In this paper, the problem of multiple speaker localization via speech separation based on model-based sparse recovery is studies. We compare and contrast computational sparse optimization methods incorporating harmonicity and block structures as well as autoregressive dependencies underlying spectrographic representation of speech signals. The results demonstrate the effectiveness of block sparse Bayesian learning framework incorporating autoregressive correlations to achieve a highly accurate localization performance. Furthermore, significant improvement is obtained using ad-hoc microphones for data acquisition set-up compared to the compact microphone array.