In this study, we investigate the estimation of the relative delay, the azimuth and elevation angle and the complex amplitude of a known received signal with the space alternating generalised expectation (SAGE) maximisation algorithm. This optimisation algorithm is used to replace the high-dimensional optimisation procedure, necessary to compute the joint maximum likelihood estimate of the parameters using several separate maximisation processes, which can be performed sequentially. Spherical arrays provide wide scan coverage with low grating lobe levels. Because a uniform antenna element distribution on this spherical surface gives rise to the smallest variations in received signal levels over the whole angular space, a uniform distribution of antennas on a sphere is used. For this completely general three-dimensional array, we have for the fitst time investigated the resolution of the SAGE algorithm, the convergence and the bit error rate as a function of the signal to noise ratio. We will show that this algorithm is a powerful tool that can be applied successfully for high-resolution parameter extraction.