GMTI and GMTIm are important functions of SAR system. However, since the moving targets have additional motions, two problems must be solved in the SAR moving target processing.

First, the speeds of airborne and spaceborne SAR are fast, which lead to the Doppler bandwidth broaden of the clutter. Targets with slow cross-track velocities will be submerged by the clutter, and is hard to be detected [69]. Therefore, the suppression of the energy of the clutter must be done in GMTI.

Second, the imaging principle of SAR is to use the CPI between the target and the scene. To the stationary scene, the relative motions are decided by the radar platform, and the stationary SAR image can be obtained after the phase error is compensated [70]. However, as to the moving target, the relative motions are composed by both the motions of the platform and the target. Since the motion of the target is unknown, stationary SAR imaging algorithms cannot fully compensate the phase error, which will lead to the smear and dis-locate of the target, as shown in Fig. 1.1 [35, 36].

Fig. 1.1 Image of moving targets of Lynx system

The main processing steps of GMTI and GMTIm of SAR are as follows.

(a) Suppress the clutter, increase the SCR, and set judge strategy detect the moving targets;

(b) Extract the echo of the moving target, and estimate the Doppler and motion parameters;

(c) Refocus the moving target, and locate the image of the target in its actual location in the image.

The differences between the Doppler parameters of the clutter and the moving target are not only the cause of the defocus and the dis-location, but also the lead to indicate and focus the target. In 40 years, researchers have proposed many GMTI and GMTIm algorithms. These algorithms can be classified into single-channel and multi-channel algorithms. Single-channel algorithms include

(a) Spectrum filtering algorithm [71-73]. The cross-track velocity of a moving target will induce a Doppler centroid shift to the echo. Based on the Doppler centroid shift, the moving targets whose Doppler centroid locates out of the spectrum of the clutter can be detected, and the motion parameters can be estimated from the shift.

(b) Shear average algorithm [74] and RDM algorithms [75]. The along-track velocity of a moving target will induce a change of Doppler modulation rate. The Doppler modulation rate of an along-track moving target is different from that of the clutter. These two algorithms use this feature to detect moving targets and estimate the motion parameters.

(c) Time-frequency analysis algorithm: The Doppler characters of the moving target echo are used to detect the target by time-frequency analysis algorithms, such as Wigner-Ville Distribution (WVD) algorithm [76-79].

(d) Sub-aperture algorithm [80]: This sort of algorithms uses the different locations of the moving target in the stationary sub-aperture SAR images to detect targets and estimate motion parameters.

Other single-channel GMTI algorithms include Parameter searching algorithm [81], Keystone transform algorithm, Wavelet transform algorithm [82, 83] and so forth. All these algorithms are based on the different Doppler characters of the moving target. However, constrained by the single-antenna system, the single-antenna has a weaker ability in slow moving target indication. Therefore, along with the hardware development and signal processing ability, multi-channel GMTI algorithms are developed.

(a) DPCA [84-86]: Multiple phase centers are placed along the azimuth direction by DPCA, and by elimination in the complex image domain, the moving target can be extracted, and the motion parameters can be estimated. This algorithm has a high requirement of the location of multiple receivers, so it is limited in practical applications.

(b) ATI [87-89]: Same as DPCA algorithm, ATI also needs multiple phase centers that settled along the azimuth direction. However, the ATI algorithm uses the interference of two isolated echoes to eliminate the clutter, and is becoming the main multi-channel GMTI algorithm in practical applications.

(c) STAP [90-92]: This algorithm uses the multiple sets of signals obtained by antenna-array, and suppresses the clutter by joint processing of space-time signal. Theoretically, the STAP algorithm has the best performance in GMTI. However, the heavy calculation burden limits its applications.

Besides the traditional stripmap SAR mode, another widely-used mode, i.e., the wide area surveillance (WAS) mode is applied in SAR [93]. By scanning the antenna along the azimuth direction, WAS mode is able to obtain a larger observation area, and the revisit of moving target can be achieved.

FMCW SAR is another new working scheme of SAR. By combining the FMCW technique and SAR system, FMCW SAR has the advantages of small size, light weight, low cost and high resolution [94]. FMCW SAR is highly suitable for small platforms, and has a promising performance in GMTI. With the development in FMCW SAR technique, the FMCW SAR has become a hotspot in SAR research area.