Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable, applications require localization methods that assume minimal knowledge on the noise distribution. We present a scalable algorithm delimiting a tight superset of all possible target locations, assuming range measurements to known landmarks, contaminated with bounded noise and unknown distributions. This superset is of primary interest in robust statistics since it is a tight majorizer of the set of Maximum-Likelihood (ML) estimates parametrized by noise densities respecting two main assumptions: (1) the noise distribution is supported on a ellipsoidal uncertainty region and (2) the measurements are non-negative with probability one. We create the superset through convex relaxations that use Linear Fractional Representations (LFRs), a well-known technique in robust control. For low noise regimes the supersets created by our method double the accuracy of a standard semidefinite relaxation. For moderate to high noise regimes our method still improves the benchmark but the benefit tends to be less significant, as both supersets tend to have the same size (area).

翻译：定位目标在许多应用中是关键所在,比如在高吸量现实世界情景中,例如探测人类或车辆网络中的障碍。在无法准确统计测量噪音的准确数据的情况下,应用需要当地化方法,假设对噪音分布知之甚少。我们提出了一个可扩缩的算法,划定所有可能的目标地点的紧紧超集,假设对已知的地标进行范围测量,受封闭噪音和未知分布的污染。这个超集对稳健的统计最为感兴趣,因为它是一套由噪音密度而形成的最大共享(ML)估计数的紧凑主力,这一套估计数与以下两个主要假设有关:(1)噪音分布在单线性不确定区域得到支持,(2)测量结果与概率一无关。我们通过使用线性分流表示(LFFRs)这一广为人所熟知的控制技术来创建超集。对于低噪音系统来说,我们的方法产生的超集是标准的半定调的精确度的两倍。对于中度至高噪音系统来说,我们的方法仍然在改进基准,但最高的利益往往不那么明显。