In the framework of array signal processing, the rank loss of signal covariance matrix of coherent sources causes the failing of subspace decomposition algorithm, therefore the subspace fitting technique (SFT) is conventionally employed to estimate the direction of arrival (DOA) of bearings. The drawback of SFT is its high computational complexity, especially when the polarization and DOA of bearings both need to be estimated which requires a four-dimensional search. Meanwhile, due to the antenna arrays in the actual environment is mostly irregular, the generalized fast algorithm of estimation of array signal processing cannot be utilized. In the paper, the fast algorithm of joint polarization-DOA estimation is developed for irregular array under coherent sources. Aiming at the disadvantage that the polarization smoothing algorithm destroys the polarization information, the generalized subspace fitting algorithm is studied which separates the spatial angle and the polarization angle estimation. In order to fix the problem of excessive calculation of generalized subspace fitting algorithm, the oblique projection algorithm is studied. The polarization vector of the bearing signal can obtained through projection algorithm with less computational effort. Simulation proves the effectiveness of the proposed algorithms.