## 1 Introduction
Continuous development and improvement of data-fusion algorithms and strategies are essential to optimize the performance and reliability of wireless sensor networks in various applications [18]. Integrating sensor data through fusion algorithms is critical to providing enhanced and reliable information in various fields, including medical diagnostics, industrial monitoring, and environmental sensing [19; 20; 21]. The efficient timing sync protocol for sensor networks (TPSN) described in [22] creates a hierarchical structure in the network and performs synchronization to create a global time scale. Methods and protocols for synchronization, emphasizing the need for a new class of secure synchronization protocols that are scalable and energy efficient, were revealed by researchers in [23]. In [24], a comprehensive review that analyzes wireless sensor networks for structural health monitoring from different points of view is presented. Time synchronization is a critical issue in wireless sensor networks, and a study demonstrates that an optimized multilayer time-synchronized MAC with relay nodes shows better results than state-of-the-art nonsynchronized algorithms [25]. Wireless sensor networks have three key performance metrics: reliability, power consumption, and latency. The time-slotted channel-hopping technique (TSCH) introduced in the IEEE 802.15.4 standard compromises these indicators. With the help of a mathematical model based on real measurements, the authors characterize the behavior of the network and its interaction with the environment. The research showed that optimizing one of the indicators can lead to the degradation of others [26]. Data transmission in communication networks often has to meet certain deadlines. The authors developed a probabilistic model that allows one to determine the delay of sensor data in a wireless sensor network depending on the routing used. The model provides a tool for routing delay analysis, which allows one to compare the probability of missing a deadline between different routing policies [27]. The importance of time synchronization in wireless sensor networks is emphasized due to its role in accuracy, energy consumption, and computational complexity, where the main emphasis is on the energy-efficient beacon-free scheme [28]. This idea is further extended to WSNs with a low level of activity, where a new synchronization algorithm is presented [29]. To synchronize network units regarding the common clock, the authors used additional reference data packets sent by the reference node. Temperature deviations also play a part in the network-synchronization algorithms [30]. Temperature fluctuations affect the accuracy of the time calculation, according to which the network is synchronized. The authors proved that adjusting local units' time according to predefined dependency between outside temperatures and time drift makes it possible to increase network-synchronization accuracy. Similarly, synchronization in underwater sensor networks could use the Doppler effect to increase accuracy [31]. An adaptive walking detection method based on inertial sensors uses data fusion to improve detection accuracy, as presented in [32]. This data-fusion approach is extended to a support system for firefighters, where different sensors are used to monitor their gait [33] and classify predefined events using the Hiden Markov model and a neural network. Data fusion is also proven to be essential for the health monitoring of composite aircraft structures [34] and vehicle networks for creating smart cities based on 6G technology [35], offering more advanced data-synchronization capabilities. In the context of robotics, time synchronization is critical, especially for autonomous driving, where a system for precise synchronization has been developed [36]. For wireless body area networks, a new synchronization algorithm based on a fractional time approach is presented in [37]. It achieves more accurate time evaluation and minimizes energy consumption due to managing on-off stages.