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We present a novel solution to the problem of estimating the array response of the signal of interest (SOI) in case it is constrained to lie in a known subspace, aimed at coping with model errors in the known subspace. The solution is based on a novel formulation of the problem, targeted at matching the error-contaminated model-based signal subspace to its sampled-data counterpart. The solution turns out to minimize the angle between these two subspaces, which is intuitively very pleasing. We solve the problem for three different characterization of the spatial interference: (i) the spatial interference is known, (ii) the spatial interference is unknown, and (iii) the spatial interference is constrained to lie in a known subspace. We present a closed-form solution for the first case and iterative solutions for the other two cases. Based on these solutions, we derive the corresponding estimators for the SOI's waveform and their signal-to-interference+noise ratio (SINR). Simulation results, demonstrating the superiority of the derived solutions over the corresponding deterministic maximum likelihood (DML) solutions, are included.