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The Steered Response Power - Phase Transform (SRP-PHAT) algorithm has been shown to be one of the most robust sound source localization approaches operating in noisy and reverberant environments. However, its practical implementation is usually based on a costly fine grid-search procedure, making the computational cost of the method a real issue. In this letter, we introduce an effective strategy that extends the conventional SRP-PHAT functional with the aim of considering the volume surrounding the discrete locations of the spatial grid. As a result, the modified functional performs a full exploration of the sampled space rather than computing the SRP at discrete spatial positions, increasing its robustness and allowing for a coarser spatial grid. To this end, the Generalized Cross-Correlation (GCC) function corresponding to each microphone pair must be properly accumulated according to the defined microphone setup. Experiments carried out under different acoustic conditions confirm the validity of the proposed approach.