The Chinese Mars exploration mission is planned to be launched in 2020, which includes an orbiter, a lander, and a rover. High precision Martian ephemeris is very important in Mars exploration, especially for the Martian orbit insertion and the Martian lander/rover landing. In this paper, we used simulation data to analyze the short-term prediction accuracy of the Martian ephemeris. The simulation results show that the accuracy of Mars position is expected to be better than 50 m for 180-day prediction, when 90-150 days’ range measurements are used to estimate the orbit of the Mars. Range bias affects the prediction accuracy and the arc length for estimation is limited. The prediction accuracy will improve with higher orbit, and the orbit error of probes has an obvious effect on the prediction accuracy of the Martian ephemeris.
The Chinese Mars exploration mission is planned to be launched in 2020, which includes an orbiter, a lander, and a rover [
The uncertainty of the planetary ephemerides is one of the major factors that affect the accuracy of the navigation. Jet Propulsion Laboratory (JPL) has been continuously supporting the maintenance and improvement of the ephemerides since the 1960s to satisfy the needs of high precision planetary ephemeris for the deep space navigation. For the Viking mission in 1976, the ephemeris accuracy requirements for Mars orbit insertion were on the level of 50 km; in the same period, the ephemeris accuracy requirements were raised to 5 km for the Pathfinder probe, which was required for a direct entry into the Mars atmosphere. For Mars Exploration Rover (MER), which was launched in 2003, the demand was better than 1km [
The data of Mars Global Surveyor (MGS) and Mars Express (MEX) were also used for the JPL DE [
According to the time and coordinates system standard for the Chinese Mars exploration mission, DE421 ephemeris, which was released in 2008, will be adopted in this mission. DE421 included additional ranging and Very Long Baseline Interferometry (VLBI) measurements of Mars spacecraft and Venus Express spacecraft, the updated estimates of planetary masses, additional lunar laser ranging, and so on, and the Mars position accuracy predicted to 2008 was expected to be better than 300 m [
Updating ephemeris is necessary for meeting the requirements of Mars exploration. Taking the DE430 ephemeris as an example, which was released in 2013, 5 years after DE421, the Mars orbit has been improved through an updated treatment of asteroids and additional VLBI observations and range measurements [
The difference on relative positions and velocities of Mars and earth between DE421 and DE430.
The range/Doppler and VLBI techniques are used in Chinese deep space explorations. Chinese Deep Space Network (CDSN) includes Jiamusi (JMS), Kashgar (KS), and Zapala (ZP, Argentina) deep space stations. Chinese VLBI network (CVN) consists of Tianma, Beijing, Kunming, and Urumqi. Since it is different for the sensitivity of different types of measurements to the error of ephemerides, Martian ephemeris should be improved by using the most sensitive measurement data in principle.
The Chinese Mars probe will enter the 7.2 hours period mission orbit to perform remote studies of Mars. The differences of the simulated measurements using different ephemerides (DE421 and DE430) are shown in Figure
Measurement differences using DE421 and DE430.
The accuracy of range measurement is better than 1m, Doppler measurement is about 0.1mm/s, delay measurement is 0.1ns (phase delay is 10ps), and delay-rate measurement is 1ps/s. Comparing with the results shown in Figure
The orbit of the spacecraft was determined firstly, and the spacecraft orbit was fixed to determine the Mars orbit. Some researchers have processed the tracking data of MEX and analyzed the orbit determination accuracy. The tracking measurements were two-way and three-way Doppler in the S- and X-bands. Three CVN stations located at Shanghai, Kunming, and Urumqi started tracking MEX on August 7, 2009, and the tracking lasted about 8 hours. In the MEX observations, the transmitting station was New Norcia (NNO) station in Australia belonging to the ESA. The X-band uplink signals were generated from NNO station and X/S-band downlink signals were retransmitted after frequency multiplication by an on-board transponder [
We also used the software developed by Shanghai Astronomical Observatory (SHAO) named Shao Orbit Determination Program (SODP) to determine the orbit of the MEX. Table
MEX orbital tracking data.
Types of tracking data | Observation time | Stations |
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Two-way Doppler | From 2009-08-07T20:40 to 2009-08-08T04:00(UTC) | NNO-NNO |
Three-way Doppler | NNO-Shanghai, | |
NNO-Kunming, | ||
NNO-Urumqi |
The configuration of SODP in MEX POD.
Item | |
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Martian gravity field | GMM3_120 |
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N-body perturbation | Sun, planets, Moon, Phobos, and Deimos |
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Solar radiation | Fixed ratio of area to mass |
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Relativity perturbation | Schwarzschild |
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Initial coordinate | Mars J2000 |
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Mars-centered coordinate | Pathfinder model |
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Earth tropospheric correction | Hopfield model |
The reconstructed orbit differences between SODP and ROB.
Types of tracking data | Position (m) | Velocity (m/s) | ||||||
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R | T | N | Pos. | R | T | N | Vel. | |
Three-way Doppler | 1.11 | 50.20 | 23.31 | 55.36 | 0.008 | 0.004 | 0.007 | 0.011 |
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Two-way & three-way Doppler | 1.06 | 18.98 | 9.24 | 21.13 | 0.003 | 0.002 | 0.003 | 0.004 |
The postfit RMS of residuals was about 0.15mm/s, and the position and velocity differences between SODP and ROB were about tens of meters and about 0.01 m/s, respectively.
Mars orbit can be determined using range measurements with long data arcs to improve its accuracy while keeping the orbit of the spacecraft fixed. Besides measurement error, the probe orbit error is one of the main error sources in the process of Mars orbit determination.
Given a more rigorous equation of motion, Mars orbit integration needs to be performed in the framework of general relativity that is different from the framework of Newtonian physics, in which the motion of an earth satellite is considered. In the weak gravitational field of the solar system, the motion of Mars under the influence of the forces of the sun and the planets is described as
where
In this paper, simulation data was used to analyze the accuracy of improved short-term Martian ephemeris. The work flow of this simulation is as follows: Propagate a Mars orbit according to the initial state derived from the DE421 ephemeris to get the “true” Mars ephemeris. Simulate range data with noise and bias according to the “true” Mars ephemeris and the “true” Mars probe orbit. Estimate the Mars orbit and analyze the Mars ephemeris accuracy. The orbit of the probe was fixed and obtained from POD results with the orbital errors.
Various probe orbits with certain errors obtained under different trajectory determination strategies were used to perform Mars OD by Monte Carlo method, in which the measurement noise was produced at random on a certain level of precision. According to the above sensitivity analysis, for spacecraft in orbit around Mars, the Doppler measurements were used to estimate the orbit of the spacecraft and range measurements were then used to improve the Mars ephemeris. The detailed flowchart is as in Figure
The flowchart of the Mars ephemeris determination.
In our simulation, the tracking stations were JMS, KS, and ZP. The measurement noise of range rate data was 0.1mm/s and that of the range was 1m. The measurement sampling interval was 30s. The influence of the length of data arc, observing strategy, range bias, spacecraft’s orbit accuracy, spacecraft’s orbit altitude, and spacecraft’s orbit inclination on short-time prediction accuracy of the Mars orbit was analyzed. The specific analysis scheme is as in Table
Factors affecting the short-term prediction of the Martian ephemeris.
Factors | Scheme | |
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Data arcs(days) | 0/30/60/90/120/150/180/210 | |
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Observing strategy | Stations | KS, JMS and ZP; JMS and ZP |
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Range bias | 5 m/ 0 m | |
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Orbit accuracy of a probe | 10 m/ 100 m | |
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Orbit altitude of a probe | 200 km/ 5000 km | |
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Orbit inclination of a probe | 0°/30°/60°/90° |
Since the Mars velocity accuracy of JPL ephemerides is better than 0.2mm/s and it is much higher than that of Mars probe, which is about 10 mm/s, we constrained the initial velocity vectors and only estimated position components of Mars in the simulation analysis, and the initial position error of the Mars was 1km; furthermore, the calculation results of this paper were based on Monte Carlo simulations.
For the (200×200) km Mars probe orbit—with orbital inclination of 0° and orbit error of 10 m—three observing strategies shown in Table
Observing strategies and the accuracy of range measurements.
Strategy | Observing frequency | Stations | Noise level | Systematic errors |
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Strategy 1 | 2 hours every day | KS JMS ZP | 1m | 5m |
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Strategy 2 | 2 hours every day | JMS ZP | 1m | 5m |
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Strategy 3 | 2 hours every 5 days | JMS ZP | 1m | 5m |
Mars orbit was determined using 30, 60, 90, 120, 150, 180, and 210 days’ observations and predicted to 180 days, and the prediction results are shown in Figure
The Martian ephemeris short-term prediction under different observing strategies.
It can be concluded that with the accumulation of the observation arc length, the accuracy of the orbit prediction of these three strategies is on the same level. This is mainly because the requirement for the number and frequency of the observation is reduced when the observation arc is long enough. Considering the ground stations resource is limited, the following analyses on influence of range bias, spacecraft’s orbit accuracy, altitude, and inclination on short-time prediction accuracy of the Mars orbit were based on Strategy 3.
This section analyses the influence of different ranging systematic errors on the short-term predication accuracy of the Mars position. For the (200×200) km Mars probe orbit—with orbital inclination of 0° and orbit error of 10 m—considering the error of 0 m/5 m ranging systematic respectively, we used 30/60/90/120/150/180/210 days’ data arc to determine the position of Mars and forecast for 180 days, and the results are shown in Figure
The Martian ephemeris short-term prediction using data whether containing range bias.
It can be concluded that when the observation arc was less than 90 days, the 0 m/5 m ranging systematic error had little influence on the accuracy of the Mars position prediction. However, with the increase of the observation arc length, the prediction accuracy using the observations which included 5 m ranging systematic error was obviously decreased, while the result using the observations without ranging systematic error was stable on the level of about 40 m. This is mainly because the ranging systematic error is accumulated with the increase of the observation arc length, resulting in influencing the orbit determination accuracy of the Mars position.
According to the above analysis, consider that the ranging systematic error cannot be avoided in deep space mission; moreover, the results of using observations without ranging systematic error of 120/150/180/210 days’ data arc are on the same level. So the observations containing 5 m ranging systematic error were used in the following sections.
This section analyses the influence of different Mars probe obit accuracy on the short-term predication accuracy of the Mars position. For the (200×200) km Mars probe orbit, with orbital inclination of 0°, considering the probe orbit accuracy of 10 m/ 100 m, respectively, we used 30/60/90/120/150 days’ data arc to determine the position of Mars and forecast for 180 days, and the results are shown in Figure
The Martian ephemeris short-term prediction with different probe orbit errors.
The results showed that the prediction precision of Mars position increased with the increasing of the Mars probe orbit accuracy. The Mars position prediction error using 90/120/150 days’ data-arc length was about 300 m for 100 m orbit error, while the precision was better than 50 m for 10 m orbit error.
It can be concluded that Mars probe orbit error is an important source error which can affect the short-term prediction of the Mars position. In order to obtain the Mars orbit with position accuracy better than 50 m, the Mars probe orbit precision should be about 10 m.
For the Mars probe orbit with orbital inclination of 0° and orbit error of 10 m, considering the probe altitude of 200 km/ 5000 km, respectively, we used 30/60/90/120/150 days’ data arc to determine the position of Mars and forecast for 180 days, and the results are shown in Figure
The Martian ephemeris short-term prediction with different probe orbit altitudes.
The results indicated that the prediction precision of Mars position increased with the increasing of the Mars probe orbit altitude. For (200×200) km orbit, the Mars position prediction error using 90/120/150 days’ data-arc length was about 50 m, while the Mars position prediction error was about 20 m for (5000×5000) km orbit.
It can be concluded that the orbit height of the Mars probe is able to effect the precision of the Mars position prediction. This is mainly because the velocity error of the higher of orbiters is smaller and then the error transmitted to the Mars orbit is smaller, resulting in influencing the orbit determination accuracy of the Mars position.
Chinese Mars orbiter will fly on a large inclination orbit. The influence of orbit inclination was analyzed and the results are shown in Figure
The Martian ephemeris short-term prediction with different probe orbit inclination.
The results showed that different orbital inclinations had no obvious influence on the Mars orbit determination.
The range bias, the orbit error of probes, and the orbit altitude of probes had obvious impacts on 180-day prediction precision. Table
Position precision of the Martian ephemeris short term prediction (unit: m).
Range bias | Probes’ orbit altitude | Probes’ orbit error | Data-arcs (days) | ||||||
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30 | 60 | 90 | 120 | 150 | 180 | 210 | |||
none | 200 km | 10 m | 170.67 | 43.58 | 31.08 | 27.43 | 25.13 | 25.55 | 34.16 |
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5m | 200 km | 10 m | 170.91 | 43.45 | 34.17 | 40.45 | 56.40 | 179.68 | 277.59 |
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5m | 200 km | 100 m | 2270.27 | 517.66 | 336.74 | 293.59 | 286.08 | ||
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5m | 5000 km | 10 m | 31.40 | 14.07 | 9.05 | 23.70 | 61.72 |
Improving the accuracy of the short-term prediction of the Mars ephemeris is of great value for the engineering and scientific missions of Mars exploration. In this paper, the simulation analysis method is used to analyze the technical proposal of improving the short-term prediction of the Mars ephemeris and the accuracy that can be achieved by this method. According to the measurement accuracy and the orbit determination accuracy of probes in orbit around Mars, the short-term prediction accuracy of Mars ephemeris was analyzed in the aspects of data arc, observing strategy, range bias, spacecraft’s orbit accuracy, spacecraft’s orbit altitude, and spacecraft’s orbit inclination.
The difference between our work in this paper and the traditional development ephemerides is that instead of producing planetary ephemeris, we put forward a scheme about improving the orbit of a target object in a certain short period according to mission requirements in order that the chances for failure of a probe inserting into Mars orbit and landing can be reduced. The method in this paper is also applicable to the improvement of ephemerides of other planets in the solar system.
Simulation results show that the station distribution and observing frequency have little influence on the Martian ephemeris short-term prediction and the influence of orbit inclination is not distinct. Moreover, range bias affects the prediction accuracy and the arc length for estimation is limited.
The probe orbit accuracy had obvious impacts on the Martian ephemeris short-term prediction. For the (200×200) km orbit, using 90/120/150-day data-arc length, the Mars position prediction error was about 300 m for 100 m Mars probe orbit error, while it was less than 50 m for 10 m Mars probe orbit error.
Orbit altitude of probe could affect the precision of the Martian ephemeris short-term prediction. For the Mars probe orbit error of 10 m, using 90/120/150-day data-arc length, the Mars position prediction error was about 50 m for (200×200) km orbit, while the Mars position prediction error was about 20 m for (5000×5000) km orbit.
The planetary and lunar ephemerides DE421 and DE430 used to support the findings of this study are available at
The authors declare that they have no conflicts of interest.
This work was supported by the National Natural Science Foundation of China (Grant nos. 11473056, 11403076) and the Science and Technology Commission of Shanghai (Grant no. 12DZ2273300). This work was also supported by the Planetary Sciences Laboratory of Chinese Academy of Sciences, the Lunar Exploration Project of China, and Key Laboratory of Space Object Measurement.