Abstract: Multi-path error is a space-time environment effect, it is difficult to eliminate it through building accurate mathematical model, and the error also has no spatial correlation at both ends of the baseline, it can't eliminate it through using the differential technology, it is one of the main errors in GNSS high accuracy measurement of short baseline. To further mitigate the multi-path error, this paper take the multi-path error in GNSS carrier phase observation value as the research object, establish the multi-path error state space model, estimate the multipath error correction sequence from coordinate residual sequence adopt the standard Kalman filter and the Kalman filter with colored noise, and based on the daily repetition characteristics of multi-path error, correct the coordinate sequences of the subsequent days using the multi-path error correction sequence obtained on the first day. Finally, through the experimental analysis, it is concluded that the Kalman filter with colored noise estimation method is better than the standard Kalman filter. The research results are of great practical value to improve GNSS positioning accuracy.