Moving target detection and refined estimation for motion status are hot and difficult problems in radar signal processing. Traditional moving target detection via time-frequency distribution (TFD) cannot obtain high time and frequency resolution at the same time. Also, the estimation accuracy of motion parameters is limited by searching steps. Sparse TFD (STFD) technique combines the merits of classical TFD and high-resolution signal processing in sparse domain. The STFD is an extension of traditional transform-based methods. The concept of short-time sparse fractional representative domain is proposed. Two radar moving target detection and estimation methods are proposed accordingly, named as short-time sparse fractional Fourier transform and short-time sparse fractional ambiguity function, which achieve the high resolution representation for time-varying signals in time and sparse transform domain. It is verified using real marine radar datasets that the proposed method can improve the moving target detection performance in complex environment, and can obtain the refined estimation for motion status.