After range compression, the RCM trajectory of the moving target smears among several range cells. In order to obtain a focused image of the moving target, the RCM must be accurately corrected.

The RCM of the moving target can be divided into two parts: the range curve and the additional range walk.

It has been validated in [13] that the platform velocity is the main factor in determining the range curve since that V_{y} is far smaller than V_{a}. Therefore, compensating for the range curve caused by the platform is sufficient to the requirement of moving target imaging. The range curve correction filter in range-frequency domain can be expressed as

After range curve correction, the range walk trajectory of the moving target is a straight line. The slope of the range walk trajectory increases with the cross-track velocity, and it is independent of the Doppler ambiguity. Therefore, the actual value of the cross-track velocity can be obtained from the slope even in the presence of the Doppler ambiguity.

Hough transform is an effective tool to detect rectilinear figures, and it is capable of estimating the parameters of the rectilinear figure. During T_{a}, the cross-track and along-track motions of the moving target in 2-D image domain can be expressed, respectively, as

Therefore, the tangent of the slope of the range walk trajectory can be expressed as

where в represents the angle between the trajectory and azimuth direction. With the estimation of в, the cross-track velocity can be estimated as

With V_{r}, the range walk correction filter in range-frequency domain can be expressed as

Fig. 3.13 Flowchart of the proposed GMTIm algorithm

After RCMC, the energy of the moving target is concentrated into a single range cell. In order to estimate the third-order Doppler parameter of the moving target, we perform the third-order PFT on the echoes of the moving target.

By using PFT, the second- and third-order phase error can be accurately compensated, and V_{y} and a_{r} can be retrieved from the estimations of PFT, respectively, as

where a_{2} and a_{3} are the second- and third-order Doppler parameter estimations, respectively.

The flowchart of the proposed algorithm is shown in Fig. 3.13.