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This paper proposes a spiking neural network (SNN) of the mammalian auditory midbrain to achieve binaural sound source localisation with a mobile robot. The network is inspired by neurophysiological studies on the organisation of binaural processing in the medial superior olive (MSO), lateral superior olive (LSO) and the inferior colliculus (IC) to achieve a sharp azimuthal localisation of sound source over a wide frequency range in situations where there is auditory clutter and reverberation. Three groups of artificial neurons are constructed to represent the neurons in the MSO, LSO and IC that are sensitive to interaural time difference (ITD), interaural level difference (ILD) and azimuth angle respectively. The ITD and ILD cues are combined in the IC using Bayes's theorem to estimate the azimuthal direction of a sound source. Two of known IC cells, onset and sustained-regular are modelled. The azimuth estimations at different robot positions are then used to calculate the sound source position by a triangulation method using an environment map constructed by a laser scanner. The experimental results show that the addition of ILD information significantly increases sound localisation performance at frequencies above 1 kHz. The mobile robot is able to localise a sound source in an acoustically cluttered and reverberant environment.