A Theoretical Analysis of Mobility Detection in Connectivity-Based Localization for Short-Range Networks

Sangwoo Lee,Sungjin Kim,Sunwoo Kim,Ilmu Byun

doi:10.3390/en14041162

Abstract

This paper presents a theoretical analysis of mobility detection in connectivity-based localization, which exploits connectivity information as range measurements to anchors at a known location, to investigate how well and how precise mobility can be detected with connectivity in short-range networks. We derive mobility detection, miss detection, and false alarm probabilities in terms of a mobility detection threshold, defined as the minimum distance to detect the mobility, under the shadow fading channel and arbitrary mobility models to take into account practical and general scenarios. Based on the derivations, we address the threshold determination with the criteria in the sense of the minimum average error from miss detection and false alarm. Numerical and simulation evaluations are performed to verify our theoretical derivations, to show that increasing anchor numbers can improve the mobility detection probability with a smaller detection threshold, and that the probabilities are bounded by the weights of miss detection and false alarm. This work is the first attempt at addressing the performance of mobility detection using connectivity, and it can be utilized as a baseline for connectivity-based mobility tracking.

Highlights

Connectivity-based localization has been highlighted for wireless networks with short-range communications (e.g., WiFi, Bluetooth, and Zigbee) where explicit range measurements such as time-of-arrival, time-difference-of-arrival, and angle-of-arrival are not available due to systematic and/or cost reasons or where the range measurements are likely to be severely corrupted due to environmental reasons [1]
The importance of connectivity-based localization is increasing with the fast-growing IoT (Internet-ofThings) applications based on device-to-device communication and mesh networking capabilities [2]
The determination of the optimal detection threshold was made with respect to the anchor number from the perspective of the average error cost minimization

Summary

Introduction

Connectivity-based localization has been highlighted for wireless networks with short-range communications (e.g., WiFi, Bluetooth, and Zigbee) where explicit range measurements such as time-of-arrival, time-difference-of-arrival, and angle-of-arrival are not available due to systematic and/or cost reasons or where the range measurements are likely to be severely corrupted due to environmental reasons [1]. It is obvious that as the dimension of the constraints increases, a smaller box is drawn and results in improvement in computational efficiency, and tracking accuracy They all have missed one important point: that the underlying assumption on the maximum movable distance can adversely affect the performance, and the worst case occurs when a node is not moving. We first provide a general framework of the connectivity-based mobility detection in terms of a mobility detection threshold Based on this framework, three performance metrics, which are mobility detection, miss detection, and false alarm probabilities, are defined and derived under the shadow fading channel model and arbitrary mobility models. N (u, Σ) represents a normal distribution with mean u and covariance Σ. φ(·) denotes the probability density function (PDF) of the standard normal distribution and Φ(·) is its cumulative distribution function (CDF)

System and Channel Models

Asymptotic Analysis

Threshold Determination for Minimizing the Average Error

Numerical Results and Discussion

Conclusions