Estimating time-difference-of-arrival (TDOA) remains a challenging task when acoustic environments are reverberant and noisy. Blind channel identification approaches for TDOA estimation explicitly model multipath reflections and have been demonstrated to be effective in dealing with reverberation. Unfortunately, existing blind channel identification algorithms are sensitive to ambient noise. This papers hows how to resolve the noise sensitivity issue by exploiting prior knowledge about an acoustic room impulse response (RIR), namely, an acoustic RIR can be modeled by a sparse-nonnegative FIR filter. This paper shows how to formulate a single-input two-output blind channel identification into a least square convex optimization, and how to incorporate the sparsity and nonnegativity priors so that the resulting optimization remains convex and can be solved efficiently. The proposed blind sparse-nonnegative (BSN) channel identification approach for TDOA estimation is not only robust to reverberation, but also robust to ambient noise, as demonstrated by simulations and experiments in real acoustic environments.