# Topology-Aware Anchor Node Selection Optimization for Enhanced DV-Hop Localization in IoT
## 1 Introduction  
As a key component of next-generation information technology, the Internet of Things (IoT) connects physical objects to the Internet via information-sensing devices, forming a ubiquitous network architecture [1]. It bridges the physical and digital worlds, enabling seamless data exchange and communication among devices. This endows systems with intelligent capabilities, including identification, localization, tracking, monitoring, and management. Currently, IoT technology is widely applied across diverse domains--such as smart homes, intelligent transportation, industrial automation, and healthcare--playing a vital role in each [2]. Node localization plays a central role in the core technological framework of the IoT [3]. Accurate determination of IoT device locations is essential for implementing various IoT applications. As a foundational service for environmental sensing, data association, and decision-making optimization, node localization defines the spatial awareness capability of IoT systems. Its performance directly impacts the effectiveness and reliability of IoT applications. Node localization techniques are generally classified into two categories based on their principles and implementation: range-based and range-free approaches [4]. Range-based methods estimate inter-node distances by measuring physical parameters such as signal strength, time delay, or angle. Representative techniques include Time of Arrival (TOA) [5], Time Difference of Arrival (TDOA) [6], Received Signal Strength Indicator (RSSI) [7], and Angle of Arrival (AOA) [8]. The TOA method calculates distance by measuring the time required for a signal to travel from the transmitting node to the receiving node. It provides high localization accuracy but demands strict time synchronization. The TDOA method determines location by measuring the arrival time differences at multiple receivers, effectively mitigating synchronization errors. The RSSI method estimates distance based on signal strength attenuation, but its accuracy is highly susceptible to environmental interference. The AOA method determines location by measuring the angle of signal arrival; however, it requires specialized hardware and is sensitive to interference in complex environments. In general, while range-based techniques offer higher accuracy, they involve greater complexity and higher implementation costs. Range-free localization techniques do not require precise distance measurements or additional hardware. Instead, they estimate positions based on network topology or other contextual information. These methods are cost-effective but typically provide lower localization accuracy. Several range-free localization methods have been proposed, including DV-Hop [9], centroid localization [10], fingerprint-based localization [11], and the Approximate Point in Triangulation Test (APIT) [12]. The core principle of DV-Hop is to estimate unknown node positions by computing the number of hops and the average distance per hop. Centroid localization estimates the position of an unknown node as the geometric centre of nearby anchor nodes. Fingerprint-based localization constructs a fingerprint database by collecting signal characteristics at known reference points, and estimates the node position by matching current signal features to those in the database. The APIT algorithm estimates a node position by checking whether it lies within the triangle formed by three anchor nodes. Compared to other range-free localization methods, the DV-Hop algorithm requires only inter-node communication to perform localization. This characteristic offers significant advantages in hardware requirements, implementation complexity, and network scalability, making DV-Hop a prominent method among range-free localization techniques. The DV-Hop algorithm consists of three main stages: hop count calculation, average hop distance estimation, and position determination of unknown nodes.