## 2 Related Works
### Anchor-Free Localization
The sensors determined their positions based on the vertical elevation angle of the antenna, the horizontal rotation angle, and distance information from the node to the base station antenna. In comparison, the CRSSA approach diverges significantly by being designed to work with the inherent capabilities of almost all commercial sensors, eliminating the need for specialized hardware. This adaptability makes the CRSSA not only more cost-effective but also more versatile, as it can be implemented in a wider range of environments without the need for complex setups or additional equipment. In [17], the authors utilized the LDLLA approach and introduced the sunflower algorithm (SFO) for implementing range-free anchor-free localization in WSNs using distance vector-hop (Dv-Hop) and considering the distance vector routing protocol. This method adopted a radio channel model based on free space attenuation, a simplification that may not align with the complexities of real-world signal propagation in various environments. While this approach provides a basic framework, it potentially overlooks the nuanced signal behaviors often encountered in environments with physical obstructions or interference. CRSSA diverges from this conventional one, adopting a more realistic view of signal propagation behavior in WSN environments. CRSSA enhances the accuracy and reliability of localization, adapting to the diverse and dynamic nature of signal interactions. This adaptability is particularly crucial in real-world applications where signal propagation can be unpredictable and complex. Table 1 summarizes anchor-free localization studies as well as used techniques and approaches. In localization techniques utilizing RSS, it is essential to consider the precision and variability of the signal across different fading models. However, the majority of localization studies in WSN assume a propagation model where the received power is related to distance by a path loss model with zero-mean Gaussian noise, such as in [18; 19; 20]. An anchor free algorithm for one-hop nodes is proposed in [21], where it computes the inter-node distances based on RSS and the centroid techniques. The nodes are then located by using the average of the inter-node distances. However, this algorithm does not provide highly accurate position estimates, especially in situations with a high degree of measurement noise or non-line-of-sight conditions, and it does not take into account signal propagation characteristics. An anchor-based hybrid localization algorithm in the absence of knowledge of the transmit power and PLE value is presented in [18]; these parameters are estimatedusing a Kalman filter, and an unknown node is localized based on RSS/AOA (angle of arrival) information. The authors in [19] proposed a method that utilized the RSS value at the unknown node and the most valuable player algorithm to localize it in the grid system. Also, in [20], the authors proposed anchor-based range-free algorithms based on RSS measurements, namely support vector regression (SVR) and SVR + Kalman filter (KF). On the other hand, many studies, including [22; 23], emphasize the importance of accurate signal propagation models in wireless communication systems, especially when accounting for phenomena like multi-path fading and shadowing effects. Traditional models like the lognormal distribution for large-scale shadowing effects [24] and the gamma distribution as an alternative [25] have their limitations. In realistic environments, where these phenomena coexist, a composite fading distribution becomes necessary. For our CRSSA method, we have utilized the Nakagami-m model, as detailed in [26; 27; 28]. This model is particularly effective in capturing the variability of signal fading in diverse environmental conditions. Employing the Nakagami-m model enhances the adaptability and accuracy of the CRSSA, ensuring its effectiveness across a range of WSN scenarios and solidifying it as a robust solution for the complexities of real-world signal propagation.