To get the position of the receiver, when the receiver clock is strictly synchronized with the GPS standard, the position to be solved is 3 unknown variables, and 3 independent equations are needed to solve it. However, in practice, it is difficult to achieve strict synchronization between the receiver clock and the GPS standard time. In this way, we also take the receiver time and GPS standard time deviation as an unknown variable. In this way, four independent equations are required to solve, that is, we need to have 4 observation satellites. Fig. 1 Schematic diagram of GPS positioning (without considering time offset) Assuming that the receiver position is (xu, yu, zu) and the receiver time offset is tu, the distance offset caused by the time offset is the obtained pseudorange observation value. We can obtain the simultaneous equation (5) and linearize the above equation, that is, perform Taylor series expansion at the real position (xu, yu, zu), ignoring the high-order terms, and obtain (6) where, Equation (6) is the actual The calculation iteration formula, the iteration termination condition is that the change of the real position (xu, yu, zu) is less than a certain threshold, and the final result can be used as the basis for adjusting the receiver time deviation, and the calculation is generally solved by a matrix method. To solve this equation, we also need to know in advance the positions of the 4 satellites (xj, yj, zj), which can be obtained from the ephemeris of that satellite. The GPS satellite ephemeris gives the ephemeris of the local star, and the real-time position of the satellite can be calculated according to the ephemeris, and the parameters for eliminating satellite clock errors, relativistic errors, earth rotation errors, ionosphere and troposphere errors are given in the ephemeris. , the satellite positions calculated according to these parameters can basically eliminate the above errors. The basic steps for solving the satellite position are: Calculate the average angular velocity of satellite operation ①Calculate the naturalization time; ②Calculate the average perigee angle at the observation moment; ③Calculate the partial perigee angle; ④Calculate the satellite vector radius; ⑥ Calculate the angular distance of the ascending node; ⑦ Calculate the perturbation correction term; ⑧ Calculate the perturbation-corrected ascending distance angle, satellite vector radius, and orbit inclination; ⑨ Calculate the longitude of the ascending node at the time of observation; ⑩ Calculate the satellite in the geocentric coordinate system in the location. It is particularly worth pointing out that when calculating the satellite true anomaly Vk, formula (7) should be used where e is the eccentricity, and Ek is the satellite eccentric anomaly. In some reference books, the formula for calculating the true perigee angle of the satellite is incorrect, which will cause the quadrant ambiguity of the true perigee angle of the satellite, so that the correct position of the satellite cannot be obtained. After the above calculation, each error is further eliminated according to each error parameter broadcast in the ephemeris. In this way, we get a complete process of using GPS ephemeris for navigation and positioning solution.

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