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A biologically inspired azimuthal broadband sound localisation system is introduced to simulates the functional organisation of the human auditory midbrain up to the inferior colliculus (IC). Supported by recent neurophysiological studies on the role of the IC and superior olivary complex (SOC) in sound processing, our system models two ascending pathways of the auditory midbrain: the ITD (Interaural Time Difference) pathway and ILD (Interaural Level Difference) pathway. In our approach to modelling the ITD pathway, we take account of Yinpsilas finding that only a single delay line exists in the ITD processing from cochlea to SOC for the ipsilateral ear while multiple delay lines exists for the contralateral ear. The ILD pathway is modelled without varied delay lines because of neurophysiological evidence that indicates the delays along that pathway are minimal and constant. First, two-dimensional (2D) tonotopical ITD and ILD spike maps over frequency and ITD/ILD are calculated by a spiking neural network which follows the biological delay structure. Then these maps are weighted considering the advance of ITD in low frequency and ILD in middle and high frequency. Finally, ITD and ILD maps are merged together to find out the best estimation of the sound source. Experimental results involving noise and voice show that our model performs sound localisation that approaches biological performance. Our approach brings not only new insight into the brain mechanism of the auditory system, but also demonstrates a practical application of sound localisation for mobile robots.