Mathematical Models and Localization Algorithms Wireless Networks

Authors

DOI:

https://doi.org/10.18372/1990-5548.83.19874

Keywords:

wireless sensor networks, localization algorithms, DV-Hop algorithm, anchor-based calculation, MDS-MAP algorithm, received signal strength indicator, time of arrival, signal power optimization, multidimensional scaling, node localization, energy efficiency, mesh networks, distance measurement, root mean square error

Abstract

This paper comprehensively analyzes mathematical models and localization algorithms for wireless sensor networks deployed in resource-constrained environments. Precise node localization is crucial in ensuring the efficiency and reliability of various systems, including environmental monitoring, disaster response, industrial automation, and logistics tracking. Accurate spatial information enables context-aware data processing, improves routing efficiency, and enhances overall network performance.

The study focuses on several established and emerging localization techniques, including the Distance Vector-Hop (DV-Hop) algorithm, anchor-based positioning methods, and the Multidimensional Scaling (MDS-MAP) approach. These algorithms are assessed regarding localization accuracy, computational complexity, scalability, and energy consumption. A detailed review of mathematical models used for estimating distances—based on signal strength (RSSI), time of arrival (ToA), and time difference of arrival (TDoA)—is provided. Particular emphasis is placed on error minimization strategies using Kalman filters, smoothing algorithms, and hybrid measurement techniques. Furthermore, the influence of deployment-specific parameters such as node density, radio signal multipath propagation, environmental interference, antenna specifications, and frequency band selection is thoroughly examined. The simulation results demonstrate that the MDS-MAP algorithm achieves the highest localization precision, with root mean square error (RMSE) values below 1%, although it demands considerable computational resources. In contrast, more straightforward methods such as Distance Vector-Hop or heuristic-based algorithms show moderate accuracy but require fewer resources, making them suitable for devices with limited processing power and battery capacity. The study offers practical recommendations for optimizing node placement and localization configurations to balance precision and system overhead in real-world applications. The results are particularly relevant to scenarios where the infrastructure is limited or temporary and adaptability and robustness to environmental dynamics are essential. This work will be of significant interest to researchers, engineers, and system architects working in wireless sensor networks, particularly those developing localization solutions under operational constraints or in unpredictable environments. It contributes theoretical insights and applied guidance for improving localization efficiency and reliability in low-power distributed systems.

Author Biographies

Andriy Dudnik , Taras Shevchenko National University of Kyiv

Doctor of Engineering

Associate Professor

Department of Network and Internet Technologies

Vladyslav Fesenko , State Non-Profit Enterprise "State University "Kyiv Aviation Institute"

PhD student

Department of Telecommunication and Radio Electronic Systems

 

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Published

2025-04-09

Issue

Vol. 1 No. 83 (2025)

Section

TELECOMMUNICATIONS AND RADIO ENGINEERING

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