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The problem of detection of moving targets and estimation of their parameters by means of a multi-look single-antenna synthetic aperture radar is considered. The detection of moving targets is based on the displacement of the target images with respect to the static ground scene on the consequent looks. A system of linear algebraic equations has been derived in order to estimate the range to the moving target, the module and the radial component of the relative velocity vector of the target. It is shown that for the target moving uniformly and rectilinearly along a known path its location and own velocity can be found from a system of quadratic algebraic equations. The proposed approach is illustrated with both simulated and real data.