Articles January 2010 Vol.55 No.8: 1−10 doi: 10.1007/s11434-010-0074-x
Astronomy
SPECIAL TOPICS:
Precise orbit determination for geostationary satellites with multiple tracking techniques GUO Rui1,2,3*, HU XiaoGong1, TANG Bo3, HUANG Yong1, LIU Li3, CHENG LiuCheng3 ＆ HE Feng3 1
Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China; Graduate University of Chinese Academy of Sciences, Beijing 100039, China; 3 Beijing Global Information Application and Development Center, Beijing 100094, China 2
Received September 26, 2009; accepted November 28, 2009
A new precise orbit determination (POD) strategy based on the combination of satellite laser ranging (SLR) and C-band transfer ranging for geostationary satellites (GEO) is presented. Two approaches to calibrate ranging biases of the C-band ranging system are proposed, namely the two tracking system co-location comparison and the combined POD method, with calibration accuracies estimated to be 0.5 ns and 1 ns respectively. Using data from a C-band tracking network in China, POD experiments indicate that meter-level POD accuracy is achievable for GEO. Root-mean-square (RMS) of the post-fit C-band ranging data is about 0.205 m. The radial component errors of POD are evaluated with SLR data from a station in Beijing, with residual RMS of 0.133 m. Orbital overlapping experiments show the total orbit error is a few meters. Computations of SLR residuals also suggest that for 2-hour prediction, the predicted radial error is about 0.373 m. precise orbit determination, equipment ranging delay, GEO, SLR Citation:
Guo R, Hu X G, Tang B, et al. Precise orbit determination for geostationary satellites with multiple tracking techniques. Chinese Sci Bull, 2010, 55: 1−6, doi: 10.1007/s11434-010-0074-x
Meter-level precise orbit determination (POD) for geostationary satellites (GEO) is difficult to achieve because (1) tracking geometry for GEO is almost unchanged due to the geostationary feature of the GEO satellite, resulting in weak dynamical constraints; and (2) systematic measurement errors or ranging biases, may not be separated from the radial component of orbital errors. For example, as a conventional GEO tracking technique, united S-band ranging (USB) systems generally attain hundred-meter-level POD accuracy with ranging biases of 3－5 m. To support navigation and other applications, meter-level POD accuracy is desirable, demanding the development of new tracking techniques. One such effort is the development of Chinese Area Position System (CAPS), whose space segment consists of 5 GEO satellites. CAPS proposed a new GEO tracking technique based on C-band ranging by transfer using transpond*Corresponding author (email:
[email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2010
ers onboard GEO satellites designed for communication, with reporting position accuracy of several meters level [1–5]. For CAPS, high precision time synchronization between tracking stations is not necessary (1 μs would be enough), but the instrumental system errors for time delay and satellite transponder delay, which are equivalent to ranging bias, must be precisely calibrated to separate it from the radial component of orbit. A calibration system is implemented at each CAPS station, but the error needs being modeled during the POD process. To prevent the weakening of orbit estimation with incorporation of bias estimates for each CAPS station, a corrective measure was taken based on the assumption that the sum of all ranging biases is zero. Although the assumption sounds reasonable, no independent verification has been done. Due to the lack of independent, accurate and reliable tracking data, POD validation is not available. A candidate for independent, accurate and reliable trackcsb.scichina.com
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ing system is satellite laser ranging (SLR), a tracking technique with centimeters or even millimeters ranging accuracy. POD research based on SLR has been carried out, such as for GPS satellites PRN 35 and PRN36; orbit accuracy evaluation and systematic errors calibration for altimetry satellites such as TOPEX, prove that SLR is an effective approach for POD and systematic errors calibration. However, SLR ranging to GEO is difficult because the range of more than 36000 km presents a great challenge to the performances of SLR telescopes and laser systems [6–13]. Shanghai Astronomical Observatory of the Chinese Academy of Sciences recently succeeded in obtaining SLR measurement to a GEO satellite, with about 40000 km slant range. With an accuracy of about 3 cm, SLR holds a potential to improve POD accuracy for GEO. We report in this article the efforts to combine SLR and C-band ranging data for the POD of GEO satellites. The C-band ranging technique is relatively cheap and able to realize all-weather ranging with the limitation that ranging bias could not be accurately calibrated. By contrast, SLR is highly accurate and almost bias-free, but it is expensive and vulnerable to weather conditions. In this article, two new accurate ranging bias calibration approaches are proposed and implemented, namely co-location comparison approach and combined orbit determination approach. POD experiments with real data show that these two approaches produce accurate and reliable C-band ranging biases calibration, and consequently benefit both of the tracking techniques, leading to a much better accuracy than each technique alone.
1 Ranging bias calibration based on co-location comparison approach Biases in the C-band ranging system deteriorate the POD accuracy, in particular for GEO satellites. However, with a co-located SLR station, the C-band ranging biases could be calibrated by comparing the range measurements, as demonstrated below. In this study, the SLR station and C-band ranging system is 200 m apart, qualifying co-location. With an apriori GEO orbit, the range between the satellite and C-band system may be predicted, as well as the range between the satellite and the SLR station. The differential range is computed from these two ranging predictions, which is insensitive to orbital errors. However the differential range is sensitive to the atmospheric effects because laser and C-band ranging signals experience different atmospheric corrections. The relationship is
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⎧Δρˆ = ρˆCC − ρˆlaser , ⎪ ⎨ ρCC = ρˆCC + ΔρCC_Tran + ΔρCC_Delay , ⎪ ⎩ ρlaser = ρˆlaser + Δρlaser_Tran + Δρlaser_Delay ,
(1)
where ρˆ CC is the predicted distance between C-band station and satellite, ρˆ laser is the theoretical predicted distance between SLR station and satellite, Δρˆ is the difference between the two predicted distances, ρCC and ρ laser are two ranging measurements, ΔρCC_Tran and Δρ laser_Tran are propagation delays which could be corrected by models, Δρ CC_Delay and Δρ laser_Delay are ranging biases, while
Δρ laser_Delay could be accurately calibrated for the SLR system. A GEO satellite’s transponder delay which is contained in the C-band ranging measurements, could be calibrated before launch, and the residuals translate into ranging biases for each C-band station. In eq. (1), propagation delays could be deducted from measurements, and then ranging bias can be calculated through Δρ CC_Delay = ( ρCC − ρ laser ) − ( ρˆ CC − ρˆ laser ) (2) − (Δρ CC_Tran − Δρ laser_Tran ) + Δρ laser_Delay . Fortunately in the tracking network of C-band transfer, there are two co-location stations in Beijing, one is C-band station (No. 1013), and the other is SLR station (No. 7821). The ranging bias calibration of station 1013 was implemented with SLR measurements. Table 1 lists the results of calibrated ranging biases on June 9−11, 2009, and the detailed calibration results are shown in Figure 1. Ranging biases are very stable during the consecutive 3 days, with a mean value of −2.002 m and standard deviation of 0.075 m. Differences among 3 days are about 0.25 ns because of the errors of propagation delay model and delay jitter of satellite transponder (about 0.2 ns), and the calibration accuracy is estimated to be better than 0.5 ns.
Figure 1 Detailed ranging bias calibration results of co-location comparison approach on June 9, 2009.
Table 1 Ranging bias calibration results of Beijing station (1013) Date Ranging bias (m) SLR data number
2009-06-09 −1.987 5424
2009-06-10 −2.084 13317
2009-06-11 −1.936 679
Mean −2.002 –
Std 0.075 –
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Mean value of the three days is interpreted as the ranging bias of C-band tracking station 1013, with an accuracy of better than 0.5 ns. It is important that to achieve reasonable co-location comparison accuracy, not only co-location stations are necessary, but also sufficient SLR measurements, which pose a serious problem for SLR to reach a target more than 36000 km away.
2 Ranging bias calibration based on combined POD approach Given that only the limited SLR stations are available in the C-band ranging network, ranging biases of other C-band tracking stations could not be calibrated based on the co-location comparison approach, and therefore another effective approach is desirable. One such effort is the combined orbit determination using simultaneously SLR and C-band ranging measurements. Since SLR and its co-location C-band measurements are almost bias-free, ranging biases of other C-band stations could be estimated in the combined POD process. Therefore the estimated ranging biases are laser-based. This is a new ranging bias calibration method, namely combined POD approach. Ranging biases calibration has been implemented on June 9–11, 2009 in the combined dynamical orbit determination process based on SLR and C-band ranging measurements [14]. Data from the SLR station No. 7821 in Beijing, along with data from five C-band ranging stations are analyzed, which are from Beijing, Hainan, Sichuan, Heilongjiang and Guangdong, respectively. Beijing station is almost bias-free after co-location calibration. Dynamical models include Earth’s gravitation, non-spheric gravitational perturbation, Sun and Moon 3-body perturbation, planetary perturbation, solid Earth tide, and solar radiation pressure. JGM-3 Earth gravitation model truncated to 10 by 10 de-
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gree and order, JPL DE403 planetary ephemeris, IAU80 nutation model, and Box-Wing solar radiation pressure model are employed in the POD. 24-hour arc is employed, and estimated parameters include ranging biases of all C-band stations but Beijing, satellite initial orbital elements and one solar radiation pressure parameter for a 24-hour arc. With orbital pre-processing, measurement errors are corrected. Firstly antenna phase offset errors of tracking stations are corrected, secondly reductions of satellite antenna phase center to satellite mass center are made, and finally propagation errors are corrected. Table 2 lists the calibrated ranging bias results of the 4 stations during 3 consecutive days by the combined POD. Standard deviations of all ranging biases in Table 2 are less than 0.3 ns, except for Sichuan station, whose bias reaches about 0.6 ns variation because of its noisy measurements (about 40 cm). Suppose it is not a co-location station, the ranging bias of Beijing 1013 could not be calibrated based on the co-location comparison approach, but has to be estimated in the combined POD process. Combined POD experiments were carried out over again, and the ranging biases of all C-band stations including Beijing were estimated. Different from ref. [1], SLR measurements were used as validation in the combined POD process. Table 3 shows the calibration results of ranging biases. The ranging bias difference of Beijing station between Tables 2 and 3 is about 9 cm, due to errors caused by the satellite orbit. The number of SLR measurements is the greatest on June 10 with higher calibration precision obtained, when only 2 cm calibrated difference between Tables 2 and 3 is found. By contrast, there are only 679 SLR measurements on June 11 and the calibrated ranging bias is of lower precision consequently. Therefore the amount of SLR measurements plays a significant part in ranging bias calibration. Although there are several-centimeter differ-
Table 2 Ranging bias calibration results I during 3 consecutive days (m) Date 2009-06-09 2009-06-10 2009-06-11 Mean Std
Hainan
Sichuan
Heilongjiang
Guangdong
−3.280 −3.221 −3.239 −3.247 0.030
−0.795 −0.517 −0.860 −0.724 0.182
−2.014 −2.124 −2.047 −2.062 0.056
−3.714 −3.718 −3.526 −3.653 0.110
POD residual 0.218 0.184 0.214 0.205 0.019
Table 3 Ranging bias calibration results II during 3 consecutive days (m) Date 2009-06-09 2009-06-10 2009-06-11 Mean Std
Beijing
Hainan
Sichuan
Heilongjiang
Guangdong
−1.894 −1.978 −1.868 −1.913 0.057
−3.197 −3.205 −3.109 −3.170 0.053
−0.761 −0.520 −0.775 −0.685 0.143
−1.914 −2.102 −1.902 −1.973 0.112
−3.601 −3.690 −3.365 −3.552 0.168
POD residual 0.216 0.184 0.213 0.204 0.018
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ences in calibrated results of other stations between Tables 2 and 3, with the ranging bias of Beijing station estimated with other stations, the system consistence may be maintained. The calibration errors of all ranging biases obtained with POD are correlated to radial orbit errors. Evaluated with the SLR data, the radial orbit error is 0.133 m for a 24-hour arc, so the calibration accuracy of this approach is better than 1 ns. The mean values of these three days are used as the final ranging biases of all stations, with an accuracy of better than 1 ns.
3 POD experiments Upon the completion of ranging bias calibration based on the two approaches in Sections 1 and 2, the biases are fixed for POD experiments. GEO satellite POD experiments are carried out in order to evaluate the credibility of these two calibrations and the accuracy of the calibrated ranging biases, with accuracy analysis of orbit determination and prediction. SLR measurements used for evaluation are not used in the ranging bias calibration. Five POD experiments are carried out in May and June, 2009, by employing transfer measurements from C-band tracking network in China. Three stations are involved in May, which are Beijing, Hainan and Sichuan, and five stations are involved in June, with Heilongjiang and Guangdong stations added. In the orbital pretreatment, various kinds of errors have also been corrected, which are the same as in Section 2. Different from Section 2, the ranging biases of five stations are mean values of data from June 9–11, 2009, which are not estimated in the POD process. The satellite initial orbital elements and one solar radiation pressure parameter for a 24-hour arc are estimated, and dynamical models are the same as above. Table 4 shows the POD experimental results of the five days. Figure 2 displays the detailed POD residuals of all stations and radial orbit errors evaluated with SLR, where 1013 represents Beijing station, 1043 Hainan station, 1091 Sichuan station, and 7821 SLR station. Table 4 indicates that the mean POD residual of these five days is 0.205 m (about 0.684 ns) and the radial orbit error evaluated with SLR is 0.133 m (about 0.444 ns), with a standard deviation of 0.049 m. In the viewpoint of the
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relationship between radial errors and three-dimensional position errors (about 1:20), POD position accuracy is better than 5 m. POD residuals in Figure 2 show that the mean residuals of all tracking stations are close to zero, while it is reflected that the transfer ranging noise level is very low. The ranging noise of Sichuan station is significantly large, with a standard deviation of about 40 cm. The POD accuracy is also observed in Figure 2, with a radial orbit error of 0.166 m evaluated with SLR. Such GEO satellite POD accuracy is better than that of a MEO satellite POD based on L-band pseudo-range and phase measurements, which was also evaluated with SLR, with a radial orbit accuracy of about 0.30 m in China [15]. Ref. [1] mentioned that GEO satellite POD accuracy was about 2 m based on C-band tracking technique, as represented by orbital overlapping (overlapping arc length is 24 hours for a 3-day arc). We employ the measurements of May 17–19, 2009, to determine orbit over again, with 1.5 days of overlapping arc. Table 5 shows the detailed orbital overlapping results of different arc lengths. The orbit overlapping accuracy is better than 5 m with 8-hour overlapping arc, 1 m with 10-hour overlapping arc. We conclude that the orbital overlapping accuracy is relevant to arc lengths, and POD accuracy results evaluated with SLR in Table 4 are more robust and objective. Besides POD accuracy, orbit prediction accuracy of GEO satellite is also an effective way to evaluate the calibrated ranging biases. POD experiments were carried out for a 24-hour arc. Orbit prediction accuracy is evaluated with SLR after 2 h, which means that the last epoch of POD is about 2 h before the first SLR data epoch. It is important
Figure 2
POD residuals and radial orbit errors, 2009-05-17.
Table 4 POD accuracy statistics (m) Date Station number POD residual Radial orbit error evaluated with SLR SLR measurement number
May 17 3 0.222
May 18 3 0.151
May 19 3 0.220
June 22 5 0.222
June 23 5 0.211
Mean – 0.205
Std – 0.031
0.166
0.164
0.048
0.151
0.134
0.133
0.049
3082
2579
94
894
1096
–
–
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Table 5 POD accuracy statistics of orbital overlapping (m) Overlapping arc length (h)
Radial error
Along-track error
Cross-track error
Position error
2
1.34
15.19
4.63
15.93
4
1.21
15.54
2.56
15.80
6
0.67
7.77
2.22
8.10
8
0.28
4.57
0.29
4.59
10
0.09
0.63
0.69
0.94
Table 6
Orbit predication accuracy (2-hour predication, unit: m) Date
May 17
Station number Radial orbit error evaluated with SLR SLR measurements number
3
3
3
5
5
–
–
0.317
0.634
0.102
0.083
0.729
0.373
0.298
3082
2579
94
894
1096
–
–
Figure 3
May 18
Orbit predication accuracy on May 17–18, 2009.
that the POD arc of orbit prediction is not the same as that of orbit determination, with several hours’ differences in tracking measurements. Table 6 lists the orbit prediction accuracy results of 5 days. Figure 3 displays the radial orbit errors of 2-hour predication, as evaluated with SLR on May 17–18, 2009. The accuracy of orbit predication shows that the mean radial orbit error is 0.373 m and the standard deviation is 0.298 m with 24-hour POD and 2-hour predication arc. This is another important evidence to validate the calibrated ranging biases. For 2-hour orbital predication, Figure 3 shows an accurate but variable accuracy of the radial component. The errors grow fast with long-time predication, with the dynamical model errors perhaps being the main error sources. For both orbit determination and predication accuracy, the ranging bias calibration approaches are effective and Table 7
May 19
June 22
June 23
Mean
Std
reliable, ensuring that the GEO satellite orbit accuracy is better than 5 m with the regional tracking network in China. Experiments show that the valid interval for ranging bias calibration is approximately 1 month during which the biases may be fixed to their calibrated values, but after the 1-month interval, new calibration must be carried out considering the variability of the system performance. With the support of SLR measurements, the ranging bias calibration could be carried out regularly. In these POD experiments, SLR measurements were merely employed in the orbit evaluation without participating in the POD process. Then POD experiments have been carried out with a 24-hour arc, combining SLR and C-band transfer. POD strategy and dynamical models of POD are the same as the above, and Table 7 shows the detailed results. Compared with the results of Table 4, POD residuals level improves a little because of the restriction from SLR measurements. The more the SLR measurements applied, the lower the POD residuals level are. Though orbit accuracy could not be evaluated with SLR, which is included in the POD process, it is reasonable to expect that the accuracy of orbit determination and predication is equivalent with the results of Tables 4 and 6 at least, or even better. It is worth mentioning that the C-band tracking network used in this study is not good enough, with poor GEO satellite tracking geometry. If the tracking network could be expanded by adding more tracking stations abroad, tracking geometry and orbit accuracy could be improved notably. To conclude, GEO satellite POD has been realized with a regional tracking network, combining multiple measurement techniques. And the ranging biases have been calibrated accurately.
Accuracy statistics of combined POD (m) Date
May 17
May 18
May 19
June 22
June 23
Mean
Std
Station Number POD residual SLR residual SLR measurements number
4 0.196 0.111 3082
4 0.148 0.131 2579
4 0.219 0.044 94
6 0.221 0.129 894
6 0.210 0.091 1096
– 0.199 0.101 –
– 0.030 0.036 –
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Conclusions
A new strategy of GEO satellite precise orbit determination is proposed by combining the two tracking techniques, SLR and C-band transfer ranging. The accurate and effective approaches of ranging bias calibration have been implemented. The results can be concluded as follows: (1) Both co-location comparison and combined orbit determination approaches are effective and reliable in C-band ranging bias calibration, with accuracies of 0.5 ns and 1 ns respectively. (2) With calibrated biases, C-band regional tracking network is able to achieve POD accuracy, meeting navigation requirements for GEO satellites. Evaluated with SLR data, the radial orbit error is approximately 0.133 m for a 24-hour arc, while the radial orbit error of 2-hour prediction is about 0.373 m. (3) Precise orbit determination combining SLR and C-band transfer ranging is an effective and reliable strategy for GEO satellites, and the validation shows that the accuracy with SLR is better than 5 m three-dimensional position accuracy. For 2-hour orbital predication, which is more relevant to navigation applications, experiments show accurate but variable accuracy of the radial component. The errors grow fast with long-time predication, the dynamical model errors being the main error sources. For example, in the POD process, only simple solar radiation pressure model or box-wing model was used. For the future research, more realistic solar radiation pressure model will be established and empirical accelerations will be used to “absorb” un-modeled errors. In summary, thanks to the excellent performance of the regional C-band ranging network as well as SLR station, this article takes full advantages of both techniques. All-weather and high precision ranging to GEO satellites has been realized after accurate ranging bias calibration. The results show that the orbit accuracy is able to meet regional navigation demands. The two ranging bias calibration approaches and the combined POD strategy are expected to support satellite telemetry, tracking and control, and space exploration with a better orbit determination accuracy.
This work was supported by the National High-Tech Research and Development Program of China (Grant No. 2007AA12Z345), Space Navigation and Positioning Technique Laboratory of Shanghai Municipality (Grant No. 06ZD22101) and Wuhan University Satellite Navigation and Positioning Laboratory of Education Department (Grant No. GRC-2009004). 1
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