{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T15:31:01Z","timestamp":1785511861227,"version":"3.56.0"},"reference-count":13,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2012,12,13]],"date-time":"2012-12-13T00:00:00Z","timestamp":1355356800000},"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>The integration of the Inertial Navigation System (INS) and the Global Positioning System (GPS) is widely applied to seamlessly determine the time-variable position and orientation parameters of a system for navigation and mobile mapping applications. For optimal data fusion, the Kalman filter (KF) is often used for real-time applications. Backward smoothing is considered an optimal post-processing procedure. However, in current INS\/GPS integration schemes, the KF and smoothing techniques still have some limitations. This article reviews the principles and analyzes the limitations of these estimators. In addition, an on-line smoothing method that overcomes the limitations of previous algorithms is proposed. For verification, an INS\/GPS integrated architecture is implemented using a low-cost micro-electro-mechanical systems inertial measurement unit and a single-frequency GPS receiver. GPS signal outages are included in the testing trajectories to evaluate the effectiveness of the proposed method in comparison to conventional schemes.<\/jats:p>","DOI":"10.3390\/s121217372","type":"journal-article","created":{"date-parts":[[2012,12,13]],"date-time":"2012-12-13T11:07:43Z","timestamp":1355396863000},"page":"17372-17389","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["On-Line Smoothing for an Integrated Navigation System with Low-Cost MEMS Inertial Sensors"],"prefix":"10.3390","volume":"12","author":[{"given":"Kai-Wei","family":"Chiang","sequence":"first","affiliation":[{"name":"Department of Geomatics, National Cheng-Kung University, 1 University Road, Tainan 701, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thanh","family":"Duong","sequence":"additional","affiliation":[{"name":"Department of Geomatics, National Cheng-Kung University, 1 University Road, Tainan 701, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jhen-Kai","family":"Liao","sequence":"additional","affiliation":[{"name":"Department of Geomatics, National Cheng-Kung University, 1 University Road, Tainan 701, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ying-Chih","family":"Lai","sequence":"additional","affiliation":[{"name":"Industrial Technology Research Institute, 195 Chung Hsing Road, Chutung, Hsinchu 310, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chin-Chia","family":"Chang","sequence":"additional","affiliation":[{"name":"Industrial Technology Research Institute, 195 Chung Hsing Road, Chutung, Hsinchu 310, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jia-Ming","family":"Cai","sequence":"additional","affiliation":[{"name":"Industrial Technology Research Institute, 195 Chung Hsing Road, Chutung, Hsinchu 310, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shih-Ching","family":"Huang","sequence":"additional","affiliation":[{"name":"Industrial Technology Research Institute, 195 Chung Hsing Road, Chutung, Hsinchu 310, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2012,12,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A new research approach to Linear Filtering and Prediction Problem","volume":"82","author":"Kalman","year":"1960","journal-title":"J. Basic Eng"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s10291-002-0024-4","article-title":"Multi-sensors integration using neuron computing for land vehicle navigation","volume":"6","author":"Chiang","year":"2003","journal-title":"GPS Solut"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/JPROC.2003.823141","article-title":"Unscented Filtering and Nonlinear Estimation","volume":"92","author":"Julier","year":"2004","journal-title":"Proc. IEEE"},{"key":"ref_4","unstructured":"Duong, T.T., and Chiang, K.W. (2011, January 19\u201323). Non-Linear, Non-Gaussian estimation for INS\/GPS integration. Portland, OR, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1017\/S0373463310000068","article-title":"INS\/GPS Tightly-coupled Integration using Adaptive Unscented Particle Filter","volume":"63","author":"Zhou","year":"2010","journal-title":"J. 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Inertial Navigation System with Geodetic Application, De Gruyter.","DOI":"10.1515\/9783110800234"},{"key":"ref_10","unstructured":"John, L.C., and John, L.J. (2004). Optimal Estimation of Dynamic System, Chapman&HALL\/CRC."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s001900050236","article-title":"Adaptive Kalman Filtering for INS\/GPS integration","volume":"73","author":"Mohamed","year":"1997","journal-title":"J. Geod"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"33","DOI":"10.5081\/jgps.9.1.33","article-title":"Evaluating the performance of adaptive Kalman filter method in GPS\/INS integration","volume":"9","author":"Almagbile","year":"2010","journal-title":"J. Glob. Position. Syst"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1109\/TAC.1976.1101260","article-title":"Apdatetive Sequential Estimation with Unknown Noise Statistic","volume":"21","author":"Mayers","year":"1976","journal-title":"IEEE Trans. Autom. Control"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/12\/12\/17372\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:54:14Z","timestamp":1760219654000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/12\/12\/17372"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,13]]},"references-count":13,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2012,12]]}},"alternative-id":["s121217372"],"URL":"https:\/\/doi.org\/10.3390\/s121217372","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12,13]]}}}