Vehicle tire traction torque, heavily dependent on vehicle speed and tire stiffness, is critical for improving vehicle traction performance. However, due to the limitation of existing technology and sensor cost, it becomes rather expensive to accurately measure the vehicle tire traction torque and/or other vehicle variables directly. This paper proposes to estimate the tire traction torque by estimating vehicle speed (vehicle state) and tire stiffness simultaneously based on a few available low-cost measurements from any production vehicle. Specifically, the tire and full vehicle dynamics are considered to form a unified traction torque estimation model under various vehicle operational conditions. Estimation of vehicle speed and tire stiffness is formulated into a dual-estimation problem of system states and parameters. A recursive real-time implementable solution for the dual-estimation problem is realized with the help of dual extended Kalman filter (DEKF) algorithm. The effectiveness of the proposed algorithm under different vehicle operating conditions is validated by comparing the estimated results with directly measured ones as well as those from existing estimation approaches. It is found that for a 4-wheel driving vehicle, under clutch overtaken condition, for the best case, the absolute mean square error (ASME) improves by around 20 Nm, and the relative mean square error (RMSE) reduces 12%; and under clutch slip condition, the absolute mean square error improves by around 40 Nm, and the RMSE reduces 6%.