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

TL;DR

This paper introduces a statistical framework for localizing targets using vision-based range measurements to landmarks, addressing landmark ambiguity and providing probabilistic analysis for noisy data.

Contribution

It models landmarks as a Poisson point process and demonstrates that three range measurements suffice for unique localization in 2D, even with indistinguishable landmarks.

Findings

Three noise-free range measurements are sufficient for unique landmark identification in 2D.

The framework accounts for measurement noise and characterizes the probability of correct landmark identification.

Landmark ambiguity can be resolved using geometric constraints and probabilistic modeling.

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.