GPS Non-Difference Phase Precision Single Point Positioning Technology Discussion Liu Jingnan 1 Ye Shirong 2 (Wuhan University President ’s Office, Luojia Mountain, Wuhan, 430072) (2 Wuhan University GPS Engineering Technology Research Center, 129 Luoyu Road, Wuhan, 430079) Direct The method of interpolating the precise ephemeris of the IGS satellite replaces the method of using the IGS tracking station to perform the orbit refinement method to calculate the satellite orbit parameters. The existing precise single-point positioning calculation method is simplified to make it more practical. Finally, the self-developed precision non-difference single-point positioning software was used to calculate and analyze the measured data. The calculation results show that after about 15 minutes of initialization, the accuracy of the positioning results of the non-differential phase single epoch is better than 20 cm in the X, Y, and Z directions. Chinese Library Classification: 228. In the past 10 years, GPS technology is widely used in the field of geodesy. From global plate crustal movement monitoring, regional high-level control network, urban differential continuous operation system to small-scale building deformation monitoring, GPS plays an important role. In these applications, GPS relative positioning is generally used to eliminate common errors such as receiver clock errors and satellite clock errors and weaken the effects of tropospheric delay, ionospheric delay and other related errors by forming double-difference observations. To achieve the purpose of improving accuracy. This operation method does not need to consider the complex error model, and has the advantages of simple solution model and high positioning accuracy. But there are also some deficiencies, such as at least one receiver placed on a known station to observe during operation, which affects the operation efficiency and increases the operation cost. In addition, as the distance increases, the correlation of errors such as tropospheric delay and ionospheric delay weakens, and the observation time must be extended accordingly to achieve the expected accuracy. Is there a new operating method that can overcome these shortcomings of GPS relative positioning? In 1997, Zumbeger et al. Of the United States Jet Propulsion Laboratory (JPL) proposed an effective solution, that is, a non-differential precision single-point positioning method.
They used this method to process the single-station static observation data for one day, and the internal coincidence accuracy was a few mm in the horizontal direction and a few cm in the elevation direction; the internal coincidence accuracy for processing the global dynamic data was about 8 cm in the horizontal direction and the elevation direction was about 20cmT (4) value minus the constant term calculated by rough theoretical calculation; X (i) is the parameter to be estimated; x, y and z are the three-dimensional position parameters; S is the receiver clock error parameter; Prop is the tropospheric delay parameter; is Unknown parameter for the whole week, j = 1, 2 ..., ".
When solving, position parameters can be treated as constant unknowns under static conditions; in the absence of cycle slips or repair of cycle slips, the whole week unknowns are treated as constants; in the case of cycle slips, the whole week unknowns are treated as Make a new constant parameter for processing. Because the receiver clock is unstable and there is obvious random jitter, the receiver clock difference parameter is treated as white noise; while the tropospheric effect changes more smoothly, you can use Saastamonen or other models to correct it, and then use random walk Method to estimate its residual impact. Single epoch data can be solved by least squares method or Kalman filter method.
1.2 The error of precision single-point positioning is corrected in precision single-point positioning. In addition to considering the influence of errors such as ionosphere and troposphere, the influence of satellite antenna phase center deviation, solid tide and ocean load must also be considered.
1.2.1 Correction of satellite antenna phase center deviation Since the force models used in GPS satellite orbit determination are all corresponding to the satellite center of mass, the satellite coordinates and satellite clock differences in the IGS precision ephemeris correspond to the satellite center of mass rather than to the satellite The antenna phase center, and the GPS observations correspond to the satellite antenna phase center and the receiver antenna phase center. Generally speaking, the phase center of the satellite antenna does not coincide with the center of mass of the satellite. In precise single-point positioning, the difference method cannot be used to eliminate or weaken its impact, so its correction model must be considered. In the star-solid system, the deviation of the satellite phase center relative to the satellite's center of mass is shown in Table 1.
Table 1 Satellite antenna phase deviation in satellite-solid system / m satellite type 2 Solid tide correction Solid tide and ocean tide have the same cause. The gravitational effect of celestial bodies (sun, moon) on the elastic earth causes periodic fluctuations on the solid surface of the earth, and makes the earth elongate in the direction of the connection between the center of the earth and the celestial body, and tends to be flat in the direction perpendicular to the connection , Composed of long-term terms related to the drop and periodic terms with periods of 0.5d and 1d, respectively. In GPS double-difference relative positioning, the impact of the short baseline "100km" can be ignored. For the long baseline of thousands of kilometers, there is an error of several cm, which needs to be considered in precision processing. For precise non-difference single-point positioning, since it cannot be eliminated by the method of difference between stations, its influence is about 30 cm in the radial direction and about 5 cm in the horizontal direction, and must be corrected using the model.
3 Ocean load correction The effect of ocean load on precision single-point positioning is consistent with that of solid tide, but it is one order of magnitude smaller than solid tide. Ocean load is mainly composed of daily cycle and half-day cycle. For single epochs, the positioning accuracy requires sub-m-level or cm-level static positioning of 24h observation time, and the influence of ocean load can be ignored. For sub-m-level dynamic positioning or cm-level static positioning with an observation time shorter than 24h, the influence of ocean load must be considered, unless the station is far from the coastline 2 Calculation and result analysis 2.1 Data processing method The precise single-point positioning calculation process is mainly divided into the following several Steps: â‘ For the convenience of calculation, the precision ephemeris is fitted into a polynomial form; â‘¡ The precision ephemeris is given a satellite clock difference value every 15 minutes. This interval cannot meet the precision single-point positioning requirements, and because the satellite clock difference changes faster Instead of linearly interpolating it at intervals of 30s, the GPS clock data from multiple IGS tracking stations and precision ephemeris estimates must be used to obtain the satellite clock difference at 30s epoch intervals; â‘¢Use the fitted orbital polynomial and satellite clock difference Perform precise single-point positioning calculations together with user station observation data.
2.2 Data preprocessing In precision single-point positioning, data preprocessing such as cycle slip removal and phase smoothing pseudorange must be performed first to obtain high-quality non-difference phase and pseudorange observations.
2.2.1 Combined observations to repair cycle slips In precision single-point positioning, it is an important task to remove cycle slips from non-difference GPS observation data. Since non-difference single-point positioning can only use single-station data, it cannot form double-difference or triple-difference observations. Generally, methods for eliminating cycle slips such as three-difference method and polynomial fitting method are not applicable. The method proposed by Blewitt to use dual-frequency and double-P code combination observations to repair cycle slips is very suitable for clearing non-difference cycle slips. 5. The linear combinations of GPS observations used to clear non-difference cycle slips are as follows.
* Y; i is the epoch number; 1, and 2 are the frequencies of L1 and L2; Pi and P2 are the P code pseudorange observations; b6 is the ambiguity of wide lanes.
The Melboume-WUbbena combination eliminates the effects of ionosphere, troposphere, clock difference and calculated geometric observations, and has the characteristics of longer wavelength and smaller measurement noise, so it is suitable for the detection and repair of non-differential cycle slip. If the RMS of Melboume-WUbbena is less than 0.5 wide lane wavelength (43 cm), it can be used to determine almost all wide lane cycle slips. In the actual calculation, the recursive method is used to calculate each epoch value and its residual error a: comparing the value of the adjacent epoch b6 and its residual error a can determine whether a cycle slip occurs. If a cycle slip occurs, mark the epoch in which the cycle slip occurred, take the data before this epoch as a data arc, and calculate its b6 mean and its residual error a. Restart calculation from the next epoch to detect the cycle slip , Repeat the above work until the data ends. The arc-to-circle cycle slip size island 6 can be obtained from the average between the two segments, and island 6 has the following relationship with L1 and L2 cycle slips: After determining all wide lane cycle slips Ab6, the ionospheric change can be used Smoothness characteristics, the meter uses Geometry-free combination to repair the size of the narrow lane cycle. Generally, the N epoch data before the occurrence of the wide lane cycle is fitted to a polynomial, and the N epoch data after the occurrence of the cycle slip is fitted to another polynomial. The difference between the two polynomials at the epoch time when the cycle slip occurs The value can be regarded as the size of the narrow lane cycle, which can determine the size of 1An1-2An2. Using equation (11) again, the values ​​of Am and An2 can be obtained.
2 The use of dual-frequency observations to eliminate ionospheric delays. The general correction accuracy of the ionospheric model is only dm, which cannot meet the requirements of non-differential precision positioning. In addition, the method of using the inter-station differential to eliminate or reduce the influence of the ionosphere is also not suitable for non-differential positioning. As the precision single-point positioning operation generally uses dual P-code dual-frequency receivers, the dual-frequency observations can be used to eliminate the ionospheric delay, and the correction accuracy can reach cm level.
3 Phase smoothed pseudorange observations Pseudoranges, as auxiliary observations, still play a major role in the initial stage of precision single-point positioning. The quality of pseudorange observations will affect the initialization time and the determination of the non-differential integer ambiguity.
Therefore, in order to improve the accuracy of pseudorange observation, the pseudorange is generally smoothed by using phase observation data that has eliminated the cycle slip and eliminates the effects of ionospheric delay.
2.3 Analysis of results In the example calculation, the IGS precision ephemeris was used, and the precise single-point positioning software developed by the author was used to process the data of 226d in 2000 in the IGS tracking station KOKB station in Hawaii, USA.
The observation values ​​for single-point positioning calculation can adopt multiple types of observation values ​​such as pseudorange, phase smooth pseudorange and non-difference phase. In order to compare the results of precise single-point positioning using different observations, the examples were calculated using phase smoothed pseudorange and non-difference phase observations. When using the non-differential phase for precise single-point calculation, in order to determine the phase ambiguity faster, the pseudorange is still used as an auxiliary observation, but the non-difference phase observation is given a higher weight. The pseudorange observation Give lower power. The observation noise of the P code pseudorange is 1m, and the observation noise of the phase observation value is 0.01 week.
To facilitate analysis, the high-precision ITRF coordinates of the KOKB station published by IGS are used as known values, and the positioning results of different observations are compared with known values. Represents the difference between the calculated results of the phase smoothed pseudorange observations and the known coordinates of the station in the X, Y, and Z directions; indicates that the calculated results using the non-differential phase observations and the known coordinates of the station at the initial stage are at X, Y, and Z Y, the difference in the error Z direction of the residual error of the calculation result of the non-differential phase observation value of the single epoch; indicates that the single epoch result calculated by the non-differential phase observation value and the known coordinates of the station are in the X, Y, and Z directions Difference.
The results in the analysis can be concluded that the accuracy of positioning using phase smoothed pseudorange observations can only reach m level, which obviously cannot meet the application requirements of higher accuracy, but it can be used to determine the initial value of non-difference phase ambiguity. However, using non-differential phase observations for positioning, in the initial stage, because the unknown number of phases cannot be determined, the positioning result depends largely on the quality of the pseudorange observations, and the accuracy is poor. However, with the continuous increase of observation data, the unknowns of the whole week can be determined more accurately, and the accuracy of positioning is also significantly improved. At present, with the author's algorithm and software, the initialization time of the non-differential phase precision single-point positioning is about 15 minutes. After the initialization is completed, the accuracy of the single-epoch positioning result is relatively stable, and the positioning result and the known coordinates are in the X, Y, and Z directions The difference is less than 20cm, and the maximum difference between the X, Y, Z directions and points of the known coordinates is 4 respectively. The error in the single-epoch positioning residual error is less than 20cm for most of the time. There is still a systematic deviation in the solution result of a single epoch. The reason may be that the error correction model is not accurate enough. For static conditions, the effect can be partially eliminated by extending the observation time to achieve the effect of improving positioning accuracy. In future research work, the error correction model will be refined to obtain better positioning results.
3 Conclusions and suggestions Using the phase non-difference precise single-point positioning method described in this article, a single dual-frequency dual-p code receiver can perform precise positioning on a global scale. Compared with GPS relative measurement, this method has the advantage of not being limited by observation time and observation distance. It is foreseeable that phase non-difference single-point precision positioning is an important direction for the development of GPS positioning in the future and has great application potential. The experimental results show that when the initialization is completed, the static positioning accuracy of its single epoch can be better than 20cm in the X, Y, and Z directions. This accuracy is consistent and equivalent to that of similar international studies. Since the error model currently considered is not accurate enough, it may bring systematic errors to the results. In future work, various error models must be further refined to eliminate their effects. In addition, compared with static positioning, the observation model and stochastic model of dynamic positioning are more complicated, and dynamic precision single-point positioning technology is also more valuable (such as the orbit determination of low-orbit satellites). Therefore, dynamic precision single-point positioning technology will It is the main content of future research.
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