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We investigate an alternative model for signals encountered in acoustic environments to the traditional Gaussian process. The sound signals in this case are assumed to be sub-Gaussian of impulsive nature. The noise encountered in these environments predominantly stems from reverberation or multipath effects, which makes it significantly dependent on the source. Hence, the noise is also modeled as jointly sub-Gaussian. The Levy alpha-stable distribution, of characteristic exponent 0.5 and index of symmetry 1, is used together with a multivariate Gaussian density to derive the sub-Gaussian process. Based on this density, the stochastic Maximum Likelihood (ML) estimator is formulated. A separable solution of the estimator is given. Subsequently, simulations demonstrating the performance gains relative to the Gaussian-based ML estimator are provided, as well as a comparison of the two methods on localization of real sounds gathered with a 20- and 41-microphone arrays.