## 1 Introduction
The phase difference and angle measurements are highly dependent on the signal quality, and indoor noise or multipath propagation can distort the results. Indoors, reflections from walls, ceilings, and furniture can cause errors, creating false paths and complicating accurate direction determination. These factors limit the applicability of AoA and interferometry methods in real-world conditions, especially in indoor localization. Consequently, utilizing the received signal strength indicator (RSSI) is often more advantageous. Wireless RSSI technology has proven to be an effective method for range determination, due to its simplicity and practicality. By measuring the signal strength received from a transmitter, RSSI enables the estimation of distance between devices without the need for complex or costly sensors [25]. Recently, ML technologies have advanced significantly to enhance localization accuracy. These approaches facilitate the efficient processing of large volume data while considering various factors that influence the precision of location determination [26]. ML techniques enable the usage of RSSI signals from LoRa devices for fingerprint-based localization. The indoor fingerprint positioning method relies on the establishment of a database that contains pre-measured signal levels from various access points located in designated areas within the premises [27]. Under ideal indoor conditions, the distance can be estimated using RSSI measurements through the following empirical equation:  
\[RSSI=-10n\text{log}\left(d\right)+C \tag{1}\]where \(d\) represents the distance from the deployed sensor node to the base node, \(n\) denotes the path loss exponent, and \(C\) is a constant [28]. However, in real-world conditions, signals are affected by numerous interferences, including multipath reception caused by reflections and diffraction, interference from other signals within the frequency band, shadowing, and other factors that reduce accuracy. To address this issue, a variety of algorithms have been proposed [29], which effectively filter out noise and aim to minimize the impact of these interfering factors. While RSSI-based localization has certain drawbacks, including potential errors due to environmental factors, advancements in machine learning and statistical modeling techniques are enhancing the accuracy of these systems. As a result, RSSI-based localization represents a significant and promising area of research with the potential to impact a wide range of applications, including asset monitoring, inventory management, healthcare, and emergency response [30; 31] to provide wireless communication over long distances with low data rates. In [32], experiments were conducted using trilateration without continuous retraining to demonstrate the capabilities of LoRa for localizing static nodes indoors. In [33], a localization method leveraging LoRa technology is proposed, incorporating Gaussian filtering for data preprocessing to eliminate significant errors. An analysis of the current literature reveals a notable trend: wireless sensor networks that employ machine learning methods are pivotal in indoor localization technologies. The fingerprint-based localization method, which relies on measuring RSSI, offers a cost-effective and energy-efficient solution. Various approaches to data preprocessing are discussed, including the application of different filters and techniques aimed at reducing noise and enhancing signal accuracy. However, much of the existing research concentrates on static nodes and data collection, neglecting the dynamics of mobile nodes. In traditional fingerprinting methods, RSSI measurements are taken multiple times using a stationary node placed at predetermined grid points, with a fixed distance between the nodes. The accuracy of localizing moving nodes decreases due to variations in their relative positions in space during data transmission. The main contributions of this work are as follows:  
1.