  In this paper, with respect to multichannel synthetic aperture radars (SAR),
we first formulate the problems of Doppler ambiguities on the radial velocity
(RV) estimation of a ground moving target in range-compressed domain,
range-Doppler domain and image domain, respectively. It is revealed that in
these problems, a cascaded time-space Doppler ambiguity (CTSDA) may encounter,
i.e., time domain Doppler ambiguity (TDDA) in each channel arises first and
then spatial domain Doppler ambiguity (SDDA) among multi-channels arises
second. Accordingly, the multichannel SAR systems with different parameters are
investigated in three different cases with diverse Doppler ambiguity
properties, and a multi-frequency SAR is then proposed to obtain the RV
estimation by solving the ambiguity problem based on Chinese remainder theorem
(CRT). In the first two cases, the ambiguity problem can be solved by the
existing closed-form robust CRT. In the third case, it is found that the
problem is different from the conventional CRT problems and we call it a double
remaindering problem in this paper. We then propose a sufficient condition
under which the double remaindering problem, i.e., the CTSDA, can also be
solved by the closed-form robust CRT. When the sufficient condition is not
satisfied for a multi-channel SAR, a searching based method is proposed.
Finally, some results of numerical experiments are provided to demonstrate the
effectiveness of the proposed methods.
