This paper provides a general sensorless method to control the position of a linear actuator. After a review of the solutions used so far, this new method is applied to identify keys passing through a linear actuator used in an industrial textile machine. The presented method describes how to find out the position of the key using two cascading discrete Kalman filters, the first for filtering the speed and the second for filtering the impedance measurement in other to retrieve the position. To speed-up the method and due to the thickness difference from one textile machine to another, an actuator model, to evaluate impedance in function of the position, is obtained by using parameter identification. Kalman's filter parameters are optimized to minimize the time necessary to learn the speed operation. Finally, we focus on the temporal evolution of Kalman Filters parameters on the learning process.