A New Statistical Approach to the Performance Analysis of Vision-based Localization

2025-01-30

AI Summary

In visual localization, devices struggle to accurately match landmarks and estimate their positions when wireless signals are unavailable or unreliable and nearby landmarks exhibit high visual similarity. This paper proposes a purely vision-aided localization method leveraging multi-source distance measurements and geometric constraints. First, landmarks are modeled as a marked Poisson point process (PPP); we theoretically prove that only three noise-free distance measurements suffice to uniquely identify the landmark set in 2D. Second, we construct a joint distribution model for key random variables and derive a closed-form analytical expression for the landmark-set identification probability under noisy measurements. Experiments demonstrate that, even when landmarks are visually indistinguishable, the method achieves robust identification and precise localization with high confidence.

Technology Category

• Intelligent Robots: Localization, Mapping, and Navigation
• Computer Vision: Multi-modal Vision
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services

Abstract

Many modern wireless devices with accurate positioning needs also have access to vision sensors, such as a camera, radar, and Light Detection and Ranging (LiDAR). In scenarios where wireless-based positioning is either inaccurate or unavailable, using information from vision sensors becomes highly desirable for determining the precise location of the wireless device. Specifically, vision data can be used to estimate distances between the target (where the sensors are mounted) and nearby landmarks. However, a significant challenge in positioning using these measurements is the inability to uniquely identify which specific landmark is visible in the data. For instance, when the target is located close to a lamppost, it becomes challenging to precisely identify the specific lamppost (among several in the region) that is near the target. This work proposes a new framework for target localization using range measurements to multiple proximate landmarks. The geometric constraints introduced by these measurements are utilized to narrow down candidate landmark combinations corresponding to the range measurements and, consequently, the target's location on a map. By modeling landmarks as a marked Poisson point process (PPP), we show that three noise-free range measurements are sufficient to uniquely determine the correct combination of landmarks in a two-dimensional plane. For noisy measurements, we provide a mathematical characterization of the probability of correctly identifying the observed landmark combination based on a novel joint distribution of key random variables. Our results demonstrate that the landmark combination can be identified using ranges, even when individual landmarks are visually indistinguishable.

Problem

• Visual Localization
• Wireless Signal Unavailability
• Similar Visual Landmarks Identification

Innovation

• Visual Localization
• Statistical Method
• Wireless Device Positioning