? 2009SCIENCE IN CHINA PRESS
www.99jianzhu.com, shangkun@shao.ac.cn)
Supported by the Innovation Research Plan of CAS, the National Natural Science Foundation of China (Grant Nos. 10973031 and 40904006), the CAS Key Research Program (Grant No. KJCX2-YW-T13-2), and Beijing Aerospace Command and Control Center
mation of the spacecraft to support its tracking and navi-gation. Since 1970 various combinations of tracking data types have been used in different orbital phases of interplanetary spacecrafts, and around that time frame, VLBI (Very Long Baseline Interferometry) began to become a practical deep space tracking technique. Prior to the 1980s, ranging and Doppler were the main ob-servables, but subsequently differential one-way ranging and differential one-way Doppler observables based on interferometric measurement of side tone phases have prevailed. Since 2000, with high precision and low cost achieved, emphasis has been placed on stability, rapid correction and real-time response that demands better performance for new generations of radio and optical tracking systems[3].
According to the geometry of uplink and downlink, radiometric tracking can be basically divided into one-way, two-way and three-way models. On the other hand, according to the implementation of the radio links, these tracking models can be classified as either closed-loop or open-loop. The one-way tracking model is in open-loop mode, in which the tracking signals are generated by the spacecraft-equipped USO (ultra stable oscillator). But the two-way tracking model is closed-loop, in which the signals are generated by an atomic clock on an uplink ground station, and then re-transmitted after frequency multiplication by a trans-ponder on the spacecraft. The downlink signals, coher-ent with the original uplink signals, will be received later by the same ground station where the two signals are cross-correlated in real time. The three-way tracking model is the same as the two-way model, with the only exception that the transmitting and receiving stations are not the same, and is therefore in open-loop mode. Figure 1 reveals differences between the various tracking mod-els. The International Telecommunication Union (ITU) has defined the radio frequency bands (listed in Table 1) for deep-space navigation[4]. Table 2 gives the ratios (multiplying factors) of downlink and uplink frequencies used by NASA’s Deep Space Network (DSN), and rec-ommended by the Consultative Committee for Space Data Systems (CCSDS).
Among these basic tracking modes, the two-way tracking is a closed-loop model where the receiving and transmitting stations are the same. But one-way and three-way tracking are open-loop models. The main dif-ference between closed-loop and open-loop tracking models is that the transmitted and received signals are
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coherent in the closed-loop mode, whereas in the open- loop model the signals are non-coherent. The open-loop measuring process is more difficult than the closed-loop process because of the instability of the clock that gen-erates the tracking signals and the systematic errors of the non-coherent signals. Earlier deep-space navigation missions were dominated by closed-loop tracking, such as Apollo, Viking and Voyager. The closed-loop tracking model has been perfected as the current USB (Unified S-Band) system. In the late 1980s, the stability of on-board ultra-stable oscillators (USO) has been greatly enhanced, making open-loop tracking possible. Open- loop tracking models include one-way or multi-way Doppler, and differential one-way or multi-way Dop-pler/ranging[3].
Figure 1 Two-way and three-way tracking modes[5].
Table 1 Uplink and downlink frequencies for deep-space communica-tion
Frequency band S X Ka
Uplink frequency Downlink frequency
(MHz) (MHz) 2110－2120 2290－2300 7145－7190 8400－8450 34200－34700 31800－32300
Table 2 Frequency multiplying ratios
Uplink band Downlink band Ratio (downlink/uplink)
S S 240/221 S X 880/221 S Ka 3344/221 X S 240/749 X X 880/749 X Ka 3344/749
Compared with traditional closed-loop measurements, the open-loop measuring mode has the following ad-vantages. First of all, since no uplink station is needed in one-way tracking, a lot of resources can be saved and the model can be conveniently used in very-remote deep
Jian N C et al. Sci China Ser G-Phys Mech Astron | Dec. 2009 | vol. 52 | no. 12 | 1849-1857
space missions (such as Voyager). Secondly, in those very remote missions, radio signal propagation may take an extremely long time (sometimes up to several hours)?a situation that is really bad for conventional USB tracking whereas the three-way tracking model would be more practical. Third, in some special orbital phases such as transitioning between planets, the one-way VLBI/DOR tracking model has some obvious advantages. In the last 30 years, the NASA/DSN has used the open-loop tracking models in dozens of deep- space exploration missions, through which the models have matured and have become particularly important today[6].
The differential tacking types include one-way and multi-way (generally 3- or 4-way) Doppler/ranging. The precision of differential observables is higher than that of the direct observables because the instability of the uplink clock and some of the path effects can be re-moved by differencing the two individual Doppler measurements[7,8]. On the other hand, most of the line-of- sight information about the spacecraft motion has been eliminated after differencing. Hence differen-tial observables alone should not be used for orbit de-termination, but must be combined with other non-differential observables in order to recover some of the missing information about the spacecraft dynam-ics[9].
On October 24, 2007, the first Chinese lunar explora-tion satellite Chang’E-1 was launched on the Xichang launching site, and on December 11, 2007 Chang’E-1 began to orbit the moon and send back a large amount of scientific data. The tracking model of Chang’E-1 mainly depends on China’s USB network which can support closed-loop two-way Doppler and ranging data for orbit determination. In addition to USB tracking, the Chinese VLBI network (CVN) also uses angle tracking data for orbit determination. In the USB tracking model, an up-link station transmits S-band signals to the satellite, which are then re-transmitted by a transponder on the satellite. Later the transmitted and received signals are brought together and processed, so that the embedded Doppler and ranging information can be extracted for tracking in a typical closed-loop model.
Following Chang’E-1 will be the Sino-Russian joint Mars mission to be carried out in September or October 2009. The Russian Phobos-Grunt and the Chinese YH-1 satellites will be launched by a Russian carrier rocket,
which is expected to arrive in August or September, 2010 at Mars, about 2 AU (astronomical units) from the earth. As China has no powerful uplink station for re-mote telecommunication, tracking the YH-1 must rely on the open-loop one-way model and the CVN will be used for such tracking activities. In the last couple of years, Chang’E-1 has provided a very good test platform for developing China’s primitive open-loop tracking technique. During the mission, three-way Doppler and differential three-way Doppler demonstrations have been successfully completed. The Doppler data were collected from three CVN stations (namely the Nanshan station in Shanghai, Kunming station in Yunnan prov-ince, and Nanshan station in Urumqi) and then sent to Shanghai through special high-speed Internet links for post-processing. The three-way Doppler and the corre-sponding differential Doppler results have been fully verified for future open-loop tracking of the YH-1 satel-lite between 2010-2011.
1 Principles of open-loop Doppler meas-urement
1.1 Open-loop Doppler formulas
Doppler effects of electromagnetic waves arise from the relative velocities and different time scales between the transmitter and receiver. If we ignore the different time scales in a gravitational field, the first-order approximation of Doppler can be expressed in the framework of the spe-cial theory of relativity[5] as follows:
?v?1?way
≈?1??fT. (1) fR
?c?
In this formula, fT is the transmitted frequency andvis the velocity of the transmitter relative to the receiver. When the distance between the transmitter and receiver is in-creased,vis positive.
In the case of three-way Doppler, the signal propagation can be divided into two processes: uplink and downlink. For the uplink process, the relationship between the trans-mitted frequency fT, the satellite received frequency fS, the relative velocity of the uplink station and satellite v1, and the speed of light c is given by[5]
?v?
fs≈?1?1?fT. (2)
c??
For the downlink process, the relationship between the sat-ellite received frequency fS, the frequency multiplying
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Jian N C et al. Sci China Ser G-Phys Mech Astron | Dec. 2009 | vol. 52 | no. 12 | 1849-1857
environment. Frequency drift rate is related to device
at the downlink station, and the relative velocity of aging. The Doppler systematic deviations can be re-moved by differencing.
downlink station and satellitev2is given by
The simple frequency evolution model is given by
?v? fT=fT0+Bt+A?rand(t), (9) fR≈?1?2?fs?M. (3)
c??
where fT0 is the nominal frequency, B is the linear
So the three-way Doppler frequency can be expressed as
evolution factor, and A is the noise intensity expressed ?v1??v2??v1+v2?
fR≈?1???1??fT?M≈?1??fT?M. (4) as the Allen variance. ccc??????
In the one-way Doppler measurement, the accuracy of
Here second- and higher-order small quantities have been
the observable depends on the USO on the satellite. The
ignored.
relationship between the systematic measurement error
For convenience, the three-way Doppler observable is
and USO accuracy is given by
defined as the average ofv1andv2.
?v?1?way
ΔfR=ΔfT?1??≈ΔfT. (10)
?2v?3?way?c?fR ≈?1?3w?fT?M, (5)
c??In the three-way Doppler measurement, the accuracy of 3?waythe observable depends on the atomic clock at the uplink ?fT?M1fR
v3w≈???c. (6) station. The relationship between the systematic meas-fT?M2
urement errors and the clock accuracy is given by
Equation (6) is the first-order formula of three-way Dop-?2v?3?waypler which depends on the transmitted frequency, received ΔfR=ΔfTM?1?3w?≈ΔfTM. (11)
c??frequency, re-transmission frequency ratio and the velocity
of light The one-way differential Doppler measurement errors
are given by 1.2 Differential Doppler formulas
faction M for re-transmission, the received frequency fR
If the two receiving stations record the downlink signals
simultaneously, differential one-way Doppler can be formulated. The differential one-way Doppler can be expressed as the difference of frequencies recorded at the two stations.
1?way1?way,S21?way,S1D_fR=fR(tR)?fR(tR)
1?way
ΔD_fR≈ΔfT(tT2)?ΔfT(tT1), (12) 12
in which tT1 and tT2 are related to two different trans-mission moments. Finally, the three-way differential
Doppler measurement error is given by
3?way
ΔD_fR≈??ΔfT(tT2)?ΔfT(tT1)???M. (13) 1,2
Through the above analysis we can draw the follow-ing conclusions: (1) The systematic accuracy of one-way Doppler is equal to the accuracy of the on-board USO; (2) The systematic accuracy of the three-way Doppler is equal to M times of the ground station clock accuracy; (3) The differential Doppler accuracy depends on the frequency change between the two transmission mo-ments tT1 and tT2, so the non-differential measure-
?vS2??vS1?
=?1??1?.ftft?T(T2)??T(T1)(7)
cc????
The corresponding formula of differential three-way Doppler then becomes
3?way3?way,S2
D_fR=fR(tR)?fR3?way,S1(tR)
S2S1 ?2v3??2v3?ww
=??1?c??fT(tT2)M???1?c??fT(tT1)M.????
(8)
In our demonstration the main measurement errors are the frequency deviations of the USO (on the satellite) or the atomic clock (at the uplink station). The frequency source involves mainly three indices, namely, frequency accuracy, frequency stability and frequency drift rate. Frequency accuracy is the systematic deviation between the measurements and the nominal value. Frequency stability refers to the frequency dispersion due to the
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ment accuracy depends on the frequency source accu-racy whereas the differential measurement accuracy de-pends on the short-term stability of the source. The simulation results show that the time difference of the two transmission moments is about 0.01 second and so the frequency change is very small (probably under 1 mHz). On the other hand, the accuracy of the source includes long-term drifts that can reach several Hz. Thus the accuracy of the differential measurements is much higher than the non-differential case.
Jian N C et al. Sci China Ser G-Phys Mech Astron | Dec. 2009 | vol. 52 | no. 12 | 1849-1857
The radio frequency signals transmitted by the space-2 Open-loop Doppler experiments on
craft are received by an antenna at a ground station Chang’E-1
2.1 Introducing the Chang’E-1 beacon
The Chang’E-1 satellite transmits both S- and X-band
signals. The X-band signals, which are white noise and cannot be used to extract Doppler, are intended for VLBI tracking only. The S-band has two channels near 2210 MHz, one of which is for one-way tracking while the other is reserved for re-transmitting the uplink sig-nals. Our experimental results show that the stability of the one-way signals is not too good, with a dispersion of about 1 Hz. The corresponding stability of the USO on the satellite is about 4.5×10?10 and so the velocity preci-sion is about 0.1 m/s. Hence one-way Doppler cannot be used for orbit determination because of its poor preci-sion. The uplink stations of Chang’E-1 are Qingdao and Kashi stations, both of which have relatively stable ru-bidium clocks. Three-way Doppler data analysis indi-cates that the short-term stability of these clocks is about 1.31×10?11 so that the precision of three-way Doppler is 20 mHz and the corresponding precision of velocity is 3 mm/s, which can be used only for common orbit deter-mination. The following discussion is based on the three-way Doppler and differential three-way Doppler models.
2.2 Introducing the data recording devices and data flow
where they are subsequently down-converted to inter-mediate frequency. The intermediate frequency signals are then down-converted to baseband signals by a base-band converter (BBC). In our experiment we properly set the local oscillator frequency and let the carrier sig-nal of Chang’E-1 be located at about 500 kHz in the baseband. The whole recording process can be con-trolled by a remote computer. After recording, post- progressing is performed to extract the Doppler infor-mation from the recorded data as shown in Figure 2.
Figure 2 The flow chart for open-loop Doppler data processing.
2.3 Algorithms for open-loop Doppler extraction
Experiments are supported by the CVN network and three CVN stations mentioned above are equipped with the same data recording device. For trial we use two different recording devices which are NUDAQ (PCI- 9812/9810) and K5/vssp32 VLBI data sampling card provided respectively by ADLINK and NICT (National Institute of Information and Communications Tech-nology) of Japan. NUDAQ is a 32-bit bus-based high-performance data acquisition card that can sample data at 20 Mbps and record the data simultaneously on hard disks. The ADLINK card has been further devel-oped, including an outer clock trigger, an outer clock pre-trigger, an outer frequency standard module[10], as well as long time recording function.
The K5/vssp32 designed for VLBI data recording has two types of working models. The one-channel module has a sampling rate of up to 64 Mbps, while the four-channel model is up to 256 Mbps. There are four quantization modes: 1 bit, 2 bits, 4 bits and 8 bits.
The signals transmitted by the Chang’E-1 satellite are different than those from natural radio sources in that they have higher energy levels and SNR (signal-to-noise ratios). We have tried two methods, which are identical in the same integration time, to extract open-loop Dop-pler information from the recorded data.
1. After being down-converted and filtered, the origi-nal data are smoothed and compressed. Then the Dop-pler values can be extracted from the baseband signals using phase counting algorithms.
2. The Doppler values can also be extracted from the baseband using polynomial fitting algorithms that use polynomials to fit the data phase.
Two algorithms are tried to compute the open-loop differential Doppler value.
1. By the time-domain method (also known as “spacecraft narrowband interferometry” or INS), the original signals received by the two stations are mixed and the differential Doppler is extracted.
2. The frequency-domain method (also known as “differenced Doppler”) is to separately extract the open-loop three-way Doppler from the original data at each station, and then difference them to form the dif-ferential three-way Doppler.
In theory, observables based on these two methods are equivalent, but in practice they may differ a lot as
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Jian N C et al. Sci China Ser G-Phys Mech Astron | Dec. 2009 | vol. 52 | no. 12 | 1849-1857
they have rather different accuracies that may depend on a number of factors. Our test results indicate that the two algorithms agree with each other quite well. Since the second method takes less computing resources and does not require bringing the voluminous data together for cross-correlation processing, we often use the second method in practical applications if we can tolerate some loss of precision.
Using eqs. (1)－(8) that relate Doppler frequencies and changes in relative velocity, we can compute the Chang’E-1 satellite’s Doppler velocities and differential Doppler velocities for orbit determination. In practical applications the integration time is usually 1 second for the three-way Doppler and the differential Doppler, but other integration times may be tried for better results as discussed below.
while Figure 3(b) stands for the USB result. The effec-tive three-way data covers about 9 hours as opposed to 13 hours of USB data.
3 Open-loop Doppler measurements for the Chang’E-1 mission
3.1 Open-loop three-way Doppler experiment
Figure 3 Fitted Doppler residuals. (a) The open-loop three-way; (b) the closed-loop two-way (USB).
The open-loop three-way Doppler observation of Chang’E-1 began in May, 2008. The sampling equip-ments were set up at Sheshan station (Shanghai) and at the same time the signal processing algorithm was being developed. The same equipments were set up at Nan-shan station (Urumqi) and Kunming station (Yunnan) in the experiment. The whole system was tested many times during the Chang’E-1 mission. This paper takes the observation of Chang’E-1 on December 18, 2008 as an example to illustrate the data processing task.
The three-way Doppler observation carried out on December 18, 2008 at Sheshan station is the longest ob-servation among the several experiments we performed. The Chang’E-1 perilune is 17 km and the apolune is about 100 km. The uplink stations are Kashi and Qing-dao stations. The effective open-loop three-way Doppler observation lasted for about 9 hours, during which the uplink site is moved from Kashi to Qingdao. At the same time the Chinese USB network provides the closed-loop Doppler tracking data that can be used to validate the open-loop three-way Doppler data.
Figure 3 gives the open-loop and USB closed-loop Doppler observation results covering the period from UTC 18:00, December 18 to UTC 24:00, December 19. Some outliers have been eliminated and the discontinu-ous data in the figure is due to the change of uplink sta-tion. Figure 3(a) shows the three-way Doppler result
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A direct polynomial segment fitting is performed on the three-way Doppler data as mentioned above. The RMS (Root Mean Square) of the fitting residuals is used to represent the Doppler precision. The polynomial segment fitting residuals are shown in Figure 3, most of which vary within ±1 cm but some are outside the ±2 cm range due to discontinuities in the data recording. The statistics of fitted residuals without outliers[11,12] show that the precision of the open-loop three-way Doppler is about 2.63 mm/s and that of the closed-loop USB is about 3.65 mm/s. Hence the precision of the open-loop three-way Doppler is slightly higher than that of the closed-loop two-way Doppler (USB), both using 1-sec integration time.
The precision of the open-loop three-way Doppler can be evaluated for orbit determination with the GEODYN II software package provided by NASA/ GSFC to examine the data residuals. We use the publi-cized precise orbit as the initial orbit and use the three- way Doppler data to modify the initial orbit. This method has the advantage to remove systematic errors so that the random errors can be revealed. Figure 4 gives the residuals of Doppler that can reflect the seriousness of random errors. Figure 4(a) shows the residuals of three-way Doppler assuming the 100×100 lunar gravity model. Figure 4(b) shows the residuals of the two-way Doppler (USB). Both sub-figures show that the residuals
Jian N C et al. Sci China Ser G-Phys Mech Astron | Dec. 2009 | vol. 52 | no. 12 | 1849-1857
are not normally distributed and there are obvious “structures” in the residuals. The long-term trend of the structure in Figure 5 is related to the periodic motion of Chang’E-1, which is about 2 hours per cycle. The short- term features of the structure are perhaps contributed by the high orders of the lunar gravity field[13,14]. The three- way Doppler residuals and the two-way Doppler residuals show obvious correlation, indicating that the two tracking models have similar precision levels. In our experiment the open-loop Doppler data can be used only to evaluate the observation precision but cannot be used to evaluate the orbit determination precision because of deficient tracking data. Application of the open-loop tracking data to orbit determination will be the focus of future work.
statistics of the systematic and random errors. Figure 8 shows the differential results of the first arc on August 29.
4 Discussion and conclusion
From May 2008 through December 2008 we performed twenty open-loop Doppler tracking experiments for Chang’E-1, with results indicating that the precision (~3 mm/s) of the non-differential three-way Doppler is in agreement with the short-term stability (about 10?11) of the rubidium clock at the uplink station. Such perform-ance is expected to be further improved when the ground-station uplink clock is replaced in the future by a more stable atomic clock (such as a hydrogen clock)
with short-term stability as good as 10?15－10?16. But the degree of improvement is ultimately limited by other factors such as noise levels of the receiving stations and radio signal transmission media (viz. solar plasma, tro-posphere and ionosphere). Media effects are among the most important error sources of the Doppler observable and so must be properly corrected (see sec. 13.3.2 of ref. [16]) for better performance in both tracking and radio science applications.
Our experimentation shows that longer integration times can help to increase the measurement accuracy by averaging out some of the noise in the signals. The re-
siduals error RMS (Sheshan station) drops from 3.2
Figure 4 Doppler residuals. (a) The open-loop three-way; (b) the closed-
mm/s to as little as 0.56 mm/s if the integration time is loop.
increased from 1 second to 34 seconds, whereas the er-ror of Nanshan station, due to differences in receiver 3.2 Differential open-loop three-way Doppler
On August 29, 2008 an open-loop three-way Doppler electronics, drops from 4.0 mm/s to only 0.8 mm/s.
These results are comparable to the best S-band Doppler experiment was carried out. The original Doppler data of
performance reported by NASA/JPL[3] in the 1980s. two arcs were recorded at the Sheshan and Nanshan sta-However, we must be aware of the fact that longer inte-tions from which we obtained the differential three-way
Doppler data for the first time. We developed some gration times will not always result in better Doppler simple software to compute the theoretical differential measurements because as the integration time increases
to a certain point, other sources of error may appear. In three-way Doppler values because GEODYN II does not
support this observation data type. Table 3 gives the our tests, the error RMS increases if the integration time is longer than 34 seconds. Table 3 Statistics of open-loop Doppler residuals for Chang’E-1
In applications (such as spacecraft tracking in the
Random Different three-way Systematic errors
cruising stage) in which the spacecraft dynamics are Doppler residuals (mean) errors (σ )
much weaker, very long integration times can be in-Sheshan 4.3 cm/s 3.3 mm/s
August 29
Nanshan 4.5 cm/s 3.5 mm/s voked to get highly accurate Doppler measurements. For First arc
Differential 4.0 mm/s 1.0 mm/s example, for the radio science project in the Cassini Sheshan 5.2 cm/s 3.2 mm/s mission, a whopping 300-sec integration time was used
August 29
Nanshan 5.4 cm/s 4.0 mm/s to get an extremely low error RMS of about 0.0022 Second arc
Differential 3.9 mm/s 1.2 mm/s
mm/s[15]! To achieve such an impressive result takes
Jian N C et al. Sci China Ser G-Phys Mech Astron | Dec. 2009 | vol. 52 | no. 12 | 1849-1857 1855
Figure 5 Residuals of differential Doppler (the first arc of August 29). (a) Non-differential; (b) differential.
careful calibration based on a multi-frequency link differential observables for high-precision orbit deter-
mination, since the differencing has undesirably elimi-strategy working in the X and Ka bands to minimize the
effects of the radio signal transmission media in some nated a great deal of information about the spacecraft highly demanding radio science experiments, such as dynamics.
“Traditional” VLBI (range and range rate measure-verification of general relativity theories and PPN pa-
rameter testing. These measures are also the key to ments on random “white noise” signals from spacecraft)
and differential one-way Doppler measurements based high-performance spacecraft tracking for future Chinese
on open-loop signal recording will be the main data deep-space exploration.
processing modes for China’s upcoming YH-1 Mars Our data have also demonstrated the effective appli-
cation of differential techniques to remove most of the orbiter mission. Three carriers with test tones in the long-term drifts and some of the random errors of the X-band will be used for spacecraft tracking and orbit
determination. Stability of the on-board USO is about ground station clock. Higher precisions of ~1 mm/s and
0.8 mm/s have been obtained using 1-sec and 34-sec 10?12 which is expected to provide higher precision than integration times respectively. It must be emphasized, Chang’E-1. In radio science research, open-loop Dop-however, that the differential three-way Doppler ob-pler can be used for planetary gravity field inversion, servable must be combined with some other non- planetary occultation, planetary ionosphere and mag-1856 Jian N C et al. Sci China Ser G-Phys Mech Astron | Dec. 2009 | vol. 52 | no. 12 | 1849-1857
netic field studies[2]. system with a 10?13 USO can perform as well as a two- Compared with other key observables (such as dif-way Doppler system[17].
ferential one-way ranging DOR), differential one-way Further research will be aimed at accurately estimat-Doppler has two advantages: lower sensitivity to re-ing the frequency/phase information from low-intensity ceiver delay calibration, and no need for an extremely signals received from spacecrafts at Martian distances. stable USO. NASA’s Jet Propulsion Laboratory has We will improve the Doppler extracting algorithms for shown that when the interferometric technique (i.e. the low-SNR data, enhance the efficiency of the processing so-called “time-domain method” described in sec. 2.3 software, and increase the stability of USO for future above) is used with support of a top-quality signal proc-Mars missions.
essing algorithm and a high-precision orbit determina-
The authors would like to thank the Chinese USB network and CVN net-tion program, an USO with 10?12 short-term stability is work for providing the tracking data. We also thank NASA/GSFC for adequate to provide km-level accuracy, while a tracking providing the GEODYN II POD software package.
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