Global positioning system(GPS) for vehicle applications in the urban area is challenged by low signal intensity. The carrier loop based on fast Fourier transform(FFT) can obtain a high signal to noise ratio(SNR) gain by increasing the observation time. However, this leads to a major problem that the acceleration cannot be ignored. The performance of the FFT-based loop will decline with the acceleration increasing. This paper discusses the effect of the dynamic on FFT first. Then a high performance carrier tracking loop for weak GPS L5 signals is proposed. It combines discrete chirp-Fourier transform(DCFT) and the phase fitting method to estimate Doppler frequency and Doppler rate simultaneously.First, a sequence of integration results is used to perform DCFT to estimate coarse Doppler frequency and Doppler rate. Second, the phase of the sequence is calculated and used to perform linear fitting. By the phase fitting method, the fine Doppler frequency and Doppler rate can be estimated. The computation cost is small because the integration results are used and the phase fitting method needs only coarse estimates of Doppler frequency and Doppler rate. Compared with FFT and DCFT, the precision of the phase fitting method is not limited by the resolution. Thus the proposed loop can get high precision and low carrier to noise ratio(C/N0) tracking threshold. Simulation results show this loop has a great improvement than conventional loops for urban weak-signal applications. Global positioning system (GPS) for vehicle applications in the urban area is challenged by low signal intensity. The carrier loop based on fast Fourier transform (FFT) can obtain a high signal to noise ratio (SNR) gain by increasing the observation time. However, This leads to a major problem that the acceleration can not be ignored. The performance of the FFT-based loop will decline with the acceleration increased. This paper discusses the effect of the dynamic on FFT first. Then a high performance carrier tracking loop for weak It contains discrete chirp-Fourier transform (DCFT) and the phase fitting method to estimate Doppler frequency and Doppler rate simultaneously. First, a sequence of integration results is used to perform DCFT to estimate coarse Doppler frequency and Doppler rate . Second, the phase of the sequence is calculated and used to perform linear fitting. By the phase fitting method, the fine Doppler frequency and Doppler rate can be estimated. T he computational cost is small because the integration results are used and the phase fitting method needs only coarse estimates of Doppler frequency and Doppler rate. Compared with FFT and DCFT, the precision of the phase fitting method is not limited by the resolution. loop can get high precision and low carrier to noise ratio (C / N0) tracking threshold. Simulation results show this loop has a great improvement than conventional loops for urban weak-signal applications.