Stochastic Geometry Analysis of Localizability in Vision-Based Geolocation Systems
Stochastic Geometry Analysis of Localizability in Vision-Based Geolocation Systems
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DOI：
10.1109/ieeeconf59524.2023.10477066
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发表时间：
2023-10
期刊：
影响因子：
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通讯作者：
Student Member Ieee Haozhou Hu;F. I. Harpreet S. Dhillon;F. I. R. Michael Buehrer
中科院分区：
文献类型：
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作者：
Student Member Ieee Haozhou Hu;F. I. Harpreet S. Dhillon;F. I. R. Michael Buehrer
本文采用随机几何工具来严格分析基于视觉的地理定位系统的性能。尽管基于视觉的定位算法取得了重大进展，但其数学基础尚未得到深入探讨，而这正是本文的主要目标。由于传感器分辨率、先验信息的详细程度和计算资源的限制，我们可能无法区分外观相似的地标，例如树木、灯柱和公交车站。虽然使用单个非唯一地标无法准确确定绝对目标位置，但如果目标可以看到其在地图上的几何位置是唯一的多个地标，则可以获得近似定位。将这些难以区分的地标的位置建模为泊松点过程 (PPP)，我们开发了一种全新的方法来分析这种情况下的定位性。我们将定位能力定义为目标从视觉信息中确定其周围无法区分的正确地标集的能力。我们的分析表明，当地标强度趋于无穷大时，可定位概率接近 1，这意味着在此限制范围内可以实现无差错定位。
This paper employs stochastic geometry tools to rigorously analyze the performance of vision-based geolocation systems. Despite significant algorithmic advances in vision-based positioning, its mathematical underpinnings have not been explored in depth, which is the main objective of this paper. Due to limitations in sensor resolution, the level of detail in prior information, and computational resources, we may not be able to differentiate between landmarks that are similar in appearance, such as trees, lampposts, and bus stops. While one cannot accurately determine the absolute target position using a single non-unique landmark, it is possible to obtain an approximate position fix if the target can see multiple landmarks whose geometric placement on the map is unique. Modeling the locations of these indistinguishable landmarks as a Poisson point process (PPP), we develop a fundamentally new approach to analyze localizability in this setting. We define localizability as the ability of the target to determine the correct set of indistinguishable landmarks around it from the visual information. Our analysis reveals that the localizability probability approaches one when the landmark intensity tends to infinity, which means that error-free localization is achievable in this limiting regime.