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A new robust adaptive processing algorithm is proposed for speech parameters estimation in noisy environments; it is based on the extended least squares (ELS) method with running spectrum filtering (RSF). By utilizing RSF, we can retain speech characteristics while noise is effectively eliminated. Then, by using ELS, formants of ARMA parameters can be estimated accurately. In experiments with real speech contaminated by white Gaussian noise, it is shown that the proposed method provides robust spectrum estimation against additive noise.