X-y positions of a digital pen's tip may be determined by using a calibration parameter to map the x-y positions of the respective centers of images captured by the pen's camera. The calibration parameter may be generated by iteratively calculating estimates of the calibration parameter. The iteratively calculated estimates may be based on a gradient of an error function of the iteratively generated estimates. Calibration input data may be produced by a user placing the pen tip in a fixed location on a surface, which may be a positionally encoded medium, such as paper, and then rotating the pen and/or moving the opposite end of the pen in various directions to capture multiple images for use in generating the calibration parameter. A user may perform such a calibration procedure without the need for complicated calibration equipment typically used in connection with conventional calibration techniques.