First, the design of deep-space open-loop velocity measurement on the basis of China’s DSN (CDSN) is presented. The process of deep-space open-loop velocity measurement contains six steps. First, Tienwen-1 probe sends X-band downlink signals. Second, ground deep-space stations track Tianwen-1 by using guiding ephemeris to effectively capture its downlink signals. Third, downlink signals are amplified by low-noise amplifiers of ground stations and converted from X-band radio-frequency signals to intermediate-frequency ones of 320 MHz by local down-converters. Fourth, intermediate-frequency signals of Tianwen-1 are collected and recorded in multiple channels using the equipment of baseband conversion and intermediate-frequency signal recording in ground stations. Signals are recorded in a very-long baseline interferometry (VLBI) science receiver format. Fifth, using the self-developed software of deep-space open-loop velocity measurement, the signal processing center processes signals of Tianwen-1 to generate high-precision open-loop velocity observables. Last, open-loop velocity observables are sent to orbit determination systems, and measurement results are provided to science-application analysis systems as needed. The focus lies on signal processing of open-loop velocity measurement which is shown in Fig. 3. The estimated received downlink frequency *f _{est}* of the probe obtained by open-loop velocity measurement is given by

*f*=

_{est}*f*+

_{model}*f*. Wherein, the modeled main carrier frequency in an integration period is calculated by substituting the midpoint time

_{res}*T*/2 of the integration period according to a frequency least-square polynomial fitting model

*f*(

*t*), i.e.,

*f*=

_{model}*f*(

*T*/2), and the least-squares fitting of the second degree is used for higher-precision estimation of residual frequency, i.e., Σ

*(2π*

_{j}*f*– 𝜙

_{res}T*)*

_{j}^{2}= min.

Credit: Space: Science & Technology

First, the design of deep-space open-loop velocity measurement on the basis of China’s DSN (CDSN) is presented. The process of deep-space open-loop velocity measurement contains six steps. First, Tienwen-1 probe sends X-band downlink signals. Second, ground deep-space stations track Tianwen-1 by using guiding ephemeris to effectively capture its downlink signals. Third, downlink signals are amplified by low-noise amplifiers of ground stations and converted from X-band radio-frequency signals to intermediate-frequency ones of 320 MHz by local down-converters. Fourth, intermediate-frequency signals of Tianwen-1 are collected and recorded in multiple channels using the equipment of baseband conversion and intermediate-frequency signal recording in ground stations. Signals are recorded in a very-long baseline interferometry (VLBI) science receiver format. Fifth, using the self-developed software of deep-space open-loop velocity measurement, the signal processing center processes signals of Tianwen-1 to generate high-precision open-loop velocity observables. Last, open-loop velocity observables are sent to orbit determination systems, and measurement results are provided to science-application analysis systems as needed. The focus lies on signal processing of open-loop velocity measurement which is shown in Fig. 3. The estimated received downlink frequency *f _{est}* of the probe obtained by open-loop velocity measurement is given by

*f*=

_{est}*f*+

_{model}*f*. Wherein, the modeled main carrier frequency in an integration period is calculated by substituting the midpoint time

_{res}*T*/2 of the integration period according to a frequency least-square polynomial fitting model

*f*(

*t*), i.e.,

*f*=

_{model}*f*(

*T*/2), and the least-squares fitting of the second degree is used for higher-precision estimation of residual frequency, i.e., Σ

*(2π*

_{j}*f*– 𝜙

_{res}T*)*

_{j}^{2}= min.

Fig. 3. Flow of deep-space open-loop velocity measurement.

Then, authors verify the performance of deep-space open-loop velocity observables in independently supporting the precise orbit determination of the probe taking China’s Tianwen-1 probe as an example, this section. From 8 to 10 June 2021, the deep-space TT&C system organized the deep-space stations JM01 and KS01 to carry out tests of 3 consecutive days on open-loop velocity-measurement-based orbit determination of Tianwen-1. During the testing, the baseband equipment of deep-space stations and the software of deep-space open-loop velocity measurement generated high-precision velocity observables synchronously. In addition, baseband equipment synchronously output distance observables, while the deep-space TT&C interferometry system and the VLBI orbit-measurement subsystem of Chinese Academy of Sciences both output angle observables. All these observables were used for precise orbit determination of Tianwen-1. To test independent support of velocity measurement for orbit determination, the orbit determination of Tianwen-1 with the sole application of baseband and open-loop velocity measurement are implemented respectively. The results show that the accuracy of baseband velocity measurement is between 0.38 and 0.43 mm/s (1δ and integration time of 1 s), while that of open-loop velocity measurement is between 0.15 and 0.2 mm/s. The accuracy of deep-space open-loop velocity measurement is 2 times higher than that of baseband velocity measurement. To further verify the effect of using velocity observables alone for orbit determination of Tianwen-1, the accuracy of orbit determination is verified by mutual comparison. During the orbit determination, a group of orbit values is calculated by distance, velocity, and VLBI delay observables, named *orbit_all*. A group of orbit values is calculated by only using baseband velocity observables, named *orbit_baseband*. A group of orbit values is calculated by only using open-loop velocity observables, named *orbit_openloop*. Figure 6 shows the deviations between orbit_baseband and orbit_all, while Fig. 7 shows those between orbit_openloop and orbit_all. Both groups of orbital position deviations are less than 50 m. The 50-m orbit determination accuracy mentioned in the paper is an internal verification accuracy. Thus, orbit determination accuracy of 50 m of Tianwen-1 can be achieved on the basis of open-loop velocity observables alone.

Fig. 6. Comparison result of independent orbit determination of Tianwen-1 by baseband velocity measurement.

Fig. 7. Comparison result of independent orbit determination of Tianwen-1 by open-loop velocity measurement.

Finally, authors present application of open-loop velocity measurement to planetary atmosphere detection. Tianwen-1 orbiting Mars provides good conditions for autonomous Martian atmospheric and ionospheric retrieval based on Mars-to-Earth radio occultation. When Mars happens to gradually occult downlink signals of Tianwen-1, downlink signals happen to pass through the Martian atmosphere and ionosphere and can be received by the ground station. Ground-received signals contain the influence of Martian atmosphere and ionosphere on signal frequency and phases. By theoretical methods of atmospheric and ionospheric retrieval, the Martian atmosphere and ionosphere can be retrieved effectively on the basis of autonomously measured data. According to the orbit prediction of Tianwen-1, it was estimated in advance that downlink signals of Tianwen-1 would be occulted by Mars between 18:37 and 19:19 Beijing time on 27 May, forming the condition of observing Mars-to-Earth radio occultation. KS01 of CDSN carried out a 2-way measurement of Tianwen-1 from 16:00 to 20:00 after which baseband velocity measurement results and open-loop velocity measurement results are obtained. Figure 9 illustrates relevant orbit determination residuals of velocity observables. From the enlarged figure (i.e., Fig. 10), the oscillating residual Doppler frequency caused by radio occultation is clearly visible, with obvious occultation characteristics, and random jitter noise of open-loop velocity measurement is lower than that of baseband velocity measurement. In addition, residuals after precise orbit determination of Tianwen-1 are explained to effectively demonstrate the measurement accuracy of Tianwen-1. For normal orbit determination of Tianwen-1, it is not necessary to include measurement data of radio occultation. On the basis of radio-occultation measurement data of Tianwen-1, Beijing Aerospace Control Center carried out Martian ionospheric retrieval. Their results preliminarily verify that open-loop velocity observables can effectively support the research on Mars radio science as well.

Fig. 9. Orbit determination residuals in radio-occultation observation arc on 27 May 2023.

Fig. 10. Orbit determination residual during radio occultation on 27 May 2023 (left, occultation ingress; right, occultation egress).

#### Journal

Space: Science & Technology

#### Article Title

Method and Application of High-Precision Open-Loop Velocity Measurement of Tianwen-1 Probe

#### Article Publication Date

29-Jan-2024

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