## 2 Signal Model and Adaptive Clutter Cancellation  
Consider \(K\) identical spaceborne SARs flying along the same orbit when viewed from the ground. This semiactive configuration is named SAR-Train [1]. The \(K\) SAR flies on the same orbital arc in an Earth frame, which means that the SARs are generally on different orbit planes because of the across orbit Earth rotation between successive passes. The main formation flying constraint is the width of the tube containing the satellite trajectories. The time intervals between the satellites, which cause the temporal decorrelation of the backscatter, is supposed to be very short. In the train of \(K\) monostatic/bistatic spaceborne SARs, the first satellite known as master satellite transmits/receives radar signal/echo, while other satellites, known as slave satellites, only receive the radar echo. The phase centers of these satellite constellations are aligned to form a sparse linear array. Based on the configurations and the monostatic/bistatic SAR imaging techniques, the \(K\) phase centers focus on the processed point at different times [6; 15; 22; 23]. The complex SAR images of the same area can be obtained with identical geometry of every satellite and with uniform/nonuniform along-track baselines. In other words, the multi-aperture SAR images are sampled with time delay determined by baseline permutation and combination. Image alignment can be performed in the coregistration stage. Firstly, some realistic assumptions are described as follows: (1) since the along-track baseline distance is short for the multibaseline spaceborne SAR-GMTI system, the target's movement is smaller than the resolution cell size within the small time delay; (2) stationary clutter is modeled as a Gaussian distributed process; (3) the multilook SAR resolution cell size is larger than the spatial dimension of the target that contains both clutter and the moving target; the clutter power can no longer be neglected; (4) moving target travel with constant velocity without acceleration or brake; (5) magnitude and phase errors caused by mismatched SAR processing or channel unbalance have been eliminated prior to the detection [26]; and (6) the subpixel coregistration precision can be obtained using the maximum-spectrum image registration method. Two hypotheses H\({}_{0}\) and H\({}_{1}\) are defined as clutter and noise (H\({}_{0}\)) andsignal plus clutter and noise (H\({}_{1}\)). For image pixel index \((m,n)\), the \(K\) dimensional SAR image vector can be modeled as the following [15; 22; 23],  
\[ \begin{split}\text{Hypothesis H}_{0}&:\overset{ \rightharpoonup}{Z}(m,n)=\overset{\rightharpoonup}{C}(m,n)+\overset{ \rightharpoonup}{N}(m,n)\\ \text{Hypothesis H}_{1}&:\overset{\rightharpoonup}{Z}(m,n )=\overset{\rightharpoonup}{S}(m,n)+\overset{\rightharpoonup}{C}(m,n)+ \overset{\rightharpoonup}{N}(m,n)\end{split}  \tag{1}\]  
where \(\overset{\rightharpoonup}{C}\) is the clutter vector that is assumed to be independent with an identically distributed (i.i.d.) circular Gaussian with zero mean in the local terrain. \(\overset{\rightharpoonup}{N}\) is the additive noise vector. The moving target's signal vector \(\overset{\rightharpoonup}{S}\) is modeled as a statistically independent point target. \(\overset{\rightharpoonup}{S}(m,n)=\overset{\rightharpoonup}{\beta} \overset{\rightharpoonup}{a}(\psi)\odot\overset{\rightharpoonup}{S}_{Nor}(m,n)\). \(\overset{\rightharpoonup}{S}_{Nor}(m,n)\) is the normalized complex moving target's image pixel vector. \(\beta\) is the amplitude of the moving target. \(\overset{\rightharpoonup}{a}(\psi)\) is the normalizedspatial steering vector. \(\gamma\) is the unknown moving target's interferometric phase between the master and the first slave satellite. \(\odot\) is the Shur-Hadamard product.