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We investigate spatial filtering techniques for interference removal in multichannel radio astronomical observations. The techniques are based on the estimation of the spatial signature vector of the interferer from short-term spatial covariance matrices followed by a subspace projection to remove that dimension from the covariance matrix, and by further averaging. The projections will also modify the astronomical data, and hence a correction has to be applied to the long-term average to compensate for this. As shown by experimental results, the proposed technique leads to significantly improved estimates of the interference-free covariance matrix.