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In this paper, we have presented a GPS and sonar based area mapping and navigation scheme for a mobile robot. A mapping is achieved between the GPS space and the world coordinates of the mobile robot which enables us to generate direct motion commands for it. This mapping enables the robot to navigate among different GPS locations within the mapped area. The GPS data is extracted online to get the latitude and longitude information of a particular location. In the training phase, a 2-D axis transformation is used to relate local robot frame with the robot world coordinates and then the actual world coordinates are mapped from the GPS data using a RBFN (radial basis function network) based Neural Network. In the second phase, direct GPS data is used to get the mapping into the world coordinates of mobile robot using the trained network and the motion commands are generated accordingly. The physical placement of sonar devices, their ranging limits and beam opening angles are considered during navigation for possible collision detection and obstacle avoidance. This scheme is successfully implemented in real time with Pioneer mobile robot from ActivMedia Robotics and GPS receiver. The scheme is also tested in the simulation to justify its application in the real world.