Global Navigation Satellite System (GNSS) safety issues of have been of concern for some time. Spoofing attacks have received much attention as they can be difficult to detect and have the potential to cause disruption at best and major damage in extremis. To mitigate such threats, a spoofing detection method based on the consistency check of Doppler positioning fixes and pseudorange positioning fixes is proposed. The primary contributions of this paper include establishing a Generalised Likelihood Ratio Test (GLRT)-based statistical detection model for the introduced spoofing detection method and efficiently improving the accuracy of the Doppler positioning method as well as the performance of the detection approach by a modified α-filter-based Doppler smoothing technique. Theoretical performance of the proposed detection model is analysed. Monte Carlo simulations were also conducted to verify the theoretical analysis. Moreover, grounded on the developed test statistic and the optimised threshold, a consistency check module was specifically realised in both software defined and real-time GNSS receivers. Additionally, a Doppler smoothing technique was applied to the receivers. Spoofing attack experiments on both software defined and real-time platforms validated the effectiveness of the statistical spoofing detection model.