It is well known that targets moving along track within a Synthetic Aperture Radar (SAR) field of view are imaged as defocused objects. The SAR stripmap mode is tuned to stationary ground targets and the mismatch between the SAR processing parameters and the target motion parameters causes the energy to spill over to adjacent image pixels, thus not only hindering target feature extraction, but also reducing the probability of detection. The problem can be remedied by generating the image using a filter matched to the actual target motion parameters, effectively focusing the SAR image on the target. For a fixed rate of motion the target velocity can be estimated from the slope of the Doppler frequency characteristic. The processing is carried out on the range compressed data but before azimuth compression. The problem is similar to the classical problem of estimating the instantaneous frequency of a linear FM signal (chirp). This paper investigates the application of three different time-frequency analysis techniques to estimate the instantaneous Doppler frequency of range compressed SAR data. In particular, we compare the Wigner-Ville distribution, the Gabor expansion and the Short-Time Fourier transform with respect to their performance in noisy SAR data. Criteria are suggested to quantify the performance of each method in the joint time- frequency domain. It is shown that these methods exhibit sharp signal-to-noise threshold effects, i.e., a certain SNR below which the accuracy of the velocity estimation deteriorates rapidly. It is also shown that the methods differ with respect to their representation of the SAR data.