## 2 System Principle  
### System Structure Composition  
The structure of the positioning system is shown in Figure 1. The system adopts the layout with two LCX cables, both laid along the tunnel walls in parallel. A Cartesian coordinate system is established with point A1 of LCX_1 as the origin, where the \(X\)-axisruns along the direction of LCX_1 (i.e., A1B1) and the \(Y\)-axis runs along the direction of A1A2. Both LCX cables have the length of \(L\) meters, and the distance between them is \(H\) meters. The system consists of GNSS frequency division relay equipment (FDR) and parallel LCX cables. The FDR is composed of GNSS receiving antennas, MAX2769E radio frequency (RF) front-ends, FIFO buffers (FIFO), fractional interpolation filters (FIFs), digital-to-analog converters (DACs), and RF modulation amplifiers (RFMAs). The MAX2769E is a low-cost GNSS RF front-end chip, which can be configured through SPI parameters to select and receive GNSS signals at the corresponding frequencies, outputting down-converted digital intermediate frequency (IF) signals. After being buffered by FIFO, the digital IF signals are transmitted to FIFs, which interpolates the data rate from 19.2 MHz to 200 MHz. The interpolated signals are smoothed through low-pass filter (LPF). The processed digital IF signals are then converted to analog IF signals via DACs and transmitted through IF transmission lines to the RFMA. The system receives mixed satellite signals from open-area GNSS systems through GNSS receiving antennas at known coordinates, which are fed into the FDR. The FDR separates the signals from the GPS, BDS, and GLONASS systems and outputs analog IF signals corresponding to the designated frequencies. To reduce radiation interference between GNSS signals after frequency division, the analog IF signals are transmitted via IF transmission lines to the RFMA located at the LCX cable ports. The RFMA consists of an RF modulation module and a signal power amplifier. The RF modulation module performs upconverts processing on the analog IF signals, generating GNSS RF signals that can be received by GNSS receivers. To mitigate the effects of the transmission loss of GNSS RF signals in the LCX cable, the signals are processed by the signal power amplifier before driving the LCX cable ports. In Figure 1, the BDS system signal at the B1I frequency drives the A1 port of LCX_1 and, after propagating through the LCX cables, is vertically radiated at point Cn (n = 1, 2, 3) towards the receiver. The GLONASS system signal at the G1 frequency excites the B2 segment of LCX_1 and, after propagation, is vertically radiated at point Cn (n = 1, 2, 3) towards the receiver. The GPS system signal at the L1 frequency excites the A2 port of LCX_2, after propagating through the LCX cables, and is vertically radiated at point Dn (n = 1, 2, 3) towards the receiver. By utilizing the pseudorange measurement differences from GNSS signals of different satellite systems, the receiver calculates its two-dimensional coordinates within the tunnel coordinate system. The system predefines the center of the tunnel as a reference point and calculates the errors (\(\Delta\)X and \(\Delta\)Y) between the computed coordinates and the actual coordinates of this reference point, using these as correction factors. When the user's receiver performs position calculations, it applies these correction factors to adjust the positioning result, ultimately obtaining the receiver's coordinates. Figure 1: Composition diagram of the positioning system. GNSS RF signal propagation within the tunnel is illustrated in Figure 2. The B1I frequency signal of the BDS system drives the A1 port of LCX1, propagating through the leaky coaxial cable from A1 to B1. Similarly, the G1 frequency signal of the GLONASS system drives the B1 port of LCX1 and propagates from B1 to A1, while the L1 frequency signal of the GPS system excites the A2 port of LCX2, propagating from A2 to B2.