## 1 Introduction  
As the key subsystem of train control system, the balise transmission system (BTS) completes the information transmission between ground balise and onboard equipment by means of electromagnetic induction, so as to realize train positioning and line information identification. The BTS has been widely used in the world's railway signal systems. Europe and China have issued specifications for BTS, which stipulate the conditions that BTS should meet [1; 2; 3]. However, with the deepening of international railway exchanges and the increasing use of transnational trains, the communication quality between the balise and the onboard equipment is facing new challenges. These balises and the onboard antenna unit (OAU) from different countries and manufacturers adopt different design concepts, which may lead to the loss of transmission performance due to unsatisfactory matching after these devices work together [4]. These problems further reduce the reliability of the BTS and threaten the safety of train operation [5]. Therefore, the electromagnetic coupling characteristics between the OAU and the balise of the BTS need to be fully analyzed. In recent years, some scholars have studied the electromagnetic coupling process of the BTS. In [6], the static model of balise uplink data transmission was established by the finite element method, and the electromagnetic field distribution of the process was obtainedby electromagnetic simulation. In [7], the dynamic process of uplink data transmission was modeled and analyzed using electromagnetic field theory, and the corresponding optimization suggestions were put forward from the perspective of installation height and installation mode between the OAU and the balise. According to the test method recommended by the standard, the electromagnetic coupling characteristics of BTS were tested and analyzed in [8]. The electromagnetic coupling model of the BTS was established in [9], and the reason for the induced voltage amplitude envelope of the onboard receiving antenna in the coupling process was analyzed. Reference [10] established the calculation model of the balise operating distance, and analyzed the influence of different installation modes on electromagnetic coupling characteristics. In [11], a transmission performance evaluation method based on an equivalent impedance model was proposed to monitor the downlink transmission quality of the BTS. In [12], a calculation model of the inductive voltage amplitude envelope of the balise downlink receiving antenna during the coupling process was established, and the sidelobe effect was analyzed using the model. In addition, Subset-036 provides some requirements for the BTS, but these requirements usually have a larger allowable range. However, although the electromagnetic coupling process of the BTS has been discussed and analyzed in the literature mentioned above, the problem of system matching under different engineering application conditions has not been completely solved. The influence of different installation modes, vertical distance, and lateral deviation between the OAU and the balise on the transmission characteristics of uplink telegram signal has not been fully studied. In addition, the intensity of downlink tele-powering signal also has an impact on the transmission characteristics of uplink telegram signal, but this has not been discussed in any literature. In order to fully understand the complex coupling relationship among various factors involved in the electromagnetic coupling process of the BTS and establish the electromagnetic coupling model that unifies the above factors, it is necessary to find a new research method to achieve this purpose. Digital twin (DT) is an important technology for portraying, simulating, optimizing, and visualizing the physical world in the information world. The concept of DT was first proposed by [PERSON] in 2003 [13], which was first applied in the aerospace field.