A novel model for reverberant signals; robust maximum likelihood localization of real signals based on a sub-Gaussian model

We present a novel model for signals encountered in reverberant environments using the sub-Gaussian distribution that can describe both the impulsive nature of the signals and their inter-dependence. The proposed system can be viewed as one where the sources are stochastic and Gaussian and the transfer medium is varying in a highly impulsive manner, introducing the sub-Gaussian nature at the receiver or alternatively, the impulsive transformation to the signals can be viewed as part of the source model, creating a multivariate source signal whose components can not be independent, and is of impulsiveness equal to the one of the Cauchy distribution. We formulate the separable maximum likelihood solution to an array signal processing problem based on a derived sub-Gaussian density. We proceed to give both simulations and experimental results of the validity of the algorithm. In the experiments sound signals are played from loudspeakers in a room and localized with a microphone array and it is demonstrated that the localization based on the sub-Gaussian moded significantly outperforms the one based on the traditional Gaussian model.