We present a novel and computationally-efficient solution to the localization of multiple sources with known waveforms, based on array response matching. We first derivethe multi-dimensional array response matching (ARM) solution,which amounts to a minimization problem involving the location of the sources. To simplify the computational complexity, we derive a 1-dimensional version, which is closely related to the MVDR solution. We then introduce a linearly constrained version of this solution and apply it to exploit a-priori knowledge regarding the waveforms of the sources. The proposed solution involves only a 1-dimensional search and is therefore computationally much simpler than the corresponding maximum likelihood (ML) solution, which involves an iterative multi-dimensional search. Simulation results demonstrating the close similarity in performance of the proposed solution and the ML solution, are included.