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An estimation method for direction of arrival (DOA) of muzzle blast is proposed to solve the shell-induced deviation problem in target orientation estimation of a partially shaded microphone array em¬bedded in a small-aperture gunshot detection system. The adverse effect of non-line-of-sight (NLOS) propagation on the time difference of arrival ( TDOA) is analyzed, and a convex optimization algorithm with low-rank and geometric constraints is devised to correct TDOA matrix for simultaneously suppressing the influence from both diffraction propagation and random noise. The non-shaded microphone closest to the target is chosen as the reference microphone. The statistical mean and variance values of least squares DOA estimation error are obviously decreased. The experimental results obtained using a real embedded planar array system demonstrate that the proposed method provides superior muzzle blast DOA estimation performance compared with the conventional approach, by which the cumulative probability of estimation error meeting the requirement of practical products is improved from 0. 86 to 0. 94. [ABSTRACT FROM AUTHOR]