Multipath interference in cities has always been one of the main problems leading to abnormal positioning results of a global navigation satellite system. Vector tracking is superior to conventional scalar tracking in the ability of mitigating multipath interference. However, due to the special sharing structure, fault propagation which easily occurs in the vector tracking loop leads to false alarms of normal satellite signals during multipath detection. To solve this problem, a fault‐tolerant algorithm based on robust estimation is applied to suppress fault propagation. Meanwhile, in order to improve the ability of detecting multiple short delayed multipath signals, chi‐square detection is proposed to be used before applying the fault‐tolerant algorithm. By taking advantage of the characteristic that the occurrence of multipath signals will cause significant deviation of code phase errors, the mean value of code phase errors is used as the detection metric. Both simulation test and field experiment are carried out to verify the detection performance. Experimental results show that the proposed algorithm can effectively prevent fault propagation and solve the problem of false positives of normal satellite signals. As a result, not only multipath signals are detected more accurately, but also more accurate navigation solution is obtained.