Vehicle scanning methods have recently proliferated in bridge structural health monitoring. Among the various signals available, contact point response stands out for modal identification because it is largely free of vehicle frequency interference. This study presents a general framework for jointly estimating the contact point displacement, velocity, and acceleration response using only vehicle onboard measurements and known vehicle model parameters. The framework includes (i) a method to handle different types of vehicle, bridge, and contact models, (ii) a state-space model that links the contact point response with the flexible modes of the vehicle and vehicle measurements, and (iii) an Augmented Kalman Filter (AKF) and Rauch-Tung-Striebel smoother for joint input–state estimation. Rather than a conventional random walk model, we adopt a kinematic relationship to model the evolution of the contact point response for the AKF. It remains valid as long as the wheels maintain continuous contact with the road/rail. This study validates this framework through numerical simulations that employ a 3D vehicle and bridge model.