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In speech enhancement, noise power spectral density (PSD) estimation plays a key role in determining appropriate de-nosing gains. In this paper, we propose a robust noise PSD estimator for binaural speech enhancement in timevarying noise environments. First, it is shown that the noise PSD can be numerically obtained using an eigenvalue of the input covariance matrix. A simplified estimator is then derived through an approximation process, so that the noise PSD is expressed as a combination of the second eigenvalue of the input covariance matrix, the noise coherence, and the interaural phase difference (IPD) of the input signal. Later, to enhance the accuracy of the noise PSD estimate in time-varying noise environments, an eigenvalue compensation scheme is presented, in which two eigenvalues obtained in noise-dominant regions are combined using a weighting parameter based on the speech presence probability (SPP). Compared with the previous prediction filter-based approach, the proposed method requires neither causality delays nor explicit estimation of the prediction errors. Finally, the proposed noise PSD estimator is applied to a binaural speech enhancement system, and its performance is evaluated through computer simulations. The simulation results show that the proposed noise PSD estimator yields accurate noise PSD regardless of the direction of the target speech signal. Therefore, slightly better performance in quality and intelligibility can be obtained than that with conventional algorithms.