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The precise position of the mobile station is critical for the ever increasing number of applications based on location. We introduce a novel positioning technique for positioning a GSM mobile phone in real-time. This technique is based on the GSM mobile phone feature that it can measure the signal strengths from a number of nearby base stations. We use the GSM signal strengths measured in a real environment to train an artificial neural network. The neural network is trained using the second order learning algorithm (extended Kalman filter) because of its superiority in learning speed and mapping accuracy. The mobile position can be determined with good accuracy by providing the current signal strength data to a previously trained neural network. The EKF shows its superiority to back propagation (BP) in both the general feed forward (GFF) and the multilayer perceptron (MLP) neural network architectures. The good accuracy of the calculated position with EKF training in either a GFF or MLP neural network is shown.