# Summary of Lunar Constellation Navigation and Orbit Determination Technology
## 3 Overview of Single-Satellite Navigation and Orbit Determination Methods
### GNSS Orbit Determination Technology  
GNSS (Global Navigation Satellite System) orbit determination refers to the method of positioning and orbit determination of a spacecraft using a satellite navigation system. By transmitting a set of precise radio signals, which are received and processed by ground receivers, precise positioning and orbit determination are achieved.  
The basic principles of GNSS orbit determination are that a spacecraft or mobile device receives signals from at least four satellites and calculates its position by measuring the time difference of these signals. This is because each satellite emits a precise signal that contains information about the satellite's own position and time. By receiving signals from multiple satellites, a GNSS receiver can calculate its distance from each satellite and use this distance information to determine its position.  
Specifically, the GNSS orbit determination principle includes the following key steps:  
1. Satellite signal transmission: GNSS satellites emit signals that contain information about the satellite's own position and time. These signals travel through the air via radio waves and are picked up by ground-based receivers.
2. Signal receiving and processing: After the ground receiver receives the signal transmitted by the satellite, it will process the signal. This includes amplifying, filtering, demodulating and other operations on the signal to extract useful information.
3. Signal time difference measurement: By measuring the time difference between signals received from multiple satellites, the ground receiver can calculate its distance  
Figure 5: Schematic diagram of laser ranging.  
from each satellite. This is accomplished by comparing the difference in the time it takes for the signal to arrive at the receiver.
4. Positioning calculation: By measuring the distance between four or more known satellites and the GNSS receiver, the position of the receiver can be determined through distance intersection. Therefore, the positional information of the satellite which is equipped with the GNSS receiver can be obtained. There are many methods for calculating position, among which the triangulation method and the least squares method are the most commonly used.  
As shown in the Figure 6, when the receiver only observes one satellite, it can only determine that the receiver is on a sphere with the geometric distance between the two satellites as the radius. When it observes two satellites, the two spheres intersect to form a circle, and the receiver position is located on this circle. When three satellites are observed, the three spherical surfaces intersect in pairs and form two points in space. One of the positions can be eliminated according to the conditions, and the receiver's position can be obtained. To actually determine the receiver's position, at least four satellites need to be observed. This is because the receiver's clock error is also an unknown parameter. Three types of observations can be obtained using GNSS receivers: pseudo range, carrier phase, and Doppler frequency shift. By analyzing the observations and processing the data, information on the status of the satellite can be obtained.