To solve outdoor positioning problems, global positioning system (GPS) seems to be the best solution. However, GPS is unable to accurately and precisely locate objects or humans indoors. Thus, in this paper, we propose an efficient method for localization and position estimation for mobile robot navigation using passive radio-frequency identification (RFID). In our method, it is possible to accurately locate autonomous entities such as robots and people within a defined area, and we control and monitor the position of the robot from a remote location through a mobile phone via Wi-Fi and Bluetooth network. Simulations results show that we use PID controllers to increase the efficiency of captured RFID tags, and curve fitting is used to systematically identify the revolutions per minute (RPM) of the motor. Furthermore, we estimate RPM of the motor from the curve fitting and grey theory model. Experiment results show that the number of captured RFID tags using our proposed method is greater than that of the fixed power level method.