{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T15:48:35Z","timestamp":1781020115949,"version":"3.54.1"},"reference-count":31,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T00:00:00Z","timestamp":1618963200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Fault detection and identification are vital for guaranteeing the precision and reliability of tightly coupled inertial navigation system (INS)\/global navigation satellite system (GNSS)-integrated navigation systems. A variance shift outlier model (VSOM) was employed to detect faults in the raw pseudo-range data in this paper. The measurements were partially excluded or included in the estimation process depending on the size of the associated shift in the variance. As an objective measure, likelihood ratio and score test statistics were used to determine whether the measurements inflated variance and were deemed to be faulty. The VSOM is appealing because the down-weighting of faulty measurements with the proper weighting factors in the analysis automatically becomes part of the estimation procedure instead of deletion. A parametric bootstrap procedure for significance assessment and multiple testing to identify faults in the VSOM is proposed. The results show that VSOM was validated through field tests, and it works well when single or multiple faults exist in GNSS measurements.<\/jats:p>","DOI":"10.3390\/s21092922","type":"journal-article","created":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T21:25:10Z","timestamp":1619040310000},"page":"2922","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Novel Method of Fault Detection and Identification in a Tightly Coupled, INS\/GNSS-Integrated System"],"prefix":"10.3390","volume":"21","author":[{"given":"Fan","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Intelligent System Science and Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ye","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Intelligent System Science and Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanbin","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Intelligent System Science and Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,21]]},"reference":[{"key":"ref_1","unstructured":"Farrell, J. (2008). Aided Navigation: GPS with High Rate Sensors, McGraw-Hill."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Stepanov, O.A. (2016). Optimal and Suboptimal Filtering in Integrated Navigation Systems. Aerospace Navigation Systems, John Wiley & Sons, Ltd.. Chapter 8.","DOI":"10.1002\/9781119163060.ch8"},{"key":"ref_3","first-page":"67","article-title":"Performance evaluation of Cubature Kalman filter in a GPS\/IMU tightly-coupled navigation system","volume":"119","author":"Zhao","year":"2016","journal-title":"Signal Process. Off. Publ. Eur. Assoc. Signal Process. (EURASIP)"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.isatra.2014.10.006","article-title":"A derivative UKF for tightly coupled INS\/GPS integrated navigation","volume":"56","author":"Hu","year":"2015","journal-title":"ISA Trans."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1134\/S2075108718040077","article-title":"Mathematical Analysis for the GPS Carrier Tracking Loop Phase Jitter in Presence of Different Types of Interference Signals","volume":"9","author":"Shaheen","year":"2018","journal-title":"Gyroscopy Navig."},{"key":"ref_6","unstructured":"Gautier, J.D., and Parkinson, B.W. (23\u201325, January 2003). Using the GPS\/INS generalized evaluation tool (GIGET) for the comparison of loosely coupled, tightly coupled and ultra-tightly coupled integrated navigation systems. Proceedings of the 59th Annual Meeting of The Institute of Navigation and CIGTF 22nd Guidance Test Symposium (2003), Albuquerque, NM, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1109\/70.768189","article-title":"A high integrity IMU\/GPS navigation loop for autonomous land vehicle applications","volume":"15","author":"Sukkarieh","year":"1999","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1002\/j.2161-4296.1988.tb00975.x","article-title":"Navigation system integrity monitoring using redundant measurements","volume":"35","author":"Sturza","year":"1988","journal-title":"Navigation"},{"key":"ref_9","first-page":"35","article-title":"Quality control in integrated navigation systems","volume":"5","author":"Teunissen","year":"1990","journal-title":"IEEE Position Locat. Navig. Symp."},{"key":"ref_10","unstructured":"Diesel, J., and Luu, S. (2000, January 19\u201322). GPS\/IRS AIME: Calculation of thresholds and protection radius using Chi-square methods. Proceedings of the 8th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS 1995), Salt Lake City, UT, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1061\/(ASCE)0733-9453(2010)136:1(13)","article-title":"Extended receiver autonomous integrity monitoring (e raim) for gnss\/ins integration","volume":"136","author":"Hewitson","year":"2010","journal-title":"J. Surv. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, S., Zhan, X., Zhai, Y., and Liu, B. (2020). Fault Detection and Exclusion for Tightly Coupled GNSS\/INS System Considering Fault in State Prediction. Sensors, 20.","DOI":"10.3390\/s20030590"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1109\/TSP.2009.2039731","article-title":"Robust Kalman filter based on a generalized maximum-likelihood-type estimator","volume":"58","author":"Gandhi","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","first-page":"3574","article-title":"Robust GPS-INS outlier accommodation: A Soft-Thresholded optimal estimator","volume":"50","author":"Roysdon","year":"2017","journal-title":"IFAC Pap."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1137\/0914076","article-title":"Computing the exact least median of squares estimate and stability diagnostics in multiple linear regression","volume":"14","author":"Stromberg","year":"1993","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Crespillo, O.G., Medina, D., Skaloud, J., and Meurer, M. (2018, January 23\u201326). Tightly coupled GNSS\/INS integration based on robust M-estimators. Proceedings of the 2018 IEEE\/ION Position, Location and Navigation Symposium (PLANS), Monterey, CA, USA.","DOI":"10.1109\/PLANS.2018.8373551"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1017\/S0373463319000778","article-title":"Improved Fault Detection Method Based on Robust Estimation and Sliding Window Test for INS\/GNSS Integration","volume":"73","author":"Zhang","year":"2020","journal-title":"J. Navig."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sun, R., Cheng, Q., Wang, G., and Ochieng, W.Y. (2017). A Novel Online Data-Driven Algorithm for Detecting UAV Navigation Sensor Faults. Sensors, 17.","DOI":"10.3390\/s17102243"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1017\/S0373463315001034","article-title":"A Novel Fault Detection Method for an Integrated Navigation System using Gaussian Process Regression","volume":"69","author":"Zhu","year":"2016","journal-title":"J. Navig."},{"key":"ref_20","unstructured":"Gumedze, F.N. (2009). A Variance Shift Model for Outlier Detection Andestimation in Linear and Linear Mixed Models. [Ph.D. Thesis, University of Cape Town]."},{"key":"ref_21","unstructured":"Grove, P.D. (2012). Principles of GNSS, Inertial and Multi-Sensor Integrated Navigation Systems, Artech House."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2128","DOI":"10.1016\/j.csda.2010.03.019","article-title":"A variance shift model for detection of outliers in the linear mixed model","volume":"54","author":"Gumedze","year":"2010","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1080\/02664763.2018.1508559","article-title":"Use of likelihood ratio tests to detect outliers under the variance shift outlier model","volume":"46","author":"Gumedze","year":"2019","journal-title":"J. Appl. Stat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1111\/j.2517-6161.1985.tb01329.x","article-title":"A Note on Restricted Maximum Likelihood Estimation with an Alternative Outlier Model","volume":"47","author":"Thompson","year":"1985","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"ref_25","unstructured":"Atkinson, A.C. (1985). Transformation and Regression, Clarendon Press."},{"key":"ref_26","unstructured":"Gleason, S., and Gebreegziabher, D. (2009). GNSS Applications and Methods, Artech House."},{"key":"ref_27","unstructured":"Joerger, M., and Pervan, B. (2011, January 21\u201324). Integrity risk of Kalman filter-based RAIM. Proceedings of the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, USA."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Sun, R., Zhang, W., Zheng, J., and Ochieng, W.Y. (2020). GNSS\/INS Integration with Integrity Monitoring for UAV No-fly Zone Management. Remote Sens., 12.","DOI":"10.3390\/rs12030524"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1002\/j.2161-4296.2000.tb00212.x","article-title":"Performance Analysis of a Tightly Coupled GPS\/Inertial System for Two Integrity Monitoring Methods1","volume":"47","author":"Lee","year":"2000","journal-title":"Navigation"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/s10291-008-0093-0","article-title":"Carrier phase-based integrity monitoring for high-accuracy positioning","volume":"13","author":"Feng","year":"2009","journal-title":"GPS Solut."},{"key":"ref_31","unstructured":"Mackinnon, J. (2007). Bootstrap Hypothesis Testing. Handbook of Computational Econometrics, Wiley."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/9\/2922\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:50:54Z","timestamp":1760161854000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/9\/2922"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,21]]},"references-count":31,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["s21092922"],"URL":"https:\/\/doi.org\/10.3390\/s21092922","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,21]]}}}