This paper presents an encoderless position estimation technique for miniature-sized mobile robots. Odometry techniques, which are based on the hardware components, are commonly used for calculating the geometric location of mobile robots. Therefore, the robot must be equipped with an appropriate sensor to measure the motion. However, due to the hardware limitations of some robots, employing extra hardware is impossible. On the other hand, in swarm robotic research, which uses a large number of mobile robots, equipping the robots with motion sensors might be costly. In this study, the trajectory of the robot is divided into several small displacements over short spans of time. Therefore, the position of the robot is calculated within a short period, using the speed equations of the robot's wheel. In addition, an error correction function is proposed that estimates the errors of the motion using a current monitoring technique. The experiments illustrate the feasibility of the proposed position estimation and error correction techniques to be used in miniature-sized mobile robots without requiring an additional sensor.