Locating an object is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In such applications, pointwise estimates are not enough, and the full area of locations compatible with acquired measurements should be available, for robust and safe navigation. This paper presents a scalable algorithm for creating a superset of all possible target locations, given range measurements with bounded error. The assumption of bounded error is mild, since both hardware characteristics and application scenario impose upper bounds on measurement errors, and the bounded set can be taken from confidence regions of the error distributions. We construct the superset through convex relaxations that use Linear Fractional Representations (LFRs), a well-known technique in robust control. Additionally, we also provide a statistical interpretation for the set of possible target positions, considering the framework of robust estimation. Finally, we provide empirical validation by comparing our LFR method with a standard semidefinite relaxation. Our approach has shown to pay off for small to moderate noise levels: the supersets created by our method are tighter than the benchmark ones being about 20% smaller in size. Furthermore, our method tends to be tight because the size of the supersets is, on median terms, within a 3% margin of a lower bound computed via grid search.
翻译:对象定位在许多应用中是关键所在, 即在高吸量现实世界情景中, 比如探测人类或车辆网络中的障碍。 在这样的应用中, 点度估计不够, 并且应该提供与所获取测量相兼容的全部位置, 以稳健和安全的导航。 本文提供了一个可缩放的算法, 用于创建所有可能的目标位置的超集, 给定范围测量加上受约束的误差。 受约束的误差的假设是温和的, 因为硬件特性和应用程序情景都对测量误差施加了上限, 而约束的数据集可以从误差分布的信任区域中取出。 我们通过使用线形分流代表制( LFRs) 来构建超集, 这是一种众所周知的稳健控制技术。 此外, 我们还为一组可能的目标位置提供了一种统计解释, 考虑强度估计的框架 。 最后, 我们通过将我们的 LFR 方法与标准的半定型放松调度来提供实验性验证。 我们的方法证明, 小到中度的噪声率是来自错误分布的信任区域。 我们的方法所创造的超集比基准区更紧紧的宽,, 。 以20 % 以 的平的平的平的基底的平差的平差值 。