Emissions of harmful substances into the atmosphere are a serious environmental concern. In order to understand and predict their effects, it is necessary to estimate the exact quantity and timing of the emissions, from sensor measurements taken at different locations. There exists a number of methods for solving this problem. However, these existing methods assume Gaussian additive errors, making them extremely sensitive to outlier measurements. We first show that the errors in real-world measurement datasets come from a heavy-tailed distribution, i.e., include outliers. Hence, we propose to robustify the existing inverse methods by adding a blind outlier detection algorithm. The improved performance of our method is demonstrated on a real dataset and compared to previously proposed methods. For the blind outlier detection, we first use an existing algorithm, RANSAC, and then propose a modification called TRANSAC, which provides a further performance improvement.