# (c) Phase Gradient Estimation

After circular shift and windowing, perform azimuth IFFT to the signal to estimate the phase gradient. The gradient estimation criterion is selected according to the scene and the SNR of the echo. LUMV algorithm is suitable for the estimation of echoes with high SNR [8]. The core function is

Another estimation criterion is Maximum Likeness (ML) estimation [9], with the core function:

The ML can provide an estimation theoretically equal to the Cramer-Rao bound. In the images with low SNR, FLOS criterion is often used, which shows a promising performance in the case of heavy-tailed distribution [10]. The core function is

# (d) Iterated Phase Correction

Perform integration to the estimated phase gradient, and the estimation of azimuth phase error is obtained. The PGA algorithm is operated iteratively. The threshold of the iteration is selected accordingly.

The classical PGA algorithm is presented in spotlight SAR. In the case of stripmap SAR, several adjustments have to be done.

(a) Cutting the azimuth data into small segments. For each segment, the azimuth phase error is assumed to be invariant. After the estimation of phase gradient in each segment, the phase gradient can be obtained by jointing each segment. The segment cutting is illustrated in Fig. 6.5. It can be noted that each segment is

**Fig. 6.5 ****Segments cutting and jointing**

- 50% overlapped with the neighboring segment. By using the central 50% of each segment, the jointing operation can be accurate.
- (b) Transform the data from each segment into spotlight data. The spectra of partial observed targets are filtered in this step.
- (c) Perform standard PGA algorithm in each segment, and joint the estimations of each segments to obtain the whole estimation. To remove the linear phase error in jointing, the jointing operation uses the second-order phase gradient.