{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:25:21Z","timestamp":1760243121095,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2015,9,22]],"date-time":"2015-09-22T00:00:00Z","timestamp":1442880000000},"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>Reduced inertial sensor systems (RISS) have been introduced by many researchers as a low-cost, low-complexity sensor assembly that can be integrated with GPS to provide a robust integrated navigation system for land vehicles. In earlier works, the developed error models were simplified based on the assumption that the vehicle is mostly moving on a flat horizontal plane. Another limitation is the simplified estimation of the horizontal tilt angles, which is based on simple averaging of the accelerometers\u2019 measurements without modelling their errors or tilt angle errors. In this paper, a new error model is developed for RISS that accounts for the effect of tilt angle errors and the accelerometer\u2019s errors. Additionally, it also includes important terms in the system dynamic error model, which were ignored during the linearization process in earlier works. An augmented extended Kalman filter (EKF) is designed to incorporate tilt angle errors and transversal accelerometer errors. The new error model and the augmented EKF design are developed in a tightly-coupled RISS\/GPS integrated navigation system. The proposed system was tested on real trajectories\u2019 data under degraded GPS environments, and the results were compared to earlier works on RISS\/GPS systems. The findings demonstrated that the proposed enhanced system introduced significant improvements in navigational performance.<\/jats:p>","DOI":"10.3390\/s150924269","type":"journal-article","created":{"date-parts":[[2015,9,22]],"date-time":"2015-09-22T15:36:54Z","timestamp":1442936214000},"page":"24269-24296","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["An Enhanced Error Model for EKF-Based Tightly-Coupled Integration of GPS and Land Vehicle\u2019s Motion Sensors"],"prefix":"10.3390","volume":"15","author":[{"given":"Tashfeen","family":"Karamat","sequence":"first","affiliation":[{"name":"Electrical and Computer Engineering, Royal Military College of Canada, Kingston, ON K7K 7B4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed","family":"Atia","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering, Royal Military College of Canada, Kingston, ON K7K 7B4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6614-7783","authenticated-orcid":false,"given":"Aboelmagd","family":"Noureldin","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering, Royal Military College of Canada, Kingston, ON K7K 7B4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,9,22]]},"reference":[{"key":"ref_1","unstructured":"Misra, P., and Enge, P. (2001). Global Positioning System: Signals, Measurements, and Performance, Ganga-Jamuna Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1109\/TSMCC.2007.905750","article-title":"Survey of wireless indoor positioning techniques and systems","volume":"37","author":"Hui","year":"2007","journal-title":"IEEE Trans. Syst. Man Cybern. Part C (Appl. Rev.)"},{"key":"ref_3","unstructured":"El-Rabbany, A. (2006). Introduction to GPS: The Global Positioning System, Artech House. [2nd ed.]."},{"key":"ref_4","unstructured":"Farrell, J.A. (2008). Aided Navigation: GPS with High Rate Sensors, McGraw-Hill."},{"key":"ref_5","unstructured":"Groves, P.D. (2008). Principles of GNSS, Inertial, and Multi-sensor Integrated Navigation Systems, Artech House."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1109\/70.964672","article-title":"The aiding of a low-cost strapdown inertial measurement unit using vehicle model constraints for land vehicle applications","volume":"17","author":"Dissanayake","year":"2001","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1049\/el.2010.1633","article-title":"Real-time implementation of mixture particle filter for 3D RISS\/GPS integrated navigation solution","volume":"46","author":"Atia","year":"2010","journal-title":"Electron. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Iqbal, U., Okou, F., and Noureldin, A. (2008, January 5\u20138). An Integrated Reduced Inertial Sensor System-RISS\/GPS for Land Vehicles. Proceeding of the IEEE\/ION Position, Location and Navigation Symposium, Monterey, CA, USA.","DOI":"10.1109\/PLANS.2008.4570075"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1638","DOI":"10.1109\/TAES.2010.5595584","article-title":"Land Vehicle Dynamics-Aided Inertial Navigation","volume":"46","author":"Wang","year":"2010","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Noureldin, A., Karamat, T.B., and Georgy, J. (2013). Fundamentals of Inertial Navigation, Satellite-Based Positioning and Their Integration, Springer.","DOI":"10.1007\/978-3-642-30466-8"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Titterton, D.H., and Weston, J. (2005). Strapdown Inertial Navigation Technology, American Institute of Aeronautics and Astronautics. [2nd ed.].","DOI":"10.1049\/PBRA017E"},{"key":"ref_12","unstructured":"Lawrence, A. (1998). Modern Inertial Technology: Navigation, Guidance, and Control, Springer. [2nd ed.]."},{"key":"ref_13","unstructured":"Aggarwal, P., Syed, Z., Aboelmagd, N., and Naser, E.S. (2010). MEMS-Based Integrated Navigation, Technology and Applications, Artech House."},{"key":"ref_14","unstructured":"Karamat, T.B., Georgy, J., Iqbal, U., and Noureldin, A. (2009, January 22\u201325). A Tightly-Coupled Reduced Multi-Sensor System for Urban Navigation. Proceedings of the 22nd International Technical Meeting of the Satellite Division of the Institute of Navigation-ION GNSS 2009, Savannah, GA, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1080","DOI":"10.1109\/TCST.2006.886439","article-title":"Kalman Filter-Based Integration of DGPS and Vehicle Sensors for Localization","volume":"15","author":"Rezaei","year":"2007","journal-title":"IEEE Trans. Control Syst.Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1109\/70.897786","article-title":"Lidar design, use, and calibration concepts for correct environmental detection","volume":"16","author":"Adams","year":"2000","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1002\/j.2161-4296.2007.tb00404.x","article-title":"Tight coupling of laser scanner and inertial measurements for a fully autonomous relative navigation solution","volume":"54","author":"Soloviev","year":"2007","journal-title":"Navig. J. Inst. Navig."},{"key":"ref_18","unstructured":"Degen, C., El Mokni, H., and Govaers, F. (2012, January 9\u201312). Evaluation of a coupled laser inertial navigation system for pedestrian tracking. Proceedings of the 15th International Conference on Information Fusion, FUSION 2012, Singapore."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Soloviev, A., and Venable, D. (2010, January 4\u20136). Integration of GPS and vision measurements for navigation in GPS challenged environments. Proceedings of the Position Location and Navigation Symposium (PLANS), 2010 IEEE\/ION, Indian Wells, CA, USA.","DOI":"10.1109\/PLANS.2010.5507322"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Gamallo, C., Quintia, P., Iglesias-Rodriguez, R., Lorenzo, J., and Regueiro, C. (2011, January 22\u201324). Combination of a low cost GPS with visual localization based on a previous map for outdoor navigation. Proceedings of the 2011 11th International Conference on Intelligent Systems Design and Applications (ISDA), Cordoba, Spain.","DOI":"10.1109\/ISDA.2011.6121813"},{"key":"ref_21","unstructured":"Lin, F., Chen, B., and Lee, T. (2010, January 28\u201330). Vision aided motion estimation for unmanned helicopters in GPS denied environments. Proceedings of the 2010 IEEE Conference on Cybernetics and Intelligent Systems (CIS), Singapore."},{"key":"ref_22","unstructured":"Mannings, R. (2008). Ubiquitous Positioning, Artech House."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Miller, I., and Campbell, M. (2008, January 19\u201323). Particle filtering for map-aided localization in sparse GPS environments. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA 2008), Pasadena, CA, USA.","DOI":"10.1109\/ROBOT.2008.4543474"},{"key":"ref_24","unstructured":"Jianjun, D., and Xiaohong, C. (2011, January 16\u201318). An improved map-matching model for GPS data with low polling rates to track vehicles. Proceedings of the 2011 International Conference on Transportation, Mechanical, and Electrical Engineering (TMEE), Changchun, China."},{"key":"ref_25","first-page":"1","article-title":"Aiding MEMS IMU with building heading for indoor pedestrian navigation","volume":"2010","author":"Abdulrahim","year":"2010","journal-title":"UPINLBS"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lou, L., Xu, X., Cao, J., Chen, Z., and Xu, Y. (2011, January 20\u201322). Sensor fusion-based attitude estimation using low-cost MEMS-IMU for mobile robot navigation. Proceedings of the 2011 6th IEEE Joint International Information Technology and Artificial Intelligence Conference (ITAIC), Chongqing, China.","DOI":"10.1109\/ITAIC.2011.6030374"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Brandt, A., and Gardner, J. (1998, January 24\u201326). Constrained Navigation Algorithms for Strapdown Inertial Navigation Systems with Reduced Set of Sensors. Proceedings of the 1998 American Control Conference (ACC), Philadelphia, PA, USA.","DOI":"10.1109\/ACC.1998.707337"},{"key":"ref_28","first-page":"18","article-title":"Experimental Results on an Integrated GPS and Multisensor System for Land Vehicle Positioning","volume":"2009","author":"Iqbal","year":"2009","journal-title":"Int. J. Navig. Observ. Hindawi Publ. Corp."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s10291-010-0186-4","article-title":"Enhanced MEMS-IMU\/odometer\/GPS integration using mixture particle filter","volume":"15","author":"Georgy","year":"2010","journal-title":"GPS Solut."},{"key":"ref_30","first-page":"16","article-title":"Augmented Kalman Filter and Map Matching for 3D RISS\/GPS Integration for Land Vehicles","volume":"2012","author":"Cossaboom","year":"2012","journal-title":"Int. J. Navig. Observ."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1109\/TVT.2009.2034267","article-title":"Low-cost three-dimensional navigation solution for RISS\/GPS integration using mixture particle filter","volume":"59","author":"Georgy","year":"2010","journal-title":"IEEE Trans. Vehicul. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Iqbal, U. (2008). An Integrated Low Cost Reduced Inertial Sensor System\/GPS for Land Vehicle Applications. [Ph.D. Thesis, Royal Military College of Canada].","DOI":"10.1109\/PLANS.2008.4570075"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2426","DOI":"10.1088\/0957-0233\/15\/12\/012","article-title":"Measurement-while-drilling surveying of highly inclined and horizontal well sections utilizing single-axis gyro sensing system","volume":"15","author":"Noureldin","year":"2004","journal-title":"Meas. Sci. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1109\/TIM.2002.808025","article-title":"Accuracy Limitations of FOG-Based Continuous Measurement-While-Drilling Surveying Instruments for Horizontal Wells","volume":"51","author":"Noureldin","year":"2002","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_35","unstructured":"Gelb, A. (1974). Applied Optimal Estimation, M.I.T. Press."},{"key":"ref_36","unstructured":"Brown, R.G., and Hwang, P.Y.C. (1997). Introduction to Random Signals and Applied Kalman Filtering: With MATLAB Exercises and Solutions, Wiley. [3rd ed.]."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Grewal, M.S., and Andrews, A.P. (2008). Kalman Filtering: Theory and Practice Using MATLAB, Wiley.","DOI":"10.1002\/9780470377819"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Simon, D. (2006). Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches, John Wiley.","DOI":"10.1002\/0470045345"},{"key":"ref_39","unstructured":"Kaplan, E.D., and Hegarty, C.J. (2006). Understanding GPS Principles and Applications, Artech House. [2nd ed.]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/9\/24269\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:49:00Z","timestamp":1760215740000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/9\/24269"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,22]]},"references-count":39,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2015,9]]}},"alternative-id":["s150924269"],"URL":"https:\/\/doi.org\/10.3390\/s150924269","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2015,9,22]]}}}