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We treat the problem of beamforming for signal estimation in the presence of steering vector uncertainties, where the goal is to estimate a signal amplitude from a set of array observations. Conventional beamforming methods typically aim at maximizing the signal-to-interference-plus-noise ratio (SINR). Recently, a maximum likelihood (ML) approach was introduced that leads to an iterative beamformer. Here we suggest an expected least-squares (LS) strategy that results in a simple linear beamformer. We then demonstrate through simulations that the LS beamformer often performs similarly to the ML method in terms of mean-squared error and outperforms conventional SINR-based approaches.