A centroiding algorithm for the refinement of coarse noisy measurements (e.g. spectral or range samples) is proposed and analysed. In contrast to the current algorithms which use constant centroiding weights, in our method the coefficients are chosen usinga prioriinformation about the noise level. The criterion for selection of the optimal weights is the minimisation of the estimate error for the given signal/noise ratio. The numerical results presented demonstrate that the method provides a more effective refinement of the coarse measurements than existing methods.