位置未知距离传感器对目标形状可观测性的几何分析
Geometric Analysis of Observability of Target Object Shape Using Location-Unknown Distance Sensors
摘要：
我们几何分析的问题，通过使用随机分布的距离传感器，其位置是未知的平面上的二维目标对象的形状和大小相关的参数估计。在几何概率分析的基础上，我们讨论了这些参数的可观测性：哪些参数是可以估计的，以及估计这些参数所需要的条件。对于凸目标对象，其大小和周长是可观测的，而其他参数是不可观测的。对于一般多边形目标对象，除了其大小和周长之外，凸度也是可观察的。当满足一定条件时，凹顶点的相关参数是可观测的。我们还提出了一种用于估计目标对象的凸性和目标对象的周长的方法。
英文摘要：
We geometrically analyze the problem of estimating parameters related to the shape and size of a two-dimensional target object on the plane by using randomly distributed distance sensors whose locations are unknown. Based on the analysis using geometric probability, we discuss the observability of these parameters: which parameters we can estimate and what conditions are required to estimate them. For a convex target object, its size and perimeter length are observable, and other parameters are not observable. For a general polygon target object, convexity in addition to its size and perimeter length is observable. Parameters related to a concave vertex can be observable when some conditions are satisfied. We also propose a method for estimating the convexity of a target object and the perimeter length of the target object.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
