observation of stage position in a 2-axis nano-positioner using hybrid kalman filter

This paper presents a novel method for observation of the stage position in a 2d nano-positioning system based on a hybrid kalman filter. in the proposed method, there is no need to measure the stage position directly using complex and costly capacity sensors. instead, by using traditional piezo actuators equipped with strain gauge sensors, the deflection of the magnification system at the position of actuators is measured. then, by employing a powerful estimation algorithm named as kalman filter, the displacements of the stage are observed. the designed hybrid kalman filter uses dynamical equations of motion in the prediction step. the piezo actuators deflections are measured and exploited to correct the predicted values for the system state variables. in order to simulate realistic conditions, a relatively exact comsol model has been developed for the nano-positioner where noise has been added to the piezo displacements obtained by simulating this model and these noisy data are used as measurements in the kalman filter algorithm. the designed hybrid kalman filter is examined for three different updating time steps. the results show that the designed kalman filter appropriately estimates the stage displacements, and its accuracy is improved when the filter time step reduces.