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).

中文翻译：

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有界噪声的鲁棒定位：通过线性分数表示创建可能目标位置的超集

定位目标是许多应用程序的关键，即在高风险的现实世界场景中，例如检测车辆网络中的人或障碍物。在无法获得测量噪声的精确统计数据的情况下，应用程序需要假定对噪声分布了解最少的定位方法。我们提出了一种可扩展的算法，它界定了所有可能目标位置的紧密超集，假设距离测量到已知地标，被有界噪声和未知分布污染。该超集对稳健统计具有重要意义，因为它是由噪声密度参数化的最大似然 (ML) 估计值集的紧大化器，该估计值由尊重两个主要假设的噪声密度参数化：(1) 噪声分布在椭球不确定区域上得到支持，并且 (2) 测量结果是非负的，概率为 1。我们通过使用线性分数表示 (LFR) 的凸松弛来创建超集，这是鲁棒控制中众所周知的技术。对于低噪声状态，我们的方法创建的超集是标准半定松弛精度的两倍。对于中等到高噪声的情况，我们的方法仍然改进了基准，但好处往往不太显着，因为两个超集往往具有相同的大小（面积）。