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Improving the Accuracy of the Martian Ephemeris Short-Term Prediction

Improving the Accuracy of the Martian Ephemeris Short-Term Prediction Hindawi Advances in Astronomy Volume 2018, Article ID 8949242, 8 pages https://doi.org/10.1155/2018/8949242 Research Article Improving the Accuracy of the Martian Ephemeris Short-Term Prediction 1,2 1 1,2 3,4 3,4 1 Quan Shan , Peijia Li , Yong Huang , Min Fan, Haitao Li, and Xiaogong Hu Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China University of Chinese Academy of Sciences, Beijing 100049, China Beijing Institute of Tracking and Telecommunications Technology, Beijing 100094, China Key Laboratory of Space Object Measurement, Beijing 100094, China Correspondence should be addressed to Peijia Li; pjli@shao.ac.cn Received 13 April 2018; Accepted 28 June 2018; Published 12 July 2018 Academic Editor: Alexei S. Pozanenko Copyright © 2018 Quan Shan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. eTh simulation results show that the accuracy of Mars position is expected to be better than 50 m for 180-day prediction, when 90- 150days’rangemeasurementsareusedtoestimatetheorbitoftheMars.Rangebiasaeff ctsthepredictionaccuracyandthearclength 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. 1. Introduction requires an extremely accurate entry angle, thereby taking advantage of aerobraking and avoiding the fuel-consuming The Chinese Mars exploration mission is planned to be process of orbit insertion. launched in 2020, which includes an orbiter, a lander, and The uncertainty of the planetary ephemerides is one of a rover [1]. The orbiter will conduct global surveys of Mars the major factors that affect the accuracy of the navigation. Jet and produce maps of the Martian surface topography as Propulsion Laboratory (JPL) has been continuously support- well as other scientific data; moreover, the lander carrying ing the maintenance and improvement of the ephemerides the rover is going to perform chemical analyses on the since the 1960s to satisfy the needs of high precision planetary soil and look for biomolecules and biosignatures. Precise ephemeris for the deep space navigation. For the Viking orbit determination and prediction of the relative position mission in 1976, the ephemeris accuracy requirements for between the probe and the target object plays an important Mars orbit insertion were on the level of 50 km; in the same period, the ephemeris accuracy requirements were raised to role in deep space navigation. Based on the experience accumulated through early Mars exploration missions, most 5 km for the Pathfinder probe, which was required for a of the subsequent missions have been performed successfully. direct entry into the Mars atmosphere. For Mars Exploration Planetary spacecraft navigation is becoming more and more Rover (MER), which was launched in 2003, the demand was complicated, requiring higher accuracy. After several months better than 1km [2]. For Mars Science Laboratory (MSL), two of the Earth-Mars transfer orbit flight, any material mistake series of Jet Propulsion Laboratory Development Ephemeris in the Martian orbit insertion and the landing progress may (JPL DE) were used: DE424 [3] and DE425 [4]. DE424 was cause the spacecraft to be not placed at an optimal position generated two months before launch. It was expected that the position error between the Mars and the Earth at the and then miss the planet or have a crash landing on the surface of Mars. Accurate navigation allows the immediate time of insertion of MSL was less than 10 m in the line of entry of a spacecraft into a planet’s atmosphere, which sight, 125 m in right ascension, and 225 m in declination. In 2 Advances in Astronomy 1.5 order to reduce the uncertainly of the Martian ephemeris, the Delta Differential One-way Ranging ( ΔDOR) measurements of Mars Reconnaissance Orbiter (MRO) and Odyssey (ODY), 0.5 as well as the range measurements, were used to generate DE425 ephemerides three months before arrival to Mars [5], and the Mars-Earth relative position error was about 10 m 2020 2022 2024 2026 2028 2030 in the line of sight, 100 m in right ascension, and 150 m in 0.2 declination [6]. eTh data of Mars Global Surveyor (MGS) and Mars 0.15 Express (MEX) were also used for the JPL DE [7, 8]. Odyssey, 0.1 MGS, and MRO were in polar orbits of small-eccentricity. 0.05 Odyssey began mapping in a (390×455) km orbit (about 20 km higher than MGS) and MRO spacecraft provided 2020 2022 2024 2026 2028 2030 tracking data in a (255×320) km altitude orbit. eTh typical years from 2020 to 2030 total orbit overlap errors of the three spacecraft are about 1 m. The radial, along-track, and normal average orbit errors Figure 1: The difference on relative positions and velocities of Mars of MGS or Odyssey were 15 cm, 1.5 m, and 1.6 m, respectively and earth between DE421 and DE430. [9]. Due to the improved modeling, average overlap errors of MGS reduce to 12 cm, 0.9 m, and 0.9 m, and those of MROreach4cm,0.6m,and 0.5m[10]. Mars Express (MEX), which reached Mars in December 2003, was the DE421,theMarsorbithasbeenimprovedthroughanupdated first Mars probe of European Space Agency (ESA). It is a treatment of asteroids and additional VLBI observations and large eccentricity orbiting satellite with peri-Martian height range measurements [8]. Figure 1 shows the period from 2020 of about300 km andapomartianheightofmorethanten to 2030, and the difference on relative positions and velocities thousand kilometers [11].Therootmeansquare(RMS) of of Mars and earth between DE421 and DE430 ephemerides MEX position differences between successive 7 days’ data arcs will be about 1 km and 0.2 mm/s. u Th s, when China launches over overlap duration of 21h has been calculated by Royal the Mars probe in 2020, the error in Mars orbit in DE421 will Observatory of Belgium (ROB). The average accuracy of the increase from 300 m to about 1 km. orbits has been estimated to be around 20-25 m [12]. The range/Doppler and VLBI techniques are used in According to the time and coordinates system standard Chinese deep space explorations. Chinese Deep Space Net- for the Chinese Mars exploration mission, DE421 ephemeris, work (CDSN) includes Jiamusi (JMS), Kashgar (KS), and which was released in 2008, will be adopted in this mission. Zapala (ZP, Argentina) deep space stations. Chinese VLBI DE421 included additional ranging and Very Long Baseline network (CVN) consists of Tianma, Beijing, Kunming, and Interferometry (VLBI) measurements of Mars spacecraft and Urumqi. Since it is different for the sensitivity of dieff rent Venus Express spacecra,ft the updated estimates of planetary types of measurements to the error of ephemerides, Martian masses, additional lunar laser ranging, and so on, and the ephemeris should be improved by using the most sensitive Mars position accuracy predicted to 2008 was expected to be measurement data in principle. better than 300 m [7]; moreover, because of the perturbations The Chinese Mars probe will enter the 7.2 hours period by asteroids, the accuracy was expected to be lower. It is a mission orbit to perform remote studies of Mars. eTh great challenge for China to accomplish ‘orbiting, landing, differences of the simulated measurements using different and patrolling’ in the first Mars exploration mission in 2020. ephemerides (DE421 and DE430) are shown in Figure 2. eTh High precision Martian ephemeris can be used to improve the results indicate that the difference for range data (JMS sta- orbit determination and controlling accuracy of the crucial tion) is about 38.5m and 0.005mm/s, 0.005ns, and 0.001ps/s arcs, such as trajectory correction maneuvers (TCM) and for Doppler, VLBI delay, and rate, respectively. Mars landing [13], and reduce failure probability of mission. The accuracy of range measurement is better than 1m, In this paper, a method of improving the accuracy of the Doppler measurement is about 0.1mm/s, delay measurement short-term prediction of the Martian ephemeris is proposed; is 0.1ns (phase delay is 10ps), and delay-rate measurement furthermore, accuracy of the short-term prediction of the is 1ps/s. Comparing with the results shown in Figure 2, we Martian ephemeris is analyzed and discussed through orbit canconcludethatthe Doppler,delay, anddelay-ratemeasure- simulation. eTh related ephemeris products can be used in ments now cannot distinguish the differences between DE421 the engineering and scientific application of the Chinese Mars and DE430 clearly. For that reason, range measurements were exploration. used to estimate the Mars orbit, while the Doppler data could be used to determine the orbit of the spacecraft. In this paper, the orbit determination of Mars and the spacecraft yin fl g 2. Strategy for Short-Time Prediction of around Mars were independent. the Martian Ephemeris The orbit of the spacecraft was determined rfi stly, and Updating ephemeris is necessary for meeting the require- the spacecraft orbit was fixed to determine the Mars orbit. ments of Mars exploration. Taking the DE430 ephemeris Some researchers have processed the tracking data of MEX as an example, which was released in 2013, 5 years aer ft and analyzed the orbit determination accuracy. eTh tracking Δv (mm/s) Δr (km) Advances in Astronomy 3 38.7 0.01 38.65 0.005 38.6 38.55 −0.005 38.5 38.45 −0.01 0 2 4 6 8 10 12 0 2468 10 12 −3 −3 x 10 x 10 −2 1 −3 0.5 −4 −5 −0.5 −6 −7 −1 0 2468 10 12 0 2468 10 12 hours since 2021-07-27 Figure 2: Measurement differences using DE421 and DE430. Table 1: MEX orbital tracking data. measurements were two-way and three-way Doppler in the S- and X-bands. Three CVN stations located at Shanghai, Types of tracking data Observation time Stations Kunming, and Urumqi started tracking MEX on August Two-way Doppler NNO-NNO 7,2009,and thetrackinglastedabout8hours.Inthe From 2009-08-07T20:40 MEX observations, the transmitting station was New Norcia NNO-Shanghai, to 2009-08- (NNO) station in Australia belonging to the ESA. eTh Three-way Doppler NNO-Kunming, 08T04:00(UTC) X-band uplink signals were generated from NNO station NNO-Urumqi and X/S-band downlink signals were retransmitted after frequency multiplication by an on-board transponder [14]. Yan et al. used Mars Gravity Recovery and Analysis Software Table 2: eTh configuration of SODP in MEX POD. (MAGREAS) to process the MEX tracking data with two- Item way and three-way tracking modes separately. eTh posttfi Martian gravity field GMM3 120 residuals RMS of two-way Doppler were about 0.067 mm/s and the ones of two-way Doppler were about 0.079 mm/s. Sun, planets, Moon, Phobos, and N-body perturbation eTh orbits were compared with the orbit results from ROB, Deimos and the maximum position error was less than 8 m for two- Solar radiation Fixed ratio of area to mass way Doppler and less than 100 m for three-way Doppler Relativity perturbation Schwarzschild [15]. Ye et al. used Wuhan University Deep Space Orbit Initial coordinate Mars J2000 Determination and Gravity Recovery System (WUDOGS) Mars-centered coordinate Pathfinder model for MEX precision orbit determination (POD) with two- Earth tropospheric way Doppler, and the reconstructed orbit differences between Hopfield model correction WUDOGSandROB areon25mlevelforpositionand less than 10 mm/s for velocity [16, 17]. We also used the software developed by Shanghai Astro- nomical Observatory (SHAO) named Shao Orbit Determi- gives the force models in MEX’s POD. Analysis of the orbit nation Program (SODP) to determine the orbit of the MEX. dieff rences between the solved orbit and ROB’s reconstructed Table 1 gives the MEX orbital tracking data and Table 2 orbit is presented in Table 3. range (m) range rate (mm/s) delay (ns) delay rate (ps/s) 4 Advances in Astronomy Table 3: eTh reconstructed orbit differences between SODP and ROB. Position (m) Velocity (m/s) Types of tracking data RT 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 Two-way & three-way Doppler 1.06 18.98 9.24 21.13 0.003 0.002 0.003 0.004 The posttfi RMS of residuals was about 0.15mm/s, and The ‘true’ Mars The ‘true’ Mars the position and velocity differences between SODP and ROB probe orbit ephemeris were about tens of meters and about 0.01 m/s, respectively. Mars orbit can be determined using range measurements e Th probe orbits with long data arcs to improve its accuracy while keeping estimated aer PO ft D Range the orbit of the spacecraft fixed. Besides measurement error, (the accuracy of the measurements the probe orbit error is one of the main error sources in the orbits is 10 m or 100 m) process of Mars orbit determination. Establishing the equations of Mars Given a more rigorous equation of motion, Mars orbit motion and observations. Mars orbit integration needs to be performed in the framework of determination general relativity that is different from the framework of Newtonian physics, in which the motion of an earth satellite is considered.Inthe weakgravitational efi ldofthe solarsystem, The solved Mars Accuracy evaluation the motion of Mars under the inu fl ence of the forces of the ephemeris of Mars ephemeris sun and the planets is described as Figure 3: The flowchart of the Mars ephemeris determination. →󳨀 →󳨀 →󳨀 →󳨀 𝜇 ( 𝑟 − 𝑟) 𝜇 ( 𝑟 − 𝑟) { 2(𝛽 + 𝛾) 𝑗 𝑗 𝑗 𝑗 →󳨀 ̈ 𝑟= ∑ + ∑ − 3 3 { 2 { 𝑐 𝑟 𝑟 𝑗 𝑗 (2) Simulate range data with noise and bias according to the “true” Mars ephemeris and the “true” Mars probe 𝜇 2𝛽 − 1 𝜇 V 𝑘 𝑘 orbit. ⋅ ∑ − ∑ +𝛾( ) +(1+𝛾)( ) 𝑟 𝑐 𝑟 𝑐 𝑐 𝑠𝑘 𝑗𝑘 𝑘 𝑘 =𝑗̸ (3) Estimatethe Mars orbitand analyzethe Mars ephemeris accuracy. The orbit of the probe was fixed →󳨀 →󳨀 →󳨀 and obtained from POD results with the orbital ( 𝑟 − 𝑟) ⋅ 𝑟 3 𝑗 𝑗 1 →󳨀 →󳨀 →󳨀 ̈ [ ] − + ( 𝑟 − 𝑟 )⋅ 𝑟 (1) errors. 𝑗 𝑖 𝑗 2 2 2𝑐 𝑟 2𝑐 [ ] Various probe orbits with certain errors obtained under different trajectory determination strategies were used to →󳨀 ̇ →󳨀 ̇ ( 𝑟 − 𝑟) perform Mars OD by Monte Carlo method, in which the →󳨀 →󳨀 + ∑𝜇 {[ 𝑟 − 𝑟] 𝑗 𝑗 2 3 measurement noise was produced at random on a certain 𝑐 𝑟 level of precision. According to the above sensitivity analysis, ̈ for spacecraft in orbit around Mars, the Doppler measure- →󳨀 𝜇 𝑟 (3 + 4𝛾) 𝑗 𝑗 →󳨀 ̇ →󳨀 ̇ mentswereusedtoestimatethe orbitofthespacecraftand ⋅ [(2 + 2𝛾) 𝑟−(1+2𝛾) 𝑟 ]} + ∑ 2𝑐 𝑟 rangemeasurementswerethenusedtoimprove theMars ephemeris. The detailed flowchart is as in Figure 3. where 𝛽 and 𝛾,which areusedasthegeneralrelativity(GR) In our simulation, the tracking stations were JMS, KS, and value 1, are post-Newtonian (PN) parameters, 𝑐 is the speed ZP. eTh measurement noise of range rate data was 0.1mm/s →󳨀 of light in vacuum, 𝑟 isthepositionvectorofMarsinthe andthatofthe rangewas1m.Themeasurement sampling Barycentric Celestial Reference System (BCRS), V is the norm interval was 30s. eTh influence of the length of data arc, of velocity vector, 𝜇 is the gravitational constant of each body, observing strategy, range bias, spacecra’fts orbit accuracy, →󳨀 spacecra’fts orbit altitude, and spacecra’fts orbit inclination 𝑟 is the position vector of each body in the BCRS, and 𝑟 is on short-time prediction accuracy of the Mars orbit was distance from the jth body to Mars. eTh formula is Newtonian analyzed. eTh specific analysis scheme is as in Table 4. equation of motion, which is the rfi st term, with additional post-Newtonian correction terms. 3. Simulation Analyses In this paper, simulation data was used to analyze the accuracy of improved short-term Martian ephemeris. eTh Since the Mars velocity accuracy of JPL ephemerides is better work flow of this simulation is as follows: than 0.2mm/s and it is much higher than that of Mars probe, (1) Propagate a Mars orbit according to the initial state which is about 10 mm/s, we constrained the initial velocity derived from the DE421 ephemeris to get the “true” vectors and only estimated position components of Mars in Mars ephemeris. the simulation analysis, and the initial position error of the 𝑠𝑗 𝑠𝑗 𝑠𝑗 𝑖𝑗 𝑠𝑗 𝑠𝑗 Advances in Astronomy 5 The Martian ephemeris short term prediction Table 4: Factors aecti ff ng the short-term prediction of the Martian ephemeris. Factors Scheme Data arcs(days) 0/30/60/90/120/150/180/210 KS, JMS and ZP; JMS and Stations Observing strategy ZP Frequency Every day/Every 5 days Range bias 5 m/ 0 m 100 Orbit accuracy of a probe 10 m/ 100 m Orbit altitude of a probe 200 km/ 5000 km ∘ ∘ ∘ ∘ Orbit inclination of a probe 0 /30 /60 /90 30 60 90 120 150 180 210 data-arcs (days) The Martian ephemeris short term prediction 5-meter range bias no range bias Figure 5: eTh Martian ephemeris short-term prediction using data whether containing range bias. 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, spacecra’fts orbit accuracy, altitude, and inclination on short- 30 60 90 120 150 180 210 time prediction accuracy of the Mars orbit were based on data-arcs (days) Strategy 3. Strategy 1 3.2. eTh Inu fl ence of Measurement Systematic Errors. This Strategy 2 Strategy 3 section analyses the influence of different ranging systematic errors on the short-term predication accuracy of the Mars Figure 4: The Martian ephemeris short-term prediction under dif- position. For the (200×200) km Mars probe orbit—with ferent observing strategies. 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 Mars was 1km; furthermore, the calculation results of this the position of Mars and forecast for 180 days, and the results paper were based on Monte Carlo simulations. are shown in Figure 5. It can be concluded that when the observation arc was less than 90 days, the 0 m/5 m ranging systematic error had little 3.1. eTh Inu fl ence of Tracking Stations and Observing Fre- influence on the accuracy of the Mars position prediction. quency. For the (200×200) km Mars probe orbit—with However, withtheincreaseofthe observationarclength,the orbital inclination of 0 andorbiterrorof10m—threeobserv- prediction accuracy using the observations which included ing strategies shown in Table 5 were adopted to estimate the 5 m ranging systematic error was obviously decreased, while Mars orbit. the result using the observations without ranging systematic Mars orbitwasdeterminedusing30,60,90,120,150,180, error was stable on the level of about 40 m. This is mainly and210days’observationsand predictedto180days,and the because the ranging systematic error is accumulated with the prediction results are shown in Figure 4. For Strategy 1 and increase of the observation arc length, resulting in influencing Strategy 2, the prediction accuracy was about 50 m using 30 the orbit determination accuracy of the Mars position. days’dataarc,and it wasbetterthan50musing60, 90,and According to the above analysis, consider that the ranging 120 days’ data arcs. It was decreased when data arc was longer systematic error cannot be avoided in deep space mission; than 120 days, and it was about 300 m using 210 days’ data moreover, the results of using observations without ranging arc. Compared to Strategy 1 and Strategy 2, the accuracy was systematic error of 120/150/180/210 days’ data arc are on lower for Strategy 3, which was about 200 m using 30 days’ thesamelevel.Sotheobservations containing 5mranging data arc and about 50 m using 60, 90, 120, and 150 days’ data systematic error were used in the following sections. arcs. It can be concluded that with the accumulation of the observation arc length, the accuracy of the orbit prediction 3.3. The Inu fl ence of Orbit Accuracy of Probes. This section of these three strategies is on the same level. This is mainly analyses the influence of different Mars probe obit accuracy Prediction precision(m) Prediction precision (m) 6 Advances in Astronomy Table 5: Observing strategies and the accuracy of range measurements. Strategy Observing frequency Stations Noise level Systematic errors Strategy 1 2 hours every day KS JMS ZP 1m 5m Strategy 2 2 hours every day JMS ZP 1m 5m Strategy 3 2 hours every 5 days JMS ZP 1m 5m The Martian ephemeris short term prediction The Martian ephemeris short term prediction 2500 180 60 90 120 150 500 data-arcs (days) 30 60 90 120 150 30 60 90 120 150 data-arcs (days) data-arcs (days) orbit altitude is 200km orbit error is 100m orbit altitude is 5000km orbit error is10m Figure 7: eTh Martian ephemeris short-term prediction with Figure 6: eTh Martian ephemeris short-term prediction with dieff rent probe orbit altitudes. different probe orbit errors. about50m,while theMarspositionpredictionerrorwas on the short-term predication accuracy of the Mars position. about 20 m for (5000×5000) km orbit. It can be concluded that the orbit height of the Mars For the (200×200) km Mars probe orbit, with orbital incli- probeisabletoeeff cttheprecision oftheMarsposition nation of 0 , considering the probe orbit accuracy of 10 m/ prediction. This is mainly because the velocity error of the 100 m, respectively, we used 30/60/90/120/150 days’ data arc higher of orbiters is smaller and then the error transmitted to determine the position of Mars and forecast for 180 days, to the Mars orbit is smaller, resulting in influencing the orbit and the results are shown in Figure 6. determination accuracy of the Mars position. eTh results showed that the prediction precision of Mars position increased with the increasing of the Mars probe orbit accuracy. eTh Mars position prediction error using 3.5. The Inu fl ence of Orbit Inclination of Probes. Chinese Mars 90/120/150 days’ data-arc length was about 300 m for 100 m orbiter will yfl on a large inclination orbit. eTh influence of orbit error, while the precision was better than 50 m for 10 m orbit inclination was analyzed and the results are shown in orbit error. Figure 8. It can be concluded that Mars probe orbit error is an The results showed that different orbital inclinations had important source error which can affect the short-term no obvious influence on the Mars orbit determination. prediction of the Mars position. In order to obtain the Mars orbit with position accuracy better than 50 m, the Mars probe 3.6. Summary of the Precision of the Martian Ephemeris Short- orbit precision should be about 10 m. Term Prediction. er Th angebias,theorbiterrorofprobes,and the orbit altitude of probes had obvious impacts on 180-day prediction precision. Table 6 shows the position precision of 3.4. The Inuence fl of Orbit Altitude of Probes. For the Mars the Martian ephemeris short-term prediction using different probe orbit with orbital inclination of 0 and orbit error strategies. 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 4. Conclusions theresults areshown in Figure 7. eTh results indicated that the prediction precision of Mars Improving the accuracy of the short-term prediction of the position increased with the increasing of the Mars probe Mars ephemerisisofgreat valuefortheengineering and orbit altitude. For (200×200) km orbit, the Mars position scientific missions of Mars exploration. In this paper, the prediction error using 90/120/150 days’ data-arc length was simulation analysis method is used to analyze the technical Prediction precision (m) Prediction precision (m) Prediction precision (m) Advances in Astronomy 7 Table 6: Position precision of the Martian ephemeris short term prediction (unit: m). Data-arcs (days) Range bias Probes’ orbit altitude Probes’ orbit error 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 5m 200 km 10 m 170.91 43.45 34.17 40.45 56.40 179.68 277.59 5m 200 km 100 m 2270.27 517.66 336.74 293.59 286.08 5m 5000 km 10 m 31.40 14.07 9.05 23.70 61.72 The Martian ephemeris short term prediction probeorbit error, whileitwasless than 50mfor 10mMars probe orbit error. Orbit altitude of probe could aeff ct 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 errorwasabout20mfor(5000×5000) km orbit. Data Availability The planetary and lunar ephemerides DE421 and DE430 used to support the n fi dings of this study are available at 30 60 90 120 150 p://s ft sd.jpl.nasa.gov/pub/eph/planets/ascii. And simulation data-arcs (days) data were used to support this study. ∘ ∘ orbit inclination is 0 orbit inclination is 60 ∘ ∘ orbit inclination is 30 orbit inclination is 90 Conflicts of Interest Figure 8: eTh Martian ephemeris short-term prediction with different probe orbit inclination. eTh authors declare that they have no conflicts of interest. Acknowledgments proposal of improving the short-term prediction of the Mars This work was supported by the National Natural Science ephemeris and the accuracy that can be achieved by this Foundation of China (Grant nos. 11473056, 11403076) and the method. According to the measurement accuracy and the Science and Technology Commission of Shanghai (Grant no. orbit determination accuracy of probes in orbit around Mars, 12DZ2273300). This work was also supported by the Plane- the short-term prediction accuracy of Mars ephemeris was tary Sciences Laboratory of Chinese Academy of Sciences, the analyzed in the aspects of data arc, observing strategy, range Lunar Exploration Project of China, and Key Laboratory of bias, spacecra’fts orbit accuracy, spacecra’fts orbit altitude, and Space Object Measurement. spacecra’fts orbit inclination. 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Improving the Accuracy of the Martian Ephemeris Short-Term Prediction

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Copyright © 2018 Quan Shan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Hindawi Advances in Astronomy Volume 2018, Article ID 8949242, 8 pages https://doi.org/10.1155/2018/8949242 Research Article Improving the Accuracy of the Martian Ephemeris Short-Term Prediction 1,2 1 1,2 3,4 3,4 1 Quan Shan , Peijia Li , Yong Huang , Min Fan, Haitao Li, and Xiaogong Hu Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China University of Chinese Academy of Sciences, Beijing 100049, China Beijing Institute of Tracking and Telecommunications Technology, Beijing 100094, China Key Laboratory of Space Object Measurement, Beijing 100094, China Correspondence should be addressed to Peijia Li; pjli@shao.ac.cn Received 13 April 2018; Accepted 28 June 2018; Published 12 July 2018 Academic Editor: Alexei S. Pozanenko Copyright © 2018 Quan Shan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. eTh simulation results show that the accuracy of Mars position is expected to be better than 50 m for 180-day prediction, when 90- 150days’rangemeasurementsareusedtoestimatetheorbitoftheMars.Rangebiasaeff ctsthepredictionaccuracyandthearclength 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. 1. Introduction requires an extremely accurate entry angle, thereby taking advantage of aerobraking and avoiding the fuel-consuming The Chinese Mars exploration mission is planned to be process of orbit insertion. launched in 2020, which includes an orbiter, a lander, and The uncertainty of the planetary ephemerides is one of a rover [1]. The orbiter will conduct global surveys of Mars the major factors that affect the accuracy of the navigation. Jet and produce maps of the Martian surface topography as Propulsion Laboratory (JPL) has been continuously support- well as other scientific data; moreover, the lander carrying ing the maintenance and improvement of the ephemerides the rover is going to perform chemical analyses on the since the 1960s to satisfy the needs of high precision planetary soil and look for biomolecules and biosignatures. Precise ephemeris for the deep space navigation. For the Viking orbit determination and prediction of the relative position mission in 1976, the ephemeris accuracy requirements for between the probe and the target object plays an important Mars orbit insertion were on the level of 50 km; in the same period, the ephemeris accuracy requirements were raised to role in deep space navigation. Based on the experience accumulated through early Mars exploration missions, most 5 km for the Pathfinder probe, which was required for a of the subsequent missions have been performed successfully. direct entry into the Mars atmosphere. For Mars Exploration Planetary spacecraft navigation is becoming more and more Rover (MER), which was launched in 2003, the demand was complicated, requiring higher accuracy. After several months better than 1km [2]. For Mars Science Laboratory (MSL), two of the Earth-Mars transfer orbit flight, any material mistake series of Jet Propulsion Laboratory Development Ephemeris in the Martian orbit insertion and the landing progress may (JPL DE) were used: DE424 [3] and DE425 [4]. DE424 was cause the spacecraft to be not placed at an optimal position generated two months before launch. It was expected that the position error between the Mars and the Earth at the and then miss the planet or have a crash landing on the surface of Mars. Accurate navigation allows the immediate time of insertion of MSL was less than 10 m in the line of entry of a spacecraft into a planet’s atmosphere, which sight, 125 m in right ascension, and 225 m in declination. In 2 Advances in Astronomy 1.5 order to reduce the uncertainly of the Martian ephemeris, the Delta Differential One-way Ranging ( ΔDOR) measurements of Mars Reconnaissance Orbiter (MRO) and Odyssey (ODY), 0.5 as well as the range measurements, were used to generate DE425 ephemerides three months before arrival to Mars [5], and the Mars-Earth relative position error was about 10 m 2020 2022 2024 2026 2028 2030 in the line of sight, 100 m in right ascension, and 150 m in 0.2 declination [6]. eTh data of Mars Global Surveyor (MGS) and Mars 0.15 Express (MEX) were also used for the JPL DE [7, 8]. Odyssey, 0.1 MGS, and MRO were in polar orbits of small-eccentricity. 0.05 Odyssey began mapping in a (390×455) km orbit (about 20 km higher than MGS) and MRO spacecraft provided 2020 2022 2024 2026 2028 2030 tracking data in a (255×320) km altitude orbit. eTh typical years from 2020 to 2030 total orbit overlap errors of the three spacecraft are about 1 m. The radial, along-track, and normal average orbit errors Figure 1: The difference on relative positions and velocities of Mars of MGS or Odyssey were 15 cm, 1.5 m, and 1.6 m, respectively and earth between DE421 and DE430. [9]. Due to the improved modeling, average overlap errors of MGS reduce to 12 cm, 0.9 m, and 0.9 m, and those of MROreach4cm,0.6m,and 0.5m[10]. Mars Express (MEX), which reached Mars in December 2003, was the DE421,theMarsorbithasbeenimprovedthroughanupdated first Mars probe of European Space Agency (ESA). It is a treatment of asteroids and additional VLBI observations and large eccentricity orbiting satellite with peri-Martian height range measurements [8]. Figure 1 shows the period from 2020 of about300 km andapomartianheightofmorethanten to 2030, and the difference on relative positions and velocities thousand kilometers [11].Therootmeansquare(RMS) of of Mars and earth between DE421 and DE430 ephemerides MEX position differences between successive 7 days’ data arcs will be about 1 km and 0.2 mm/s. u Th s, when China launches over overlap duration of 21h has been calculated by Royal the Mars probe in 2020, the error in Mars orbit in DE421 will Observatory of Belgium (ROB). The average accuracy of the increase from 300 m to about 1 km. orbits has been estimated to be around 20-25 m [12]. The range/Doppler and VLBI techniques are used in According to the time and coordinates system standard Chinese deep space explorations. Chinese Deep Space Net- for the Chinese Mars exploration mission, DE421 ephemeris, work (CDSN) includes Jiamusi (JMS), Kashgar (KS), and which was released in 2008, will be adopted in this mission. Zapala (ZP, Argentina) deep space stations. Chinese VLBI DE421 included additional ranging and Very Long Baseline network (CVN) consists of Tianma, Beijing, Kunming, and Interferometry (VLBI) measurements of Mars spacecraft and Urumqi. Since it is different for the sensitivity of dieff rent Venus Express spacecra,ft the updated estimates of planetary types of measurements to the error of ephemerides, Martian masses, additional lunar laser ranging, and so on, and the ephemeris should be improved by using the most sensitive Mars position accuracy predicted to 2008 was expected to be measurement data in principle. better than 300 m [7]; moreover, because of the perturbations The Chinese Mars probe will enter the 7.2 hours period by asteroids, the accuracy was expected to be lower. It is a mission orbit to perform remote studies of Mars. eTh great challenge for China to accomplish ‘orbiting, landing, differences of the simulated measurements using different and patrolling’ in the first Mars exploration mission in 2020. ephemerides (DE421 and DE430) are shown in Figure 2. eTh High precision Martian ephemeris can be used to improve the results indicate that the difference for range data (JMS sta- orbit determination and controlling accuracy of the crucial tion) is about 38.5m and 0.005mm/s, 0.005ns, and 0.001ps/s arcs, such as trajectory correction maneuvers (TCM) and for Doppler, VLBI delay, and rate, respectively. Mars landing [13], and reduce failure probability of mission. The accuracy of range measurement is better than 1m, In this paper, a method of improving the accuracy of the Doppler measurement is about 0.1mm/s, delay measurement short-term prediction of the Martian ephemeris is proposed; is 0.1ns (phase delay is 10ps), and delay-rate measurement furthermore, accuracy of the short-term prediction of the is 1ps/s. Comparing with the results shown in Figure 2, we Martian ephemeris is analyzed and discussed through orbit canconcludethatthe Doppler,delay, anddelay-ratemeasure- simulation. eTh related ephemeris products can be used in ments now cannot distinguish the differences between DE421 the engineering and scientific application of the Chinese Mars and DE430 clearly. For that reason, range measurements were exploration. used to estimate the Mars orbit, while the Doppler data could be used to determine the orbit of the spacecraft. In this paper, the orbit determination of Mars and the spacecraft yin fl g 2. Strategy for Short-Time Prediction of around Mars were independent. the Martian Ephemeris The orbit of the spacecraft was determined rfi stly, and Updating ephemeris is necessary for meeting the require- the spacecraft orbit was fixed to determine the Mars orbit. ments of Mars exploration. Taking the DE430 ephemeris Some researchers have processed the tracking data of MEX as an example, which was released in 2013, 5 years aer ft and analyzed the orbit determination accuracy. eTh tracking Δv (mm/s) Δr (km) Advances in Astronomy 3 38.7 0.01 38.65 0.005 38.6 38.55 −0.005 38.5 38.45 −0.01 0 2 4 6 8 10 12 0 2468 10 12 −3 −3 x 10 x 10 −2 1 −3 0.5 −4 −5 −0.5 −6 −7 −1 0 2468 10 12 0 2468 10 12 hours since 2021-07-27 Figure 2: Measurement differences using DE421 and DE430. Table 1: MEX orbital tracking data. measurements were two-way and three-way Doppler in the S- and X-bands. Three CVN stations located at Shanghai, Types of tracking data Observation time Stations Kunming, and Urumqi started tracking MEX on August Two-way Doppler NNO-NNO 7,2009,and thetrackinglastedabout8hours.Inthe From 2009-08-07T20:40 MEX observations, the transmitting station was New Norcia NNO-Shanghai, to 2009-08- (NNO) station in Australia belonging to the ESA. eTh Three-way Doppler NNO-Kunming, 08T04:00(UTC) X-band uplink signals were generated from NNO station NNO-Urumqi and X/S-band downlink signals were retransmitted after frequency multiplication by an on-board transponder [14]. Yan et al. used Mars Gravity Recovery and Analysis Software Table 2: eTh configuration of SODP in MEX POD. (MAGREAS) to process the MEX tracking data with two- Item way and three-way tracking modes separately. eTh posttfi Martian gravity field GMM3 120 residuals RMS of two-way Doppler were about 0.067 mm/s and the ones of two-way Doppler were about 0.079 mm/s. Sun, planets, Moon, Phobos, and N-body perturbation eTh orbits were compared with the orbit results from ROB, Deimos and the maximum position error was less than 8 m for two- Solar radiation Fixed ratio of area to mass way Doppler and less than 100 m for three-way Doppler Relativity perturbation Schwarzschild [15]. Ye et al. used Wuhan University Deep Space Orbit Initial coordinate Mars J2000 Determination and Gravity Recovery System (WUDOGS) Mars-centered coordinate Pathfinder model for MEX precision orbit determination (POD) with two- Earth tropospheric way Doppler, and the reconstructed orbit differences between Hopfield model correction WUDOGSandROB areon25mlevelforpositionand less than 10 mm/s for velocity [16, 17]. We also used the software developed by Shanghai Astro- nomical Observatory (SHAO) named Shao Orbit Determi- gives the force models in MEX’s POD. Analysis of the orbit nation Program (SODP) to determine the orbit of the MEX. dieff rences between the solved orbit and ROB’s reconstructed Table 1 gives the MEX orbital tracking data and Table 2 orbit is presented in Table 3. range (m) range rate (mm/s) delay (ns) delay rate (ps/s) 4 Advances in Astronomy Table 3: eTh reconstructed orbit differences between SODP and ROB. Position (m) Velocity (m/s) Types of tracking data RT 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 Two-way & three-way Doppler 1.06 18.98 9.24 21.13 0.003 0.002 0.003 0.004 The posttfi RMS of residuals was about 0.15mm/s, and The ‘true’ Mars The ‘true’ Mars the position and velocity differences between SODP and ROB probe orbit ephemeris were about tens of meters and about 0.01 m/s, respectively. Mars orbit can be determined using range measurements e Th probe orbits with long data arcs to improve its accuracy while keeping estimated aer PO ft D Range the orbit of the spacecraft fixed. Besides measurement error, (the accuracy of the measurements the probe orbit error is one of the main error sources in the orbits is 10 m or 100 m) process of Mars orbit determination. Establishing the equations of Mars Given a more rigorous equation of motion, Mars orbit motion and observations. Mars orbit integration needs to be performed in the framework of determination general relativity that is different from the framework of Newtonian physics, in which the motion of an earth satellite is considered.Inthe weakgravitational efi ldofthe solarsystem, The solved Mars Accuracy evaluation the motion of Mars under the inu fl ence of the forces of the ephemeris of Mars ephemeris sun and the planets is described as Figure 3: The flowchart of the Mars ephemeris determination. →󳨀 →󳨀 →󳨀 →󳨀 𝜇 ( 𝑟 − 𝑟) 𝜇 ( 𝑟 − 𝑟) { 2(𝛽 + 𝛾) 𝑗 𝑗 𝑗 𝑗 →󳨀 ̈ 𝑟= ∑ + ∑ − 3 3 { 2 { 𝑐 𝑟 𝑟 𝑗 𝑗 (2) Simulate range data with noise and bias according to the “true” Mars ephemeris and the “true” Mars probe 𝜇 2𝛽 − 1 𝜇 V 𝑘 𝑘 orbit. ⋅ ∑ − ∑ +𝛾( ) +(1+𝛾)( ) 𝑟 𝑐 𝑟 𝑐 𝑐 𝑠𝑘 𝑗𝑘 𝑘 𝑘 =𝑗̸ (3) Estimatethe Mars orbitand analyzethe Mars ephemeris accuracy. The orbit of the probe was fixed →󳨀 →󳨀 →󳨀 and obtained from POD results with the orbital ( 𝑟 − 𝑟) ⋅ 𝑟 3 𝑗 𝑗 1 →󳨀 →󳨀 →󳨀 ̈ [ ] − + ( 𝑟 − 𝑟 )⋅ 𝑟 (1) errors. 𝑗 𝑖 𝑗 2 2 2𝑐 𝑟 2𝑐 [ ] Various probe orbits with certain errors obtained under different trajectory determination strategies were used to →󳨀 ̇ →󳨀 ̇ ( 𝑟 − 𝑟) perform Mars OD by Monte Carlo method, in which the →󳨀 →󳨀 + ∑𝜇 {[ 𝑟 − 𝑟] 𝑗 𝑗 2 3 measurement noise was produced at random on a certain 𝑐 𝑟 level of precision. According to the above sensitivity analysis, ̈ for spacecraft in orbit around Mars, the Doppler measure- →󳨀 𝜇 𝑟 (3 + 4𝛾) 𝑗 𝑗 →󳨀 ̇ →󳨀 ̇ mentswereusedtoestimatethe orbitofthespacecraftand ⋅ [(2 + 2𝛾) 𝑟−(1+2𝛾) 𝑟 ]} + ∑ 2𝑐 𝑟 rangemeasurementswerethenusedtoimprove theMars ephemeris. The detailed flowchart is as in Figure 3. where 𝛽 and 𝛾,which areusedasthegeneralrelativity(GR) In our simulation, the tracking stations were JMS, KS, and value 1, are post-Newtonian (PN) parameters, 𝑐 is the speed ZP. eTh measurement noise of range rate data was 0.1mm/s →󳨀 of light in vacuum, 𝑟 isthepositionvectorofMarsinthe andthatofthe rangewas1m.Themeasurement sampling Barycentric Celestial Reference System (BCRS), V is the norm interval was 30s. eTh influence of the length of data arc, of velocity vector, 𝜇 is the gravitational constant of each body, observing strategy, range bias, spacecra’fts orbit accuracy, →󳨀 spacecra’fts orbit altitude, and spacecra’fts orbit inclination 𝑟 is the position vector of each body in the BCRS, and 𝑟 is on short-time prediction accuracy of the Mars orbit was distance from the jth body to Mars. eTh formula is Newtonian analyzed. eTh specific analysis scheme is as in Table 4. equation of motion, which is the rfi st term, with additional post-Newtonian correction terms. 3. Simulation Analyses In this paper, simulation data was used to analyze the accuracy of improved short-term Martian ephemeris. eTh Since the Mars velocity accuracy of JPL ephemerides is better work flow of this simulation is as follows: than 0.2mm/s and it is much higher than that of Mars probe, (1) Propagate a Mars orbit according to the initial state which is about 10 mm/s, we constrained the initial velocity derived from the DE421 ephemeris to get the “true” vectors and only estimated position components of Mars in Mars ephemeris. the simulation analysis, and the initial position error of the 𝑠𝑗 𝑠𝑗 𝑠𝑗 𝑖𝑗 𝑠𝑗 𝑠𝑗 Advances in Astronomy 5 The Martian ephemeris short term prediction Table 4: Factors aecti ff ng the short-term prediction of the Martian ephemeris. Factors Scheme Data arcs(days) 0/30/60/90/120/150/180/210 KS, JMS and ZP; JMS and Stations Observing strategy ZP Frequency Every day/Every 5 days Range bias 5 m/ 0 m 100 Orbit accuracy of a probe 10 m/ 100 m Orbit altitude of a probe 200 km/ 5000 km ∘ ∘ ∘ ∘ Orbit inclination of a probe 0 /30 /60 /90 30 60 90 120 150 180 210 data-arcs (days) The Martian ephemeris short term prediction 5-meter range bias no range bias Figure 5: eTh Martian ephemeris short-term prediction using data whether containing range bias. 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, spacecra’fts orbit accuracy, altitude, and inclination on short- 30 60 90 120 150 180 210 time prediction accuracy of the Mars orbit were based on data-arcs (days) Strategy 3. Strategy 1 3.2. eTh Inu fl ence of Measurement Systematic Errors. This Strategy 2 Strategy 3 section analyses the influence of different ranging systematic errors on the short-term predication accuracy of the Mars Figure 4: The Martian ephemeris short-term prediction under dif- position. For the (200×200) km Mars probe orbit—with ferent observing strategies. 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 Mars was 1km; furthermore, the calculation results of this the position of Mars and forecast for 180 days, and the results paper were based on Monte Carlo simulations. are shown in Figure 5. It can be concluded that when the observation arc was less than 90 days, the 0 m/5 m ranging systematic error had little 3.1. eTh Inu fl ence of Tracking Stations and Observing Fre- influence on the accuracy of the Mars position prediction. quency. For the (200×200) km Mars probe orbit—with However, withtheincreaseofthe observationarclength,the orbital inclination of 0 andorbiterrorof10m—threeobserv- prediction accuracy using the observations which included ing strategies shown in Table 5 were adopted to estimate the 5 m ranging systematic error was obviously decreased, while Mars orbit. the result using the observations without ranging systematic Mars orbitwasdeterminedusing30,60,90,120,150,180, error was stable on the level of about 40 m. This is mainly and210days’observationsand predictedto180days,and the because the ranging systematic error is accumulated with the prediction results are shown in Figure 4. For Strategy 1 and increase of the observation arc length, resulting in influencing Strategy 2, the prediction accuracy was about 50 m using 30 the orbit determination accuracy of the Mars position. days’dataarc,and it wasbetterthan50musing60, 90,and According to the above analysis, consider that the ranging 120 days’ data arcs. It was decreased when data arc was longer systematic error cannot be avoided in deep space mission; than 120 days, and it was about 300 m using 210 days’ data moreover, the results of using observations without ranging arc. Compared to Strategy 1 and Strategy 2, the accuracy was systematic error of 120/150/180/210 days’ data arc are on lower for Strategy 3, which was about 200 m using 30 days’ thesamelevel.Sotheobservations containing 5mranging data arc and about 50 m using 60, 90, 120, and 150 days’ data systematic error were used in the following sections. arcs. It can be concluded that with the accumulation of the observation arc length, the accuracy of the orbit prediction 3.3. The Inu fl ence of Orbit Accuracy of Probes. This section of these three strategies is on the same level. This is mainly analyses the influence of different Mars probe obit accuracy Prediction precision(m) Prediction precision (m) 6 Advances in Astronomy Table 5: Observing strategies and the accuracy of range measurements. Strategy Observing frequency Stations Noise level Systematic errors Strategy 1 2 hours every day KS JMS ZP 1m 5m Strategy 2 2 hours every day JMS ZP 1m 5m Strategy 3 2 hours every 5 days JMS ZP 1m 5m The Martian ephemeris short term prediction The Martian ephemeris short term prediction 2500 180 60 90 120 150 500 data-arcs (days) 30 60 90 120 150 30 60 90 120 150 data-arcs (days) data-arcs (days) orbit altitude is 200km orbit error is 100m orbit altitude is 5000km orbit error is10m Figure 7: eTh Martian ephemeris short-term prediction with Figure 6: eTh Martian ephemeris short-term prediction with dieff rent probe orbit altitudes. different probe orbit errors. about50m,while theMarspositionpredictionerrorwas on the short-term predication accuracy of the Mars position. about 20 m for (5000×5000) km orbit. It can be concluded that the orbit height of the Mars For the (200×200) km Mars probe orbit, with orbital incli- probeisabletoeeff cttheprecision oftheMarsposition nation of 0 , considering the probe orbit accuracy of 10 m/ prediction. This is mainly because the velocity error of the 100 m, respectively, we used 30/60/90/120/150 days’ data arc higher of orbiters is smaller and then the error transmitted to determine the position of Mars and forecast for 180 days, to the Mars orbit is smaller, resulting in influencing the orbit and the results are shown in Figure 6. determination accuracy of the Mars position. eTh results showed that the prediction precision of Mars position increased with the increasing of the Mars probe orbit accuracy. eTh Mars position prediction error using 3.5. The Inu fl ence of Orbit Inclination of Probes. Chinese Mars 90/120/150 days’ data-arc length was about 300 m for 100 m orbiter will yfl on a large inclination orbit. eTh influence of orbit error, while the precision was better than 50 m for 10 m orbit inclination was analyzed and the results are shown in orbit error. Figure 8. It can be concluded that Mars probe orbit error is an The results showed that different orbital inclinations had important source error which can affect the short-term no obvious influence on the Mars orbit determination. prediction of the Mars position. In order to obtain the Mars orbit with position accuracy better than 50 m, the Mars probe 3.6. Summary of the Precision of the Martian Ephemeris Short- orbit precision should be about 10 m. Term Prediction. er Th angebias,theorbiterrorofprobes,and the orbit altitude of probes had obvious impacts on 180-day prediction precision. Table 6 shows the position precision of 3.4. The Inuence fl of Orbit Altitude of Probes. For the Mars the Martian ephemeris short-term prediction using different probe orbit with orbital inclination of 0 and orbit error strategies. 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 4. Conclusions theresults areshown in Figure 7. eTh results indicated that the prediction precision of Mars Improving the accuracy of the short-term prediction of the position increased with the increasing of the Mars probe Mars ephemerisisofgreat valuefortheengineering and orbit altitude. For (200×200) km orbit, the Mars position scientific missions of Mars exploration. In this paper, the prediction error using 90/120/150 days’ data-arc length was simulation analysis method is used to analyze the technical Prediction precision (m) Prediction precision (m) Prediction precision (m) Advances in Astronomy 7 Table 6: Position precision of the Martian ephemeris short term prediction (unit: m). Data-arcs (days) Range bias Probes’ orbit altitude Probes’ orbit error 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 5m 200 km 10 m 170.91 43.45 34.17 40.45 56.40 179.68 277.59 5m 200 km 100 m 2270.27 517.66 336.74 293.59 286.08 5m 5000 km 10 m 31.40 14.07 9.05 23.70 61.72 The Martian ephemeris short term prediction probeorbit error, whileitwasless than 50mfor 10mMars probe orbit error. Orbit altitude of probe could aeff ct 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 errorwasabout20mfor(5000×5000) km orbit. Data Availability The planetary and lunar ephemerides DE421 and DE430 used to support the n fi dings of this study are available at 30 60 90 120 150 p://s ft sd.jpl.nasa.gov/pub/eph/planets/ascii. And simulation data-arcs (days) data were used to support this study. ∘ ∘ orbit inclination is 0 orbit inclination is 60 ∘ ∘ orbit inclination is 30 orbit inclination is 90 Conflicts of Interest Figure 8: eTh Martian ephemeris short-term prediction with different probe orbit inclination. eTh authors declare that they have no conflicts of interest. Acknowledgments proposal of improving the short-term prediction of the Mars This work was supported by the National Natural Science ephemeris and the accuracy that can be achieved by this Foundation of China (Grant nos. 11473056, 11403076) and the method. According to the measurement accuracy and the Science and Technology Commission of Shanghai (Grant no. orbit determination accuracy of probes in orbit around Mars, 12DZ2273300). This work was also supported by the Plane- the short-term prediction accuracy of Mars ephemeris was tary Sciences Laboratory of Chinese Academy of Sciences, the analyzed in the aspects of data arc, observing strategy, range Lunar Exploration Project of China, and Key Laboratory of bias, spacecra’fts orbit accuracy, spacecra’fts orbit altitude, and Space Object Measurement. spacecra’fts orbit inclination. 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