We present a novel solution to the problem of direction-of-arrival estimation, aimed at coping with the critical problem of model errors. Unlike the existing approaches to this problem, the proposed solution copes with model errors implicitly, without any parameterization or statistical modeling of these errors. The solution is based on matching the error-contaminated model-based signal subspace to its noisy sampled-data-based counterpart, and is referred to as signal subspace matching (SSM) solution. The resulting multidimensional optimization problem amounts to finding the directions-of-arrival for which the angle between these two subspaces is minimal. To simplify the computational load involved in this multidimensional optimization problem, we derive an iterative solution involving only 1-dimensional optimization, which is inspired by the alternating projection (AP) solution to the deterministic maximum likelihood (DML) cost function. Simulation results demonstrating the performance are included. The results show the clear performance superiority of the SSM solution over the DML and MUSIC solutions, especially in the case of high modeling errors and in challenging scenarios involving low number of samples, low angular separation and highly correlated signals.