In most practical situations, the cross-track velocity of the moving target cannot maintain constant during the entire data acquisition T_{a}. If the cross-track velocity is inconstant, the energy of the moving target will spread on multiple Doppler centroids.

The cross-track velocity error has a significant impact on the Doppler centroid of the moving target. For example, consider a typical Ku-band airborne SAR system, in which k is 0.0194 m, R_{0} is 19000 m, and V_{a} is 100 m/s, the Doppler centroid of the moving target can be calculated as

Suppose V_{x} is 10 m/s, then f_{ac} is 1031 Hz. However, if V_{x}(t_{a}) varies from 9 to 11 m/s, f_{dc} changes between 927.9 and 1134.1 Hz, as shown in Fig. 6.8. In other words, in the existence of the cross-track velocity error, the moving target cannot be focused into a single Doppler centroid, even though the high-order phase errors are compensated. Therefore, the cross-velocity error of the moving target must be compensated in the real data processing.

Fig. 6.7 Impact of the platform velocity error on the Doppler centroid of the moving target

Fig. 6.8 Doppler centroid of a target with cross-track velocity error in time-frequency domain