# Algorithmic Coverage Quantification and Visualization in Range-Free Sensor Networks
## 1 Introduction  
Coverage in wireless sensor networks (WSN) has been a major area of research, especially in recent years [1; 2; 3; 4; 5; 6; 7]. The present study proposes an innovative tool that combines satellite imagery with long-range, direction-only sensors (SRs) to effectively visualize and quantify coverage areas and thereby enhance the detection of new transmitters (TRs). Through our review of the existing literature, we encountered diverse methodologies that address the coverage problem in WSN [1; 2; 3; 4; 5; 6; 7]. Although various approaches to coverage optimization have been explored, none precisely aligns with our objectives. Many studies focus on maximizing coverage by placing numerous SRs capable of detecting signals over considerable distances. For example, a recent study [1] introduces the greedy placement based on the iterative Delaunay triangulation algorithm, which minimizes the number of SRs required for completely confident information coverage (CIC) in obstructed areas, thus offering superior efficiency and computational performance. Other studies, such as [4], view the WSN coverage as a decision-making problem, aiming to determine if every point in an area of interest (AoI) is adequately covered by a specified number of SRs. Various aspects are examined, including network deployment types, node-sensing models, and application attributes like energy-saving or connectivity. In the same study, the authors demonstrate efficiency in processing time by proposing an algorithm focused on assessing the sufficiency of SR coverage along the perimeter. Another critical aspect of WSNs is network lifetime optimization, considering the random distribution of SRs across an AoI. The authors in [8] propose an efficient metaheuristic-based method (mutant grey wolf optimizer) that operates in an environment-aware manner to deploy a large number of SRs,achieving maximum coverage while maintaining connectivity between the SRs. However, a closer examination of their work reveals that such algorithms are best suited for WSNs where the monitored areas use a medium-to-large number of SRs, typically characterized by very short sensing ranges, often shorter than their transmission ranges. While these algorithms effectively maximize coverage, they do so at the cost of deploying hundreds of interconnected SRs. In our scenario, there is no need for communication between the SRs, as they are connected to the network independently, with their primary goal being to locate unknown TRs within their monitoring area. One survey [6] emphasizes the prevalence of partial or probabilistic coverage problems in real-world applications; this study explores strategies for maximizing coverage quality and network lifespan while minimizing the number of SR nodes. The authors in [3] conduct an exhaustive taxonomy of coverage techniques in WSNs while also considering other critical parameters such as connectivity, power consumption, scalability, accuracy with respect to the type of coverage (area, point or barrier). Upon reviewing relevant studies (please also refer to [5]), we considered multilateration and triangulation as primary methods for determining the position of TRs. Both triangulation and multilateration are methods used for determining the location of devices in wireless SR networks, but they differ in their underlying principles, accuracy, complexity, and requirements. Triangulation involves measuring the angles of arrival (AoA) of signals from the TR to multiple reference SRs [9], while multilateration involves measuring the distance between the TR and multiple reference SRs. Given our specific scenario with few SRs and long-distance coverage requirements, received signal strength emerged as the most suitable technique, as it remains unaffected by line-of-sight constraints and is capable of real-time localization with resilience to malicious interference.