## 1 Introduction  
Indoor Positioning Systems (IPSs) are crucial in diverse fields, from emergency services to industrial automation [1]. The most used satellite technologies, like the Global Navigation Satellite System (GNSS) [2], are ineffective indoors due to signal attenuation caused by building materials and environmental factors [3]. Ultra-wideband (UWB) technology has been increasingly recognized as an efficacious strategy for IPSs due to its high accuracy, low transmission cost, and robustness to environmental perturbations [4]. The Federal Communication Commission (FCC) defines the UWB signal by one of the two conditions: (1) The signal bandwidth should be wider than 0.2 times the carrier frequency, or (2) the signal bandwidth should be wider than 500 MHz. The fine time resolution and broad bandwidth of UWB technology enable precise location tracking, making it superior to other IPSs like WiFi or Bluetooth [5], especially in complex indoor scenarios. For instance, [PERSON] et al. demonstrated UWB's capability to track athletes with an average error of 20 cm [6]. Similarly, [PERSON] et al. showcased the precision of UWB in static and dynamic item tracking within an indoor environment [7]. [PERSON] et al. introduced a system integrating BIM with UWB for accurate indoor navigation and robot tracking, enhancing construction efficiency and safety [8]. [PERSON], et al. [9] proposed a trust-assessment-based distributed localization algorithm that can achieve accurate localization. However, the accuracy of the UWB system is affected by various error sources. Notably, non-line-of-sight (NLOS) conditions can degrade positioning accuracy substantially due to signal obstruction, with errors up to several meters [10; 11]. Multipath propagation, due to NLOS signals in combination with the original LOS signal [12], introduces errors ranging from a few centimeters to over a meter [13], depending on environmental complexity [14]. Multipath error is more common but much easier to ignore, more difficult to avoid, and significantly impacts positioning accuracy. Additionally, synchronization errors between devices and clock drift can also contribute to inaccuracies, typically within tens of centimeters [15]. Several correction methods have been developed to mitigate these challenges. Kalman-filter-based algorithms are commonly used to minimize ranging errors [16; 17]. The twice correction algorithm, combining linear fitting and polynomial methods, enhances both static and dynamic positioning accuracy [18]. Multi-sensor data fusion techniques, such as integrating UWB with inertial measurement units (IMUs) and encoders, employ Kalman filtering to enhance positioning accuracy by leveraging the complementary strengths of different sensors [19]. Despite improvements, the complexity of sensor integration [20] and the need for extensive calibration [21] can limit these methods. NLOS identification and mitigation strategies aim to detect and correct the additional path length caused by obstacles [22], but they often require complex environmental modeling [23]. The development of neural networks has introduced new possibilities for error correction in UWB indoor positioning. Neural networks can learn complex patterns and relationships from data [24], which implies their capability to correct the nonlinear error characteristics in complicated environments. The neural network can be integrated into UWB-based algorithms and maintain a stable accuracy in NLOS scenarios [25]. Another study by [PERSON] et al. utilized deep learning algorithms, including multilayer perceptron (MLP) and convolutional neural networks (CNNs), to reduce ranging errors caused by multipath components [26]. However, one possible side effect of a complex network structure is that it always needs a large amount of data and a long training time, which also brings inconvenience to use. Furthermore, retrieving more accurate and reliable reference values for training neural networks is still a challenging issue for researchers.