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To this end, a two-step procedure is proposed to retrieve the bridge surface profile from the noise-contaminated responses of a two-axle vehicle moving over bridges. Central to this is the elimination of the bridge deflection from the estimated unknown input to the test vehicle system. First, the extended Kalman filter with unknown inputs (EKF-UI) algorithm is extended to formulating the state-space equations for the moving vehicle over the bridge. Analytical recursive solutions are derived for the improved vehicle states and the unknown input vector consisting of the vehicle\u2013bridge contact displacement and surface profile. Second, the correlation between the cumulated contact residuals and contact displacements for the two axles is approximately defined by using the vehicle\u2019s parameters and location on the bridge. Then, the surface profile is retrieved from the unknown input by removing the roughness-free contact (bridge) displacement, calculated with no prior knowledge of bridge properties. The efficacy of the proposed procedure was validated by the finite element method and demonstrated in the parametric study for various properties of the system. It is confirmed that the retrieved bridge surface profile is in excellent agreement with the original (assumed). For practical use, the vehicle is suggested to run at a not-too-high speed or in a too noisy environment. The proposed technique is robust with regard to vehicle mass and bridge damping.<\/jats:p>","DOI":"10.3390\/s22093410","type":"journal-article","created":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T07:08:58Z","timestamp":1651475338000},"page":"3410","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Scanning of Bridge Surface Roughness from Two-Axle Vehicle Response by EKF-UI and Contact Residual: Theoretical Study"],"prefix":"10.3390","volume":"22","author":[{"given":"Y. B.","family":"Yang","sequence":"first","affiliation":[{"name":"National Engineering and Research Center for Mountainous Highways, Chongqing 400067, China"},{"name":"School of Civil Engineering, Chongqing University, Chongqing 400044, China"},{"name":"School of Civil Engineering and Architecture, Chongqing University of Science and Technology, Chongqing 401331, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baoquan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Chongqing University, Chongqing 400044, China"},{"name":"Xi\u2019an CCCC Civil Engineering Technology Co., Ltd., Xi\u2019an 710075, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhilu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kang","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yang, Y.B., Yau, J.D., and Wu, Y.S. 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