{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T17:15:17Z","timestamp":1771866917441,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T00:00:00Z","timestamp":1771804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Chongqing postdoctoral research project","award":["2022COBSHTB1004"],"award-info":[{"award-number":["2022COBSHTB1004"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In the domain of engineering applications, this study addresses the challenge of achieving a unified estimation of the suspension relative velocity and road gradient during vehicle operation while mitigating the significant costs associated with automotive sensors. This paper proposes a simplified system model that integrates discretized vehicle vertical dynamics and longitudinal kinematics, intentionally excluding wheel dynamics. Utilizing the front axle vertical velocity, vehicle speed, and longitudinal and vertical accelerations as inputs, an estimator is employed in conjunction with the Extended Kalman filter algorithm to concurrently predict the relative velocity of the vehicle suspension, the sprung mass velocity, and the road gradient. The feasibility of the proposed methodology is corroborated through simulation experiments. Furthermore, real-world road tests validate the efficacy and timeliness of the joint estimation approach based on a \u201c2 + 1\u201d sensor arrangement. This methodology not only optimizes sensor system configuration and reduces engineering costs but also provides substantial technical support for further advancements in vehicle parameter estimation and suspension control applications.<\/jats:p>","DOI":"10.3390\/a19020165","type":"journal-article","created":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T16:22:55Z","timestamp":1771863775000},"page":"165","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Joint Estimation Method for Suspension Status and Road Gradient Under Sparse Sensor Conditions"],"prefix":"10.3390","volume":"19","author":[{"given":"Mengdong","family":"Zheng","sequence":"first","affiliation":[{"name":"School of Aeronautics, Chongqing Aerospace Polytechnic, Chongqing 400021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechatronics and Vehicle Engineering, Chongqing Jiaotong University, Chongqing 400074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaoxue","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Mechatronics and Vehicle Engineering, Chongqing Jiaotong University, Chongqing 400074, China"},{"name":"Chang\u2019an Auto Global R&D Center, Chongqing Chang\u2019an Automobile Co., Ltd., Chongqing 401120, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingquan","family":"Li","sequence":"additional","affiliation":[{"name":"Chang\u2019an Auto Global R&D Center, Chongqing Chang\u2019an Automobile Co., Ltd., Chongqing 401120, China"},{"name":"School of Vehicle Engineering, Chongqing University of Technology, Chongqing 400054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kun","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Mechatronics and Vehicle Engineering, Chongqing Jiaotong University, Chongqing 400074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Gou","sequence":"additional","affiliation":[{"name":"Chongqing Dima Industrial Co., Ltd., Chongqing 401336, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2776","DOI":"10.1177\/09544070211006517","article-title":"Skyhook control strategy for vehicle suspensions based on the distribution of the operational conditions","volume":"235","author":"Papaioannou","year":"2021","journal-title":"Proc. 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