GNSS (Global Navigation Satellite System) spoofing has become a great threat in recent years because of its elusiveness and harmfulness. For anti-spoofing usages, utilization of additional independent sensors is a preferred choice. In this work we develop a MEMS (Micro-Electro-Mechanical-Systems) IMU (Inertial Measurement Unit) based spoofing detection and exclusion method by first analyzing the relationship between the Doppler frequency from each navigation signal and the output from the IMU and then evaluating the residual. The detector is a steady-state spoofing detector which can provide continual anti-spoofing result throughout the spoofing attack, as it only requires raw measurements from the two sensors and a rather rough prior knowledge of the position of the host. Simulations are conducted to verify the theoretical derivation and to evaluate the anti-spoofing performance of the proposed method. Field experiments are carried out and the experiment results are analyzed, in which the proposed steady-state detector exhibits improved ability of spoofing identification over traditional methods under continuous spoofing attacks, by clearly distinguishing the authentic navigation signals from the counterfeited ones. Moreover, both the simulation and the field experiment demonstrate that a prior knowledge of the position of the host with the uncertainty of hundreds of kilometers, which can be readily obtained from various methods, is acceptable for the proposed detector.