5400067"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"DeVries, L., and Paley, D.A. (2013, January 17\u201319). Observability-Based Optimization for Flow Sensing and Control of an Underwater Vehicle in a Uniform Flowfield. Proceedings of the American Control Conference, Washington, DC, USA.","DOI":"10.1109\/ACC.2013.6580030"},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Maessen, D.A., and Gill, E. (2010, January 2\u20135). Relative Orbital Element Estimation and Observability Analysis for Formation Flying Satellites Using Inter-Satellite Range Measurements Only. Proceedings of the Guidance, Navigation and Control Conference, AIAA, Toronto, ON, Canada.","DOI":"10.2514\/6.2010-7885"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1002\/navi.63","article-title":"Analytical observability analysis of INS with vehicle constraints","volume":"61","author":"Rothman","year":"2014","journal-title":"Navigation"},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Fang, Q. (2015, January 13\u201316). INS Ground Alignment through Observable Degree Analysis Based on Information Theory. Proceedings of the 15th International Conference on Control, Automation and Systems, Busan, Korea.","DOI":"10.1109\/ICCAS.2015.7364854"},{"key":"ref_64","unstructured":"Chen, C.T. (1970). Introduction to Linear Systems Theory, Holt, Rinehart and Winston."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Grewal, M.S., Weill, L.R., and Andrews, A.P. (2007). Global Positioning Systems, Inertial Navigation & Integration, John Wiley & Sons.","DOI":"10.1002\/0470099720"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1109\/MAES.2014.130191","article-title":"Navigation using inertial sensors","volume":"30","author":"Groves","year":"2015","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_67","unstructured":"Kwakernaak, H., and Sivan, R. (1972). Linear Optimal Control Systems, Wiley-Interscience Publication, Wiley Interscience."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1109\/TAES.2004.1386895","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_69","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/TAES.2006.1603406","article-title":"Fast Alignment using Rotation Vector and Adaptive Kalman Filter","volume":"42","author":"Ahn","year":"2006","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"1225","DOI":"10.1109\/9.151112","article-title":"On the connection between estimability and observability","volume":"37","year":"1992","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_71","unstructured":"Silva, F.O., LeiteFilho, W.C., and Hemerly, E.M. (2015, January 10\u201312). Design of a Stationary Self-Alignment Algorithm for Strapdown Inertial Navigation Systems. Proceedings of the Workshop on Advanced Control and Navigation for Autonomous Aerospace Vehicles, Seville, Spain."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"184","DOI":"10.5139\/IJASS.2010.11.3.184","article-title":"Design of an Initial Fine Alignment Algorithm for Satellite Launch Vehicles","volume":"11","author":"Song","year":"2010","journal-title":"Int. J. Aeronaut. Space Sci."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"26818","DOI":"10.3390\/s151026818","article-title":"Observability analysis of DVL\/PS aided INS for a maneuvering UAV","volume":"15","author":"Klein","year":"2015","journal-title":"Sensors"},{"key":"ref_74","unstructured":"Savage, P.G. (2007). Strapdown Analytics, Strapdown Analytics, Strapdown Associates."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1109\/7.165367","article-title":"Observability Analysis of Piece-Wise Constant Systems-Part I: Theory","volume":"28","year":"1992","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"246","DOI":"10.2514\/3.20300","article-title":"Inflight Observability of Gyro Reference Frame Misalignment","volume":"11","author":"Huang","year":"1988","journal-title":"J. Guid."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"385","DOI":"10.2514\/3.19744","article-title":"Effect of Acceleration Switching During INS In-Flight Alignment","volume":"4","author":"Porat","year":"1981","journal-title":"J. Guid. Control"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"337","DOI":"10.2514\/3.55999","article-title":"Azimuth Observability Enhancement During Inertial Navigation System in-Flight Alignment","volume":"3","author":"Porat","year":"1980","journal-title":"J. Guid. Control"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"12","DOI":"10.2514\/3.58624","article-title":"Inertial Navigation System Tests having Improved Observability of Error Sources","volume":"13","author":"Widnall","year":"1976","journal-title":"J. Aircr."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1016\/S0967-0661(02)00043-6","article-title":"Integrating satellite and inertial navigation\u2014Conventional and new fusion approaches","volume":"11","author":"Wagner","year":"2003","journal-title":"Control Eng. Pract."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/s10291-004-0122-6","article-title":"GNSS\/INS integration: Still an attractive candidate for automatic landing systems?","volume":"9","author":"Wagner","year":"2005","journal-title":"GPS Solut."},{"key":"ref_82","first-page":"169","article-title":"Reduced Order Kalman Filtering Without Model Reduction","volume":"35","author":"Simon","year":"2007","journal-title":"Control Intell. Syst."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/3\/439\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:29:00Z","timestamp":1760207340000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/3\/439"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,23]]},"references-count":82,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["s17030439"],"URL":"https:\/\/doi.org\/10.3390\/s17030439","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,23]]}}}