As the drive force depends in a nonlinear manner on the currents, an accurate tracking control of permanent magnet linear motors is challenging. In this paper, a cascaded control is proposed and combined with a recursive estimator. In the inner loop of the cascaded structure, an inversion-based control design is employed in combination with an eigenvalue assignment. The outer loop involves a backstepping tracking control of the armature position, where a nonlinear error dynamics is assigned. Given nonlinear friction and other disturbances, a lumped disturbance force is estimated by a dual Kalman filter - in addition to the state variables. This combination achieves a high robustness of the overall control structure. The control performance is investigated in detailed simulations, where also measurement noise and external disturbances are included.