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The weighted local polynomial approximation (LPA) of time-varying direction-of-arrival is exploited in order to derive a new form of beamforming for localization of moving sources. The weights are defined by the sample correlation matrix of observations. This new adaptive LPA beamformer demonstrates an improved performance as compared with its non-adaptive counterpart. The proposed technique can be viewed as a non-stationary extension of the popular Capon minimum variance beamformer. In this way it belongs to the class of high-resolution adaptive methods. [Copyright &y& Elsevier]