The estimation of GPS repeater jamming plays an important role in modern military applications. In this paper, based on the maximum likelihood estimation (MLE) method, a new approach for the estimation of GPS repeater jamming using Kalman filtering with coloured observation noise is proposed. The state equation and observation equation of the Kalman filter with the coloured observation noise are deduced and the generation process explained. The recursive formula for the Kalman filter used to iteratively filter for the MLE output is also derived. Experimental results show that the new design has a better performance than the MLE; hence it can be used for the precise estimation of repeater jamming signals under the condition that the carrier-to-noise density ratio is below 20 dB-Hz.