Piezoelectric bending actuators are widely used in micro positioning tasks. Due to material nonlinearities such as hysteresis and creep, the position-force control of these actuators is necessary. However, position sensors for micro scale applications are expensive and require a complex configuration. Sensorless approaches are alternative methods in which by resorting to the linear charge-position characteristic, the actuator position can be estimated. But, in piezoelectric actuators with small impedances, due to charge leakage caused by piezoelectric internal resistance, the charge-position characteristic is not linear. Due to nonlinear behavior of piezoelectric internal resistance, its compensation would be more complicated. This paper targets at a modified procedure in which with the help of nonlinear functions for the internal resistance, the linear charge-position characteristic can be obtained. To this purpose, a modified active Prandtl-Ishlinskii (PI) operator is proposed which estimates and compensates the charge leakage. As a result, the ideal linear mapping can be achieved and actuator position can be appropriately estimated. The results are finally validated by experiments and compared with previous methods.