This paper addresses the attitude estimation problem of wheeled mobile robots (WMRs) with nonholonomic constraints moving in a plane. We consider the case that only the robot’s Cartesian position and linear velocity are available from sensor measurements. Based on the kinematic model, three attitude observers are proposed. The first observer is designed directly on the Special Orthogonal group SO(2) and guarantees that for almost all initial conditions, the estimated attitude converges to the actual one with an exponential convergence rate. The second observer estimates the heading direction of the mobile robot, i.e., its dynamics evolves on the unit circle S1. The first and second observers rely on linear velocity measurements. On the other hand, the third observer presents a globally exponentially stable error dynamics and requires only Cartesian position measurements but does not evolve on S1. Additionally, a control-observer algorithm is proposed to solve the trajectory-tracking problem of WMRs. Finally, the performances of the proposed attitude observers and control law were evaluated by a set of experiments on a commercial WMR.