{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T15:40:46Z","timestamp":1772552446926,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T00:00:00Z","timestamp":1698969600000},"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>In this study, a vehicle state joint estimation method based on lateral stiffness was applied to estimate the running states of electric vehicles driven by rear-drive, in-wheel motors. Different from the estimation methods used in other research, the joint estimator designed in this study uses the least-squares (LS) algorithm to estimate the lateral stiffness of the front and rear axles of the vehicle, deploying the high-degree cubature Kalman filter algorithm to estimate the vehicle state. We establish a three-degree-of-freedom nonlinear vehicle model with longitudinal velocity, lateral velocity, and yaw rate, and the lateral stiffness of the front and rear axles as the principal parameters. For the low-speed running state of the vehicle, a linearized magic tire model with high fitting accuracy was used to calculate the lateral force of the entire vehicle. The LS algorithm with a forgetting factor was used to design a lateral stiffness estimator to assess the front-axle and rear-axle lateral stiffness of the entire vehicle. The generalized high-degree cubature Kalman filter (GHCKF) algorithm was used to design the vehicle state estimator and further improve the GHCKF algorithm. A vehicle state estimator, using the square root generalized high-degree cubature Kalman filter (SRGHCKF), was designed. Therefore, the joint estimator, comprising a lateral stiffness estimator and a vehicle state estimator, adopts the LS-GHCKF\/SRGHCKF algorithm and enables the estimation of the lateral stiffness, the longitudinal velocity, the lateral velocity, and the yaw rate of the entire vehicle during the driving process. A double lane change and slalom simulation were performed to analyze the feasibility and accuracy of the joint estimation algorithm and verify the results of the LS-GHCKF algorithm and the LS-SRGHCKF algorithm. Further, a low-speed driving experiment was carried out for electric vehicles driven by rear in-wheel motors. The inertial navigation system (INS), the global positioning system (GPS), the real-time kinematic (RTK), and an angle sensor were used to collect real-time vehicle data. The results were compared to verify the feasibility of the joint estimator and the progressiveness of the algorithm. The experimental verification and simulation both show that the vehicle state joint estimator, designed based on the LS-GHCKF\/SRGHCKF algorithm, can accurately estimate the real-time state of the vehicle. Additionally, the LS-SRGHCKF algorithm shows better effectiveness and robustness than the LS-GHCKF algorithm.<\/jats:p>","DOI":"10.3390\/s23218960","type":"journal-article","created":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T10:59:54Z","timestamp":1699009194000},"page":"8960","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Vehicle State Joint Estimation Based on Lateral Stiffness"],"prefix":"10.3390","volume":"23","author":[{"given":"Lingxiao","family":"Quan","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"},{"name":"Hebei Provincial Key Laboratory of Heavy Machinery Fluid Power Transmission and Control, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ronglei","family":"Chang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changhong","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,3]]},"reference":[{"key":"ref_1","first-page":"92","article-title":"Application Analysis of In-wheel Motor Technology in New Energy Vehicles","volume":"11","author":"Ya","year":"2023","journal-title":"Auto Time"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"115","DOI":"10.3901\/JME.2020.04.115","article-title":"Active collision avoidance adaptive control based on identification of different emergency conditions","volume":"56","author":"Wang","year":"2020","journal-title":"J. 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