A digital open-loop Doppler processing prototype for

Science in China Series G: Physics, Mechanics & Astronomy © 2009

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A digital open-loop Doppler processing prototype for deep-space navigation JIAN NianChuan1†, SHANG Kun1,2†, ZHANG SuJun1,2, WANG MingYuan1,2, SHI Xian1,2, PING JingSong1, YAN JianGuo5, TANG GeShi3, LIU JunZe3, QIU Shi1, FUNG Lai-Wo1, ZHANG Hua4, WANG Zhen4 & GOU Wei1 1

Shanghai Astronomical Observatory of Chinese Academy of Sciences, Shanghai 200030, China; Graduate School of Chinese Academy of Sciences, Beijing 100049, China; 3 Beijing Aerospace Command and Control Center, Beijing 100094, China; 4 Urumqi Astronomical Station of National Astronomical Observatories, CAS, Urumqi 830011, China; 5 State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430070, China 2

A prototype based on digital radio technology with associated open-loop Doppler signal processing techniques has been developed to measure a spacecraft’s line-of-sight velocity. The prototype was tested in China’s Chang’E-1 lunar mission relying on S-band telemetry signals transmitted by the satellite, with results showing that the residuals had a RMS value of ~3 mm/s (1 σ ) using 1-sec integration, which is consistent with the Chinese conventional USB (Unified S-Band) tracking system. Such precision is mainly limited by the short-term stability of the atomic (e.g. rubidium) clock at the uplink ground station. It can also be improved with proper calibration to remove some effects of the transmission media (such as solar plasma, troposphere and ionosphere), and a longer integration time (e.g. down to 0.56 mm/s at 34 seconds) allowed by the spacecraft dynamics. The tracking accuracy can also be increased with differential methods that may effectively remove most of the long-term drifts and some of the short-term uncertainties of the uplink atomic clock, thereby further reducing the residuals to the 1 mm/s level. Our experimental tracking data have been used in orbit determination for Chang’E-1, while other applications (such as the upcoming YH-1 Mars orbiter) based on open-loop Doppler tracking will be initiated in the future. Successful application of the prototype to the Chang’E-1 mission in 2008 is believed to have great significance for China’s future deep space exploration. open-loop Doppler, differential Doppler, deep space navigation, Chang’E-1

The radio telecommunication system of a deep space probe fulfills two main functions: the first one (uplink) is to transmit commands from a ground station to the probe; the second (downlink) is to send the telemetry signals from the probe to some ground station(s). The radio telecommunication system is used in the two areas, namely, radio science and spacecraft tracking/navigation.

Radio science refers to making use of the characteristics (including amplitude, phase and polarization) of the telemetric signals to determine a planet’s mass and mass distribution, ionosphere, atmosphere and surface features, and on some occasions conduct relativity tests[1,2]. On the other hand, the radio telecommunication system can be used to get the ranging, velocity and angle infor-

Received June 10, 2009; accepted July 23, 2009 doi: 10.1007/s11433-009-0298-4 † Corresponding author (email: [email protected], [email protected]) Supported by the Innovation Research Plan of CAS, the National Natural Science Foundation (Grant Nos. 10973031 and 40904006), and Beijing Aerospace Command and Control Center

Citation: Jian N C, Shang K, Zhang S J, et al. A digital open-loop Doppler processing prototype for deep-space navigation. Sci China Ser G, 2009, 52(12): 1-9, doi: 10.1007/s11433-009-0298-4

mation of the spacecraft to support its tracking and navigation. 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 observables, 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 transponder on the spacecraft. The downlink signals, coherent 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 models. The International Telecommunication Union (ITU) has defined the radio frequency bands (listed in Table 1) for deep-space navigation. Table 2 gives the ratios (multiplying factors) of downlink and uplink frequencies used by NASA’s Deep Space Network (DSN), and recommended 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 difference between closed-loop and open-loop tracking models is that the transmitted and received signals are 2

coherent in the closed-loop mode, whereas in the openloop 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 generates 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. Openloop tracking models include one-way or multi-way Doppler, and differential one-way or multi-way Doppler/ranging[3].

Figure 1

Two-way and three-way tracking modes[4].

Table 1 Uplink and downlink frequencies for deep-space communication Frequency band S X Ka

Uplink frequency (MHz) 2110－2120 7145－7190 34200－34700

Downlink frequency (MHz) 2290－2300 8400－8450 31800－32300

Table 2 Frequency multiplying ratios Uplink band S S S X X X

Downlink band S X Ka S X Ka

Ratio (downlink/uplink) 240/221 880/221 3344/221 240/749 880/749 3344/749

Compared with traditional closed-loop measurements, the open-loop measuring mode has the following advantages. 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

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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 deepspace exploration missions, through which the models have matured and have become particularly important today. 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 removed by differencing the two individual Doppler measurements. On the other hand, most of the line-ofsight information about the spacecraft motion has been eliminated after differencing. Hence differential observables alone should not be used for orbit determination, but must be combined with other non-differential observables in order to recover some of the missing information about the spacecraft dynamics. On October 24, 2007, the first Chinese lunar exploration 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 uplink 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. Follwoing 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 remote 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 province, 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 corresponding differential Doppler results have been fully verified for future open-loop tracking of the YH-1 satellite between 2010-2011.

1 Principles of open-loop Doppler measurement 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 special theory of relativity[4] as follows:

⎛ v⎞ f R1− way ≈ ⎜1 − ⎟ fT . ⎝ c⎠

(1)

In this formula, fT is the transmitted frequency and v is the velocity of the transmitter relative to the receiver. When the distance between the transmitter and receiver is increased, v is 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 transmitted frequency fT , the satellite received frequency f S , the relative velocity of the uplink station and satellite v1 , and the speed of light c is given by

⎛ v ⎞ f s ≈ ⎜ 1 − 1 ⎟ fT . (2) c⎠ ⎝ For the downlink process, the relationship between the satellite received frequency f S , the frequency multiplying faction M for re-transmission, the received frequency f R

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at the downlink station, and the relative velocity of downlink station and satellite v2 is given by

⎛ v ⎞ f R ≈ ⎜1 − 2 ⎟ f s ⋅ M . (3) c ⎠ ⎝ So the three-way Doppler frequency can be expressed as ⎛ v ⎞⎛ v ⎞ ⎛ v +v ⎞ f R ≈ ⎜1 − 1 ⎟⎜1 − 2 ⎟ fT ⋅ M ≈ ⎜1 − 1 2 ⎟ fT ⋅ M . (4) c ⎠⎝ c⎠ c ⎠ ⎝ ⎝ Here second- and higher-order small quantities have been ignored. For convenience, the three-way Doppler observable is defined as the average of v1 and v2 .

⎛ 2v ⎞ f R3− way ≈ ⎜1 − 3w ⎟ fT ⋅ M , c ⎠ ⎝

(5)

1 f 3− way − fT ⋅ M (6) v3w ≈ − ⋅ R ⋅ c. 2 fT ⋅ M Equation (6) is the first-order formula of three-way Doppler which depends on the transmitted frequency, received frequency, re-transmission frequency ratio and the velocity of light

1.2 Differential Doppler formulas

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. D _ f R1− way = f R1− way, S 2 ( t R ) − f R1− way, S1 ( t R ) ⎛ vS 2 ⎞ ⎛ v S1 ⎞ = ⎜1 − ⎟ fT ( tT 2 ) − ⎜ 1 − ⎟ fT ( tT 1 ) . (7) c ⎠ c ⎠ ⎝ ⎝ The corresponding formula of differential three-way Doppler then becomes D _ f R3− way = f R3− way, S 2 ( t R ) − f R3− way, S1 ( tR ) ⎛ 2v S 2 ⎞ ⎛ 2v S 1 ⎞ = ⎜⎜1 − 3w ⎟⎟ fT ( tT 2 ) M − ⎜⎜1 − 3w ⎟⎟ fT ( tT 1 ) M . c ⎠ c ⎠ ⎝ ⎝

(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 environment. Frequency drift rate is related to device 4

aging. The Doppler systematic deviations can be removed by differencing. The simple frequency evolution model is given by fT = fT0 + Bt + A ⋅ rand ( t ) , (9) where fT0 is the nominal frequency, B is the linear evolution factor, and A is the noise intensity expressed as the Allen variance. In the one-way Doppler measurement, the accuracy of the observable depends on the USO on the satellite. The relationship between the systematic measurement error and USO accuracy is given by ⎛ v⎞ Δf R1− way = ΔfT ⎜1 − ⎟ ≈ ΔfT . (10) ⎝ c⎠ In the three-way Doppler measurement, the accuracy of the observable depends on the atomic clock at the uplink station. The relationship between the systematic measurement errors and the clock accuracy is given by ⎛ 2v ⎞ Δf R3− way = ΔfT M ⎜1 − 3w ⎟ ≈ ΔfT M . (11) c ⎠ ⎝ The one-way differential Doppler measurement errors are given by ΔD _ f R112− way ≈ ΔfT ( tT 2 ) − ΔfT ( tT 1 ) ,

(12)

in which tT 1 and tT 2 are related to two different transmission moments. Finally, the three-way differential Doppler measurement error is given by

ΔD _ f R31,2− way ≈ ⎡⎣ ΔfT ( tT 2 ) − ΔfT ( tT 1 ) ⎤⎦ ⋅ M .

(13)

Through the above analysis we can draw the following 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 moments tT 1 and tT 2 , so the non-differential measurement accuracy depends on the frequency source accuracy whereas the differential measurement accuracy depends 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.

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2 Open-loop Doppler experiments on 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 signals. 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 precision is about 0.1 m/s. Hence one-way Doppler cannot be used for orbit determination because of its poor precision. The uplink stations of Chang’E-1 are Qingdao and Kashi stations, both of which have relatively stable rubidium clocks. Three-way Doppler data analysis indicates 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 determination. 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 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 Technology) 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 developed, including an outer clock trigger, an outer clock pre-trigger, an outer frequency standard module, 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 radio frequency signals transmitted by the space-

craft are received by an antenna at a ground station where they are subsequently down-converted to intermediate frequency. The intermediate frequency signals are then down-converted to baseband signals by a baseband converter (BBC). In our experiment we properly set the local oscillator frequency and let the carrier signal of Chang’E-1 be located at about 500 KHz in the baseband. The whole recording process can be controlled by a remote computer. After recording, post-progressing is performed to extract the Doppler information 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 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 Doppler information from the recorded data. 1. After being down-converted and filtered, the original data are smoothed and compressed. Then the Doppler 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 differential three-way Doppler. In theory, observables based on these two methods are equivalent, but in practice they may differ a lot as they have rather different accuracies that may depend on a number of factors. Our test results indicate that the two

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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 eq. (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.

3 Open-loop Doppler measurements for the Chang’E-1 mission

Figure 3 Fitted Doppler residuals. (a) The open-loop three-way; (b) the closed-loop two-way (USB).

3.1 Open-loop three-way Doppler experiment

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

The open-loop three-way Doppler observation of Chang’E-1 began in May, 2008. The sampling equipments 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 Nanshan 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 observation 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 Qingdao 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 discontinuous data in the figure is due to the change of uplink station. Figure 3(a) shows the three-way Doppler result while Figure 3(b) stands for the USB result. The effective three-way data covers about 9 hours as opposed to 13 hours of USB data. A direct polynomial segment fitting is performed on the

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discontinuities in the data recording. The statistics of fitted residuals without outliers 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 publicized precise orbit as the initial orbit and use the threeway 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 100x100 lunar gravity model. Figure 4(b) shows the residuals of the two-way Doppler (USB). Both sub-figures show that the residuals 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 shortterm features of the structure are perhaps contributed by

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the high orders of the lunar gravity field. 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.

Figure 4 loop.

Doppler residuals. (a) The open-loop three-way; (b) closed-

3.2 Differential open-loop three-way Doppler

On August 29, 2008 an open-loop three-way Doppler experiment was carried out. The original Doppler data of two arcs were recorded at the Shenshan and Nanshan stations from which we obtained the differential three-way Doppler data for the first time. We developed some simple software to compute the theoretical differential three-way Doppler values because GEODYN II does not support this observation data type. Table 3 gives the statistics of the systematic and random errors. Figure 8 shows the differential results of the first arc on August 29. Table 3 Statistics of open-loop Doppler residuals for Chang’E-1 Random Different three-way Systematic errors Doppler residuals (mean) errors (σ ) Sheshan 4.3 cm/s 3.3 mm/s August 29 Nanshan 4.5 cm/s 3.5 mm/s First arc Differential 4.0 mm/s 1.0 mm/s August 29 Second arc

Sheshan

5.2 cm/s

Nanshan

5.4 cm/s

3.2 mm/s 4.0 mm/s

Differential

3.9 mm/s

1.2 mm/s

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 performance 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, troposphere 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 residuals error RMS (Sheshan station) drops from 3.2 mm/s to as little as 0.56 mm/s if the integration time is increased from 1 second to 34 seconds, whereas the error of Nanshan station, due to differences in receiver electronics, drops from 4.0 mm/s to only 0.8 mm/s. These results are comparable to the best S-band Doppler performance reported by NASA/JPL[3] in the 1980s. However, we must be aware of the fact that longer integration times will not always result in better Doppler measurements because as the integration time increases to a certain point, other sources of error may appear. In our tests, the error RMS increases if the integration time is longer than 34 seconds. In applications (such as spacecraft tracking in the cruising stage) in which the spacecraft dynamics are much weaker, very long integration times can be invoked to get highly accurate Doppler measurements. For example, for the radio science project in the Cassini mission, a whopping 300-sec integration time was used to get an extremely low error RMS of about 0.0022 mm/s[15]! To achieve such an impressive result takes careful calibration based on a multi-frequency link strategy working in the X and Ka bands to minimize the effects of the radio signal transmission media in some highly demanding radio science experiments, such as

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Figure 5

Residuals of differential Doppler (the first arc of August 29). (a) Non-differential; (b) differential.

verification of general relativity theories and PPN parameter testing. These measures are also the key to high-performance spacecraft tracking for future Chinese deep-space exploration. Our data have also demonstrated the effective application of differential techniques to remove most of the long-term drifts and some of the random errors of the ground station clock. Higher precisions of ~1 mm/s and 0.8mm/s have been obtained using 1-sec and 34-sec integration times respectively. It must be emphasized, however, that the differential three-way Doppler observable must be combined with some other nondifferential observables for high-precision orbit determination, since the differencing has undesirably eliminated a great deal of information about the spacecraft dynamics. 8

“Traditional” VLBI (range and range rate measurements on random “white noise” signals from spacecraft) and differential one-way Doppler measurements based on open-loop signal recording will be the main data processing modes for China’s upcoming YH-1 Mars orbiter mission. Three carriers with test tones in the X-band will be used for spacecraft tracking and orbit determination. Stability of the on-board USO is about 10−12 which is expected to provide higher precision than Chang’E-1. In radio science research, open-loop Doppler can be used for planetary gravity field inversion, planetary occultation, planetary ionosphere and magnetic field studies[2]. Compared with other key observables (such as differential one-way ranging DOR), differential one-way Doppler has two advantages: lower sensitivity to re-

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ceiver delay calibration, and no need for an extremely stable USO. NASA’s Jet Propulsion Laboratory has shown that when the interferometric technique (i.e. the so-called “time-domain method” described in sec. 2.3 above) is used with support of a top-quality signal processing algorithm and a high-precision orbit determination program, an USO with 10−12 short-term stability is adequate to provide km-level accuracy, while a tracking system with a 10−13 USO can perform as well as a twoway Doppler system[17].

Further research will be aimed at accurately estimating the frequency/phase information from low-intensity signals received from spacecrafts at Martian distances. We will improve the Doppler extracting algorithms for low-SNR data, enhance the efficiency of the processing software, and increase the stability of USO for future Mars missions. The authors would like to thank the Chinese USB network and CVN network for providing the tracking data. We also thank NASA/GSFC for providing the GEODYN II POD software package.

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