A local positioning system is proposed for wirelessly locating an object using existing features within a static environment, such as walls, as the references for determining the position of the system. An antenna 16 attached to the object transmits RF signals which are reflected by the surroundings. During a training mode, the reflected signals are used to train a neural network 22, 43 to map the position of the object to the characteristics of the reflected signals. During a working mode, the trained neural network is to identify the position of the object based on reflected signals in working mode. Optionally, the reflected signals may be subject to a clustering process before input to the neural network.