# Doppler Centroid

The cross-track velocity is the most interesting parameter of the moving target in GMTI applications. Therefore, in most existing algorithms, the moving target is classified according to the values of their cross-track velocities [1-3]. For example, if the moving target has a slow cross-track velocity that its spectrum is submerged by the clutter, it is defined as a slow moving target. However, when the Doppler centroid of the moving target exceeds the limit of PRF, the Doppler ambiguity is induced. The Doppler ambiguity exists when the cross-track velocity meets the condition

In that case, the “fast” or “slow” cross-track velocity [4] cannot accurately reflect the spectrum character of the moving target. In the existence of the Doppler ambiguity, the moving targets can be classified according to the locations of their spectra. We classify the moving targets into three types, as shown in Fig. 2.4.

The red and black triangles in Fig. 2.4 represent the Doppler spectra of the moving target and the clutter, respectively. The spectra of the moving targets of Type I are completely located out of the clutter. Hence, a high-pass filter is able to separate the moving target from the clutter. In Type II, partial spectra of the moving

**Fig. 2.4 ****Illustration of the three types of moving targets in the range-Doppler domain**

target are submerged by the clutter. Type III represents the moving targets that are completely submerged by the clutter. The targets with slow cross-track velocities and the targets with fast cross-track velocities that aliased into the baseband, belong to Type III. In addition, given that the along-track velocity has no relationship with the Doppler centroid, the along-track moving targets also belong to Type III. The velocity information of the moving targets for each type is illustrated in Table 2.1, where *B _{a}* and

*B*denote the Doppler bandwidths of the clutter and the moving target, respectively, and k is the number of the Doppler ambiguity.

_{m}In a whole synthetic aperture, the number of azimuth samples *N _{a} = PRF • T_{a}, *where

*T*represents the synthetic aperture time. Thus the number of azimuth dislocation samples can be calculated as

_{a}

The synthetic aperture time *T _{a} = LR-,* where

*L*is the azimuth aperture size. Substitute it into Eq. 2.3.8, it yields that

_{a}**Table 2.1 **Classification of moving targets

Type I |
^{Bm} + k • PRF<^{2v} |< ^{prf} + k • PRF |

Type II |
k • PRF< |^{2}V | < t^{Ba},^{Bm} + k • PRF |

Type III |
k • PRF |

Substitute azimuth sample interval *d _{a} = L* into Eq. 2.3.9, the azimuth dislocation is

According to Eq. 2.3.10, the azimuth dislocation of a moving target is determined by its cross-track velocity.