This chapter will briefly cover previous work on the problem of robot localisation and also explore related work in computational vision and human psychophysics which is relevant to our particular approach. Work on the localisation problem can be divided into several general domains. The first two sets of methods, those of triangulation, and Kalman Filtering fall under the umbrella of geometric reasoning, which makes geometric interpretations of sensor data in order to obtain a position estimate. The third, and more recent, approach attempts to perform functional inversion of the sensor data. A related problem which we will consider is that of modelling visual attention. One goal of this thesis is to show how our particular method for position estimation successfully unites the strengths of all the domains considered in this chapter, while minimising the effects of their inherent difficulties.