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This paper proposes a two-channel noise estimator for speech enhancement in a highly nonstationary environment. The proposed noise estimator utilizes a spatial filter which has a capability of extracting noise information even in a speech presence region. We exploit a first-order recursion method with time-frequency varying smoothing coefficients to accurately estimate a noise power spectral density (PSD) in both slowly and rapidly varying regions. The smoothing coefficients are determined by measuring the nonstationarity factor of noise, e.g., degree of noise variation. The nonstationarity factor is derived through a statistical assumption of stationary background noise, which does not need any assumption on the type of nonstationary noise. Since the proposed method efficiently estimates the noise PSD both in stationary and nonstationary regions, the enhanced speech obtained by applying the proposed algorithm to the two-channel enhancement system shows superior performance to conventional approaches in various noise environments.