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AlongTrack Moving Target Indication and Imaging in FMCW SARSignal Model of Moving Targets in FMCW SARThe 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_{r}t_{a})^{2} + (V_{a} — V_{y})^{2}t^. 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
The fifth term in Eq. 5.4.3 is the range location shift induced by crosstrack velocity. A moving target is dislocated 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 crosstrack 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. 
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