# GMTI and Parameter Estimation Algorithm Based on Multiple Revisits

The along-track velocity of a moving target mainly causes the azimuth second-order phase error, and the impact can be neglected in DBS imaging. Therefore, the cross-track velocity is analyzed in the GMTI of mechanic scanning mode. The geometry of a moving target in mechanic scanning mode is shown in Fig. 4.5.

**Fig. 4.5 ****Geometry of a moving target in the mechanic scanning mode**

In Fig. 4.5, the cross-track velocity of moving target P is V_{r}. After azimuth time t_{a}, the platform flies from O to *O _{1},* while the target moves to P

_{1}. The instantaneous slant range

*R(t*can be expressed as

_{a})

After Taylor expansion, R(t* _{a})* can be approximated as

Substitute Eq. 4.4.2 into Eq. 4.2.8, the Doppler centroid of a moving target can be expressed as

Compared with Eq. 4.2.1, in the existence of V_{r}, the Doppler centroid of a moving target is shifted from that of a stationary target. The shift will result in the dis-location of a moving target in the azimuth direction in the DBS image. Therefore, the moving target can be indicated by using the Doppler filtering algorithm. The specific processing steps are as follows.

Step 1: Perform DBS imaging of the raw data to obtain the false image;

Step 2: Estimate the Doppler centroid of the clutter in the azimuth-frequency domain, and derive the LOS of the antenna;

Step 3: Eliminate the spectrum of the clutter by using the band-pass filter;

Step 4: Perform CFAR detection of the image to detect the moving targets.

The four steps above are used in the images of each frame. In order to increase the possibility of detection and decrease the false alarm rate, detection results from each frame can be correlated to further judge the existence of the moving targets.

After the indication of the moving targets, the motion parameters are estimated by using the multiple revisits. The specific processing steps are as follows.

Step 1: Perform GMTI of each DBS image to locate each moving target;

Step 2: Read the scanning angle from the subsidiary data to obtain two DBS images of neighboring visit;

Step 3: Perform image registration of the two images. There are mainly two methods: first, operate cross-correlation of the two images to search for the peak; second, use the feature point match method;

Step 4: Calculate the location change AN_{r} of the target in two images. Suppose the range sampling interval is *p*_{r}, the time interval of the imaging of the two images is *At,* the cross-track velocity can be estimated as

Step 5: By using the estimated V_{r}, the Doppler centroid shift Af_{dc} can be calculated according to Eq. 4.4.3. Suppose coherent pulses is M, the azimuth dis-location AN_{a }can be calculated as

Step 6: Re-locate the target into its actual location. If there are multiple targets, repeat these steps.