Abstract. 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 are 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 data sets come from a heavy-tailed distribution, i.e., include outliers. Hence, we propose robustifying the existing inverse methods by adding a blind outlier-detection algorithm. The improved performance of our method is demonstrated on a real data set 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.
Abstract. 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.
Estimation of the quantities of harmful substances emitted into the atmosphere is one of the main challenges in modern environmental sciences. In most of the cases, this estimation requires solving a linear inverse problem. A key difficulty in evaluating the performance of any algorithm to solve this linear inverse problem is that the ground truth is typically unknown. In this paper we show that the noise encountered in this linear inverse problem is nonGaussian. Next, we develop an algorithm to deal with the strong outliers present in the measurements. Finally, we test our approach on three different experiments: a simple synthetic experiment, a controlled real-world experiment, and real data from the Fukushima nuclear accident.
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