Accuracy is the vital indicator in location estimation used in many scenarios, such as warehousing, tracking, monitoring, security surveillance, etc., in a wireless sensor network (WSN). The conventional range-free DV-Hop algorithm uses hop distance to estimate sensor node positions but has limitations in terms of accuracy. To address the issues of low accuracy and high energy consumption of DV-Hop-based localization in static WSNs, this paper proposes an enhanced DV-Hop algorithm for efficient and accurate localization with reduced energy consumption. The proposed method consists of three steps: first, the single-hop distance is corrected using the RSSI value for a specific radius; second, the average hop distance between unknown nodes and anchors is modified based on the difference between actual and estimated distances; and finally, the least-squares approach is used to estimate the location of each unknown node. The proposed algorithm, named Hop-correction and energy-efficient DV-Hop (HCEDV-Hop), is executed and evaluated in MATLAB to compare its performance with benchmark schemes. The results show that HCEDV-Hop improves localization accuracy by an average of 81.36%, 77.99%, 39.72%, and 9.96% compared to basic DV-Hop, WCL, improved DV-maxHop, and improved DV-Hop, respectively. In terms of message communication, the proposed algorithm reduces energy usage by 28% compared to DV-Hop and 17% compared to WCL.
<abstract><p>In this manuscript, using the idea of $ b $-simulation functions, certain common fixed point results via generalized $ \Im_b $-contractions are investigated in the context of b-metric spaces. These findings generalize and supplement various numbers of established results from the existing literature. Examples and applications are also provided for the authenticity of the presented work. Besides, we ensure the existence of a unique common solution for systems of Volterra-Hammerstein integral and Urysohn integral equations, respectively, by applying the established results.</p></abstract>
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