The precise position of the mobile  station is critical for the ever  increasing
number of applications based  on location. In this  paper, 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. In this approach we  use
the GSM  signal strengths  measured in  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  the 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  the Back Propagation (BP)  in
both the General Feed Forward (GFF) and the Multi Layer Perception (MLP)  neural
network architectures. The good accuracy of the calculated position with  either
an EKF  training in  a General  Feed Forward  (GFF) or  a Multi Layer Perception
(MLP) neural network is shown.