Outlier identification for TOA-based source localization in the presence of noise

Although source localization has attracted great deal interest from the scientific community, the subject of localization in the presence of outliers has yet to receive proper attention. In many real life applications, some of the measurements are corrupted by outliers which may cause large estimation errors. Therefore, it is important to identify those outliers in order to remove the corrupted measurements from the data. Although known methods for outliers detection achieve good results, their complexity is usually high. We rely on sparse methods in order to identify and remove the outliers and obtain improved localization accuracy. We present models of Time-Of-Arrival (TOA) measurements affected by outliers and noise. We use the ℓ1 norm as a penalty function. Linear programming (LP) with the addition of threshold is used in order to detect the outliers. We prove that despite the additive noise, perfect detection of the outliers is possible when the amplitudes of the outliers are larger than a given value. The main contribution of this work is the development of a simple efficient method for outlier detection in source localization models when additive noise is present.