Research on relative phase orbit determination method of satellite carrier phase Hu Guorong 1, Ou Jikun, Cui Weihong (1. Institute of Remote Sensing Application, Chinese Academy of Sciences, Beijing 1001012. Institute of Surveying and Geophysics, Chinese Academy of Sciences, Wuhan 430077, Hubei) Observation is the carrier phase observation value. According to the characteristics of low-orbit satellite spaceborne GPS, a ambiguity resolution method suitable for the relative orbit determination of spaceborne GPS carrier phase is given, and the ambiguity resolution method . This method is applied to the measured data of GPS on-board of TOPEX / PO SEIDON satellites, and can obtain decibel-level orbit determination accuracy.
1 Introduction GPS has the advantages of all-weather, high-precision, continuous observation, and is increasingly loaded on low-orbit satellites used for remote sensing, meteorology, and marine altimetry. Because the altitude of such satellite orbits is about 450-900 km, it is greatly affected by the gravity of the earth and atmospheric resistance, and its dynamic model is difficult to accurately simulate. Using satellite-based GPS for precise orbit determination can replace many high-precision applications. The dynamic orbital data processing of the conventional ground tracking technology required for satellite orbits shows that using satellite-based GPS to orbit, the radial orbit accuracy of low-orbit satellites can reach centimeters, which is satellite remote sensing, global oceanography and global meteorology. The study provides an accurate benchmark for data processing.
The accuracy of the GPS carrier phase observations is more than 100 times better than the pseudorange observations. Therefore, the carrier phase observations become the basic observations of the precise orbit determination of the satellite-borne GPS on low-orbit satellites. Carrier phase relative orbit determination method, that is, the synchronous carrier phase observations of the receiver on the low-orbit satellite and the ground reference station (such as IGS GPS permanent station) receiver form a dynamic baseline, and the three-dimensional position of the reference station is known to determine the orbit of the low-orbit satellite position. This method can weaken or eliminate the influence of GPS satellite clock error and ephemeris error, and it is not affected by uncertainties such as atmospheric drag in the normal dynamic legal orbit, which has significant advantages compared with the conventional dynamic method. According to the characteristics of spaceborne GPS, this paper first introduces the basic principle of carrier phase relative orbit determination method, and then gives a ambiguity resolution method suitable for spaceborne GPS carrier phase relative orbit determination, and the ambiguity resolution is accurate The test method of the degree is finally verified by the TOPEX / POSEIDON satellite satellite GPS measured data.
2 Carrier phase relative orbit determination method The GPS satellite signals received by the spaceborne GPS receiver are not affected by the tropospheric delay, and it is assumed that the ionospheric delay can be corrected using a better model or method: the ground reference station receiver is dual-frequency GPS reception The ionospheric delay can be corrected well [5, 6], and the tropospheric delay can be corrected using an appropriate correction model [7]. Since the orbit is determined for post-processing, a precise ephemeris can be used (accuracy of 10-30 cm) ), Which can weaken the influence of GPS satellite ephemeris error and SA.
Taking the L1 carrier phase observation value as an example, suppose that the ground reference station receiver and the low-orbit satellite satellite receiver view the GPS satellite j, k at time t, the coordinates of the ground reference station and the approximate position of the low-orbit satellite are known), then The available linearized double-difference observation equation is: where λ is the L1 carrier phase wavelength x = (δX is the number of corrections to the 3D orbital position of the low-orbit satellite. It is a postdoctoral fellow at the Institute of Remote Sensing Applications, Chinese Academy of Sciences. It is mainly engaged in spaceborne GPS low-orbit satellite Orbit determination research, as well as GPS / GLONASS theory and application and 3S integration application research.
Journal of Remote Sensing) is the jth, three-dimensional orbit position of the k GPS satellites is double-difference ambiguity ΔΔΥ = ΔΔΥ including double-difference carrier phase observation error and linear expansion error.
If you view m satellites at the same time, you can form m 1 similar formula (1), the joint writing is: at this time, the number of unknowns is: 3m 1, that is, the orbit position parameters of 3 low-orbit satellites, m 1 is fuzzy Degree parameter. Since m 1 ≤ 3 m 1, that is, the number of equations is less than the number of unknowns, therefore, one epoch cannot solve the three-dimensional orbit position parameter of the low-orbit satellite, and it is necessary to lock the m satellites in consecutive epochs. If n epochs are locked in succession, n × (m 1) double-difference observation equations can be formed, and the number of unknowns is 3n (m 1). In order to obtain a definite solution, it must be satisfied that the epochs view the m satellites in common, It is enough to determine the three-dimensional orbit positions of these n epochs. The weight matrix of the double-difference observation value is P, which can be solved by the least square method: The error estimate in unit weight is: The error estimate in unknown is: where , Q is the i-th diagonal element in N.
3 Carrier phase ambiguity resolution method Since the prerequisite for the full-circumference ambiguity resolution is that all kinds of errors that affect the full-circumference ambiguity resolution must be eliminated to the point where the wavelet phase is relatively orbit-determined, the low-orbit satellite and the ground reference station The distance is hundreds to thousands of kilometers. Although some errors of the spaceborne GPS receiver and the ground reference station receiver have a certain correlation, it is difficult to eliminate enough errors in the spaceborne GPS carrier phase observation value, such as Multipath errors are difficult to model, and the residuals of spaceborne GPS observations corrected by the ionospheric delay correction model. These unresolved errors destroy the integer characteristics of ambiguity over the entire week. To this end, we use the Sigma method to solve the ambiguity of the whole week as much as possible. The basic principle is as follows: set the real solution of the ambiguity parameter to N and its median error σN, and if σ = y. Round to the nearest integer :) contains at least one integer) contains at most one integer.
Among them, k, l, y are the values ​​set according to the actual situation, and the ambiguity of each real number is judged until no more ambiguity parameters are rounded up. As mentioned above, the unresolved error affects the integer characteristics of the ambiguity. Using this method to solve the ambiguity of the whole cycle, in fact, the search space is directly established with the estimation accuracy of the real ambiguity. Large ambiguity cannot meet the above conditions. Then it is not rounded to the nearest integer, and the ambiguity resolved to a small real number σ is rounded to the nearest integer if the above conditions are met. Subsequent application examples show that using this method to solve part or all of the ambiguity parameters as an integer ambiguity, the accuracy of the orbit determination is significantly higher than that of the real ambiguity.
In order to test the accuracy of the ambiguity resolution, we make the following tests in the process of ambiguity resolution: (1) Ratio value test: judge by checking the quotient of σ of the adjustment before and after the ambiguity is fixed: where, F is The test value under a kind of wrong probability α, m is the number of double-difference observations, n is the number of unknown parameters excluding fixed ambiguity parameters, n is the number of fixed ambiguity parameters (2) Repeatability test: if no cycle slip occurs, the correct ambiguity should be equal or very small within a certain period, that is, repeatability, so we can use the above method to divide a certain period into two and solve separately, Compare the ambiguity of continuous observation of GPS satellites to check the correctness of the ambiguity solution of the Journal of Modular Remote Sensing (3) The ambiguity closed difference test: as shown in Figure 1, when the spaceborne GPS receiver (f) is connected to two ground reference stations simultaneously When the receiver (g1, g2) performs relative orbit determination, there is the following relationship: where the double-difference ambiguity points to the same satellite pair, and the double-difference ambiguity ΔΔN between the two ground stations can be considered to be known of. Of course, because the ground reference station and the spaceborne GPS receiver have different degrees of error source elimination, the above formula may not be completely equal. At this time, we can design a threshold ε and establish the following ambiguity closed difference test judgment conditions The test conditions can be extended to the relative orbit determination of multiple ground reference stations: 4 measured data analysis. The L1 carrier phase observation value of the GPS receiver (GPS / DR) on the satellite is relative orbit determined with the IGS ground station. The T / P spaceborne GPS receiver phase sampling rate is 1s, and the ground station GPS receiver carrier phase sampling rate is 30s. Therefore, after the double difference is formed, the epoch interval is 30s. The T / P satellite orbit altitude is about 1336km, so , In the carrier phase observations of the T / P satellite GPS receiver, the influence of the troposphere and ionosphere is negligible, only considering the influence of the ground station troposphere and ionosphere on the carrier phase observations, using the Saastamoinen tropospheric correction model [7], Meteorological parameters adopt standard atmospheric parameters and the ionospheric model obtained in the Bernese software to correct the carrier phase observation data of the ground station [9]. The position of the receiver antenna phase center of the ground reference station is known, and the T / P satellite The initial orbit position can be obtained by direct method solution or linear iterative method based on direct method. Based on the above methods, we make the following analysis: 4.1 Comparison of the relative orbit determination accuracy of the ambiguity parameter for the real solution and the solution using the Sigma method Taking the Taiwan station as an example, the ambiguity parameter for the real solution and the solution using the Sigma method, some epochs are relatively fixed The orbit accuracy is shown in Table 1. When using the Sigma method to solve, the satellite corresponding to the ambiguity rounding is the time element / s Sigma method to solve the weekly ambiguity. Method to study SV22, SV23, RSS is the three-dimensional orbit position error. It can be seen that when the ambiguity parameter is solved into an integer by using the Sigma method, the accuracy of relative orbit determination is significantly improved, and the accuracy of the three-dimensional orbit position is decimeter level.
4.2 Carrier Phase Relative Orbit Ambiguity Closed Difference Test We take the Taiwan station (TAIWAN) and Shanghai station (SHAO) as examples. For the 6 satellites continuously observed during the period of 01: 36: 00-01: 47: 30 Double-difference ambiguity is used for closed-difference test. During the calculation, satellite 19 is used as the reference satellite for double-difference observations. The Sigma method is used to solve the problem. The test results are shown in Table 2, where the subscript N indicates the satellite pair. It can be seen from Table 2 that, in different dynamic baselines, some of the same satellite's double-difference ambiguities have been solved into integers, and some are still real solutions. The ambiguity closure difference is basically within the range of 1-2 weeks.
(Week) Dynamic Baseline Double-Difference Ambiguity Closure Difference 5 Conclusions and Discussion This paper discusses the relative orbit determination method of satellite-borne GPS carrier phase from the theoretical and practical analysis. Correctly determining the full-period ambiguity is a necessary condition for obtaining high-precision positioning and orbit determination. According to the characteristics of spaceborne GPS, Sigma is used to solve the ambiguity. The three-dimensional orbit position accuracy can reach decimeter level.
It can be seen from the ambiguity closure difference in Table 2 that the accuracy of ambiguity resolution needs to be further improved. In addition, the measured data in this paper uses 1336km T / P satellite satellite GPS data, which can be considered not affected by ionospheric and tropospheric delays. At the same time, because of its good receiver quality and the use of precision ephemeris, therefore, its The accuracy of orbit determination is relatively high. For low-orbit satellites with an orbit altitude of less than 600km, these methods are fully applicable, but the accuracy of their orbit determination depends on the quality of the spaceborne GPS receiver and the accuracy of its ionospheric delay correction model, which needs further study.
It is worth mentioning that, due to the low-orbit satellites running at a speed of several kilometers per second relative to the ground station, the space-borne GPS and the ground station form a limited orbital arc segment is limited, but with the recent years, people have combined GPS / GLONASS The research and development of navigation and positioning systems [10], such as the GOCE (Gravity Field and Static Ocean Current Exploration) satellite to be launched by the European Space Agency, will carry a GPS / GLONASS receiver GPS carrier phase relative orbit prospect will become more and more broad .
Photogrammetry and Remote Sensing [M]. Beijing: Surveying and Mapping Press. 1996.] Theoretical study of GPS low-orbit satellite orbit determination [D]. Doctoral dissertation, Institute of Surveying and Geophysics, Chinese Academy of Sciences, 1999.] GPS Satellite Surveying Principles and Applications [M] .Beijing: Surveying and Mapping Publishing House, 1994.] Global Positioning System Principles and Applications [M] .Beijing: Surveying and Mapping Publishing House, 1993.] Journal of Remote Sensing Hu Guorong et al .: Spaceborne GPS Carrier Phase Relative Research on Orbit Determination Method
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