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A new algorithm, called generalized covariance differencing (GCD), is proposed for direction of arrival (DOA) estimation in the presence of coherent sources and unknown nonuniform noise. By using the difference between the forward-backward spatial smoothing matrix and its complex conjugation, the GCD method constructs a generalized covariance matrix, which can fully eliminate spatially nonuniform noise and fit for more general noise fields and low signal-to-noise ratio (SNR) environments. In addition, it can also resolve coherent and incoherent sources. The GCD covariance matrix is an imaginary-valued matrix which can reduce computational burden. By analyzing the characteristic of GCD, a rapid root-MUSIC method without eigendecomposition is also given which can further reduce computational complexity. Simulation results demonstrate that the GCD method can effectively eliminate nonuniform noise, and it possesses a lower SNR threshold as well as a smaller variance than that of conventional methods.