# Study of Fast and Reliable Time Transfer Methods Using Low Earth Orbit Enhancement
## 2 Experimental Principles  
### LEO Constellation Design and Observation Simulation  
To investigate the time transfer performance of the GNSS enhanced by LEO satellites, due to the lack of existing observation data of low orbit satellites, this study simulates the observation data of low orbit satellites. The simulation of observation data is the inverse process of positioning calculation [20]. The simulated observation data of low orbit used in this study are obtained by introducing various types of errors into the geometric distance between the satellites and the receivers. Since GNSS observations use GPS, for ease of interoperability, the simulated observation frequency for the LEO satellites is the same as that of GPS, 1575.42 MHz (L1) and 1227.60 MHz (L2). Before the simulation, fixed station coordinates, receiver clock bias, and zenith tropospheric delay are obtained through a static PPP solution in preparation for subsequent simulations. First, the LEO satellite constellation is designed with simulated orbits and clock discrepancies. This study simulates 160 low Earth orbit satellites, with 70 distributed across six polar orbits and 90 across ten inclined orbits. The inclination of the polar orbits is 90\({}^{\circ}\), while the inclination of the inclined orbits is 60\({}^{\circ}\)[21; 22]. The low Earth orbit satellite group adopts a Walker constellation, which consists of multiple circular orbit satellites with the same orbital altitude, with the satellite orbital height being 1000 km. For the simulation of the low Earth orbit satellite orbits, the initial positions and initial velocities of each satellite are calculated based on the aforementioned LEO constellation parameters, and then, the orbital dynamics are integrated to obtain full-day orbit data. The orbits are then transformed from the geocentric inertial coordinate system to the Earth-centered, Earth-fixed coordinate system (ECEF), with the orbital data interval designed to be 30 s for interoperability with IGS products. The simulation of orbit errors is achieved by combining cosine trend terms, constant trend terms, and Gaussian noise. The clock bias of the low Earth orbit satellites is simulated using the GPS satellite clock biases provided by IGS. Without considering the system time bias between LEO and GPS, the clock bias of GPS satellites is randomly substituted for the low Earth orbit satellites. The errors published by IGS are calculated clock biases from the IF combination (a linear combination of L1/L2), and the simulated clock errors absorb the pseudorange hardware delays of dual-frequency ionosphere-free combination satellites. It should be noted that the simulation results for orbit and clock errors may not be absolutely accurate, so further consideration should be given to systematic and random errors after combining satellite orbits and satellite clock errors. To simplify the process, noise of different magnitudes is directly added to the orbital components and satellite clock errors. Geometric distances are calculated using known receiver coordinates, satellite orbits, and satellite clock errors. Then, various error terms are calculated using error models. Specifically, the ionospheric delay is calculated using the projection function and total electron content from the global ionospheric maps published by the Center for Orbit Determination in Europe (CODE). For the simulation of tropospheric delay, the wet component of the troposphere delay is calculated using static PPP estimation and the GMF (Global Mapping Function) projection function, while the dry component of the troposphere delay is calculated using the Saastamonien empirical model and GMF projection function [11; 23]. The initial measurement noise for code and phase is simulated as Gaussian noise with a standard deviation of 0.5 m and 3 mm, respectively, and is inversely correlated with elevation angle. Earth rotation errors, relativistic effects, and tides are corrected using existing corresponding models.