{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:26:52Z","timestamp":1762522012901,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2017,4,29]],"date-time":"2017-04-29T00:00:00Z","timestamp":1493424000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["TRA2013-48030-C2-1-R"],"award-info":[{"award-number":["TRA2013-48030-C2-1-R"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Vehicles with a high center of gravity (COG), such as light trucks and heavy vehicles, are prone to rollover. This kind of accident causes nearly     33 %     of all deaths from passenger vehicle crashes. Nowadays, these vehicles are incorporating roll stability control (RSC) systems to improve their safety. Most of the RSC systems require the vehicle roll angle as a known input variable to predict the lateral load transfer. The vehicle roll angle can be directly measured by a dual antenna global positioning system (GPS), but it is expensive. For this reason, it is important to estimate the vehicle roll angle from sensors installed onboard in current vehicles. On the other hand, the knowledge of the vehicle\u2019s parameters values is essential to obtain an accurate vehicle response. Some of vehicle parameters cannot be easily obtained and they can vary over time. In this paper, an algorithm for the simultaneous on-line estimation of vehicle\u2019s roll angle and parameters is proposed. This algorithm uses a probability density function (PDF)-based truncation method in combination with a dual Kalman filter (DKF), to guarantee that both vehicle\u2019s states and parameters are within bounds that have a physical meaning, using the information obtained from sensors mounted on vehicles. Experimental results show the effectiveness of the proposed algorithm.<\/jats:p>","DOI":"10.3390\/s17050987","type":"journal-article","created":{"date-parts":[[2017,5,2]],"date-time":"2017-05-02T11:37:20Z","timestamp":1493725040000},"page":"987","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Sensor Fusion Based on an Integrated Neural Network and Probability Density Function (PDF) Dual Kalman Filter for On-Line Estimation of Vehicle Parameters and States"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5478-9287","authenticated-orcid":false,"given":"Leandro","family":"Vargas-Melendez","sequence":"first","affiliation":[{"name":"Mechanical Engineering Department, Research Institute of Vehicle Safety, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8061-068X","authenticated-orcid":false,"given":"Beatriz","family":"Boada","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department, Research Institute of Vehicle Safety, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5377-0023","authenticated-orcid":false,"given":"Maria","family":"Boada","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department, Research Institute of Vehicle Safety, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio","family":"Gauchia","sequence":"additional","affiliation":[{"name":"Mechanical Engineering-Engineering Mechanics Department, Michigan Tech University, 1400 Townsend Drive, Houghton, MI 49931, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vicente","family":"Diaz","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department, Research Institute of Vehicle Safety, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.jsr.2014.12.004","article-title":"Efficacy of roll stability control and lane departure warning systems using carrier-collected data","volume":"52","author":"Hickman","year":"2015","journal-title":"J. Saf. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1504\/IJHVS.2009.027413","article-title":"Active roll control using reinforcement learning for a single unit heavy vehicle","volume":"16","author":"Boada","year":"2009","journal-title":"Int. J. Heavy Veh. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rajamani, R., Piyabongkarn, D., Tsourapas, V., and Lew, J.Y. (2009, January 10\u201312). Real-time estimation of roll angle and CG height for active rollover prevention applications. Proceedings of the 2009 American Control Conference, St. Louis, MO, USA.","DOI":"10.1109\/ACC.2009.5160045"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.conengprac.2014.03.002","article-title":"Robust online roll dynamics identification of a vehicle using sliding mode concepts","volume":"29","author":"Tafner","year":"2014","journal-title":"Control Eng. Pract."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1080\/00423110601169713","article-title":"Estimation of land vehicle roll and pitch angles","volume":"45","author":"Eric","year":"2007","journal-title":"Veh. Syst. Dyn."},{"key":"ref_6","unstructured":"Doumiati, M., Baffet, G., Lechner, D., Victorino, A., and Charara, A. (2008, January 6\u20139). Embedded estimation of the tire\/road forces and validation in a laboratory vehicle. Proceedings of the 9th International Symposium on Advanced Vehicle Control, Kobe, Japan."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Vargas-Mel\u00e9ndez, L., Boada, B., Boada, M.J.L., Gauch\u00eda, A., and D\u00edaz, V. (2016). A Sensor Fusion Method Based on an Integrated Neural Network and Kalman Filter for Vehicle Roll Angle Estimation. Sensors, 16.","DOI":"10.3390\/s16091400"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1109\/TITS.2006.883110","article-title":"Integrating INS Sensors with GPS Measurements for Continuous Estimation of Vehicle Sideslip, Roll, and Tire Cornering Stiffness","volume":"7","author":"Bevly","year":"2006","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1109\/TITS.2011.2171033","article-title":"Interacting Multiple Model Filter-Based Sensor Fusion of GPS with In-Vehicle Sensors for Real-Time Vehicle Positioning","volume":"13","author":"Jo","year":"2012","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1109\/TIE.2012.2188874","article-title":"Estimation of Sideslip and Roll Angles of Electric Vehicles Using Lateral Tire Force Sensors Through RLS and Kalman Filter Approaches","volume":"60","author":"Nam","year":"2013","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhang, S., Yu, S., Liu, C., Yuan, X., and Liu, S. (2016). A Dual-Linear Kalman Filter for Real-Time Orientation Determination System Using Low-Cost MEMS Sensors. Sensors, 16.","DOI":"10.3390\/s16020264"},{"key":"ref_12","first-page":"2731","article-title":"Estimation of vehicle parameters using Kalman Filter: Review","volume":"4","author":"Burkul","year":"2014","journal-title":"Int. J. Curr. Eng. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1109\/TITS.2014.2329305","article-title":"A Novel Approach for Vehicle Inertial Parameter Identification Using a Dual Kalman Filter","volume":"16","author":"Hong","year":"2015","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_14","first-page":"1423","article-title":"Modified Dual Unscented Kalman Filter Approach For Measuring Vehicle States And Vehicle Parameters","volume":"3","author":"Nada","year":"2014","journal-title":"Int. J. Eng. Res. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.ymssp.2016.06.038","article-title":"Vehicle parameter estimation using a model-based estimator","volume":"87","author":"Reina","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Simon, D. (2007). Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches, John Wiley Publishing House.","DOI":"10.1002\/0470045345"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Yang, C., and Blasch, E. (2006, January 10\u201313). Kalman Filtering with Nonlinear State Constraints. Proceedings of the 2006 9th International Conference on Information Fusion, Florence, Italy.","DOI":"10.1109\/ICIF.2006.301553"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1109\/7.993234","article-title":"Kalman Filtering with State Equality Constraints","volume":"39","author":"Simon","year":"2002","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","unstructured":"Shimada, N., Shirai, Y., Kuno, Y., and Miura, J. (1998, January 14\u201316). Hand gesture estimation and model refinement using monocular camera-ambiguity limitation by inequality constraints. Proceedings of the Third IEEE International Conference on Automatic Face and Gesture Recognition, Nara, Japan."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1115\/1.1789153","article-title":"Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering","volume":"127","author":"Simon","year":"2005","journal-title":"J. Eng. Gas Turbines Power"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Tully, S., Kantor, G., and Choset, H. (2011, January 25\u201330). Inequality constrained Kalman filtering for the localization and registration of a surgical robot. Proceedings of the 2011 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), San Francisco, CA, USA.","DOI":"10.1109\/IROS.2011.6048358"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1006","DOI":"10.1109\/TITS.2016.2594217","article-title":"A Constrained Dual Kalman Filter Based on PDF Truncation for Estimation of Vehicle Parameters and Road Bank Angle: Analysis and Experimental Validation","volume":"18","author":"Boada","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1243\/095440703770383884","article-title":"Roll dynamics and lateral load transfer estimation in articulated heavy freight vehicles","volume":"217","author":"Kamnik","year":"2003","journal-title":"Proc. Inst. Mech. Eng. Part D J. Automob. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1080\/00423111003615204","article-title":"Observers for vehicle tyre\/road forces estimation: Experimental validation","volume":"48","author":"Doumiati","year":"2010","journal-title":"Veh. Syst. Dyn."},{"key":"ref_25","unstructured":"Eric, A., Wan, E.A., and Nelson, A.T. (1997). Dual Kalman Filtering Methods for Nonlinear Prediction, Smoothing, and Estimation. Advances in Neural Information Processing Systems 9, MIT Press."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1080\/00423110500385949","article-title":"Dual extended Kalman filter for vehicle state and parameter estimation","volume":"44","author":"Wenzel","year":"2006","journal-title":"Veh. Syst. Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/j.ijnonlinmec.2008.11.019","article-title":"Modeling of a magnetorheological damper by recursive lazy learning","volume":"46","author":"Boada","year":"2011","journal-title":"Int. J. Non-Linear Mech."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/5\/987\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:34:13Z","timestamp":1760207653000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/5\/987"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,29]]},"references-count":27,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2017,5]]}},"alternative-id":["s17050987"],"URL":"https:\/\/doi.org\/10.3390\/s17050987","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,4,29]]}}}