# Cross-Track Velocity Error of the Moving Target

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*is 1031 Hz. However, if

_{ac}*V*varies from 9 to 11 m/s,

_{x}(t_{a})*f*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.

_{dc}**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**