# Along-Track Moving Target Indication and Imaging in FMCW SAR

## Signal Model of Moving Targets in FMCW SAR

The geometry of a moving target in FMCW SAR is the same as that in a pulse SAR system, as shown in Figs. 2.2 and 2.3. To briefly compare the additional phase error of FMCW SAR, the accelerations are neglected, and the instantaneous slant range of a moving target in FMCW SAR can be expressed as

Perform Taylor expansion of Eq. 5.4.1, it can be approximated as

where *R _{A} = J(R_{0}* —

*V*(V

_{r}t_{a})^{2}+_{a}

*— V*Compare Eq. 5.4.2 with Eq. 2.3.4, two additional phase terms exists in Eq. 5.4.2. Substitute Eq. 5.4.2 into Eq. 5.2.7 and perform RVP correction, it yields

_{y})^{2}t^.

The fifth term in Eq. 5.4.3 is the range location shift induced by cross-track velocity. A moving target is dis-located in the range direction in a stationary FMCW SAR image. The sixth term in Eq. 5.4.3 is the FMCW system. The seventh term in Eq. 5.4.3 is also a range walk, which is induced by the cross-track velocity.

Many researchers have developed algorithms to indicate and focus moving targets in FMCW SAR by using the GMTI and GMTIm algorithms and correct the additional phase errors [18, 19]. However, we discovered that the moving targets can be indicated from the additional phase errors, and the motion parameters can be extracted from them.