This paper presents a novel approach for indoor acoustic source localization using sensor arrays. The proposed solution starts by defining a generative model, designed to explain the acoustic power maps obtained by Steered Response Power (SRP) strategies. An optimization approach is then proposed to fit the model to real input SRP data and estimate the position of the acoustic source. Adequately fitting the model to real SRP data, where noise and other unmodelled effects distort the ideal signal, is the core contribution of the paper. Two basic strategies in the optimization are proposed. First, sparse constraints in the parameters of the model are included, enforcing the number of simultaneous active sources to be limited. Second, subspace analysis is used to filter out portions of the input signal that cannot be explained by the model. Experimental results on a realistic speech database show statistically significant localization error reductions of up to 30% when compared with the SRP-PHAT strategies.