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A new algorithm for estimating parameters and angle-of-arrival (AOA) of chirps using matching pursuit (MP) method is presented in this paper. This algorithm is based on the concept of sparse representation of signal and applied into fractional Fourier transform (FRFT) domain and 2D AOAs estimation in the end of the paper. The problem of source localization of chirps has once been solved with time-frequency analysis which is called spatial time-frequency distribution (STDF) method. This method replaces the covariance matrix in subspace methods with the results after time-frequency transform, and then obtains AOAs as common subspace methods do. Wigner-Ville Distribution is the most popular method used for source localization, however, how to eliminate the effect of cross-item in results is still a problem which will make the estimations unacceptable sometimes. Algorithm in this paper fist constructs atom-dictionaries according to system models and then projects observations onto dictionaries, finally obtains parameters and AOAs by solving least squares problems. In order to be more resistant to noise, we preprocess observations and dictionaries with FRFT and only use values near the peak, then utilize MP method in transform domain to obtain AOAs. Numerical simulations have proved the effectivity of the algorithm.