In order to obtain the receiver's position, when the receiver clock is strictly synchronized with the GPS standard, the position to be solved is three unknown variables and requires three independent equations to solve. However, in practice, it is difficult to strictly synchronize the receiver clock with the GPS standard time. In this way, we regard the receiver time and the GPS standard time deviation as an unknown variable. In this way, four independent equations are required to solve, that is, four observation satellites are required. Figure 1 Schematic diagram of GPS positioning (time deviation is not considered) assumes that the receiver position is (xu, yu, zu) and the receiver time deviation is tu, then the distance deviation caused by time deviation is the pseudo range observation value obtained. We can get simultaneous equation (5) to linearize the above equation, that is, Taylor series expansion is performed at the real location (xu, yu, zu), ignoring the higher order terms, and we can get (6), where equation (6) is the actually calculated iteration formula, and the iteration termination condition is that the change of the real location (xu, yu, zu) is less than a certain threshold, which can be used as the basis for adjusting the receiver time deviation, The matrix method is generally used for calculation. To solve this equation, we also need to know the positions of the four satellites (xj, yj, zj) in advance, and the satellite positions can be obtained from the ephemeris of the satellite. The GPS satellite ephemeris gives the ephemeris of the star, according to which the real-time position of the satellite can be calculated. In addition, the ephemeris gives the parameters to eliminate satellite clock error, relativity error, earth rotation error, ionosphere and troposphere error. The satellite position calculated according to these parameters can basically eliminate the above errors. The basic steps to solve the satellite position are: calculate the average angular velocity of satellite operation ① calculate the domestication time; ② Calculate the angle of the horizontal approach point at the observation time; ③ Calculate the near point angle; ④ Calculate the vector diameter of the satellite; ⑤ Calculate the true perigee angle of the satellite; ⑥ Calculate the angular distance of ascending intersection point; ⑦ Calculate the perturbation correction term; ⑧ Calculate the elevation angle, satellite vector diameter and orbit inclination angle corrected by perturbation; ⑨ Calculate the longitude of the ascending intersection point at the observation time; ⑩ Calculate the position of the satellite in the geocentric coordinate system. It is particularly worth pointing out that formula (7) should be used to calculate the satellite true perigee angle Vk, where e is the eccentricity and Ek is the satellite perigee angle. Some reference books have incorrect formulas for calculating the true perigee angle of the satellite, which will lead to the quadrant ambiguity of the true perigee angle of the satellite, and thus the correct position of the satellite cannot be obtained. After the above calculation, the errors are further eliminated according to the error parameters broadcast in the ephemeris. In this way, we can get a complete navigation and positioning solution process using GPS ephemeris

Read recommendations:

Dog gps tracker Solution

Hidden GPS Trackers wholesaler

GF20-Mini Magnet GPS Tracker

GPS Global Satellite Positioning System

GPS predecessor