李培佳

(中國科學(xué)院上海天文臺上海200030)

我國月球探測工程中的定軌和定位

李培佳?

(中國科學(xué)院上海天文臺上海200030)

本論文以我國月球探測工程為研究背景,使用仿真分析和實測數(shù)據(jù)處理相結(jié)合的方法,結(jié)合多種VLBI(very long baseline interferometry)技術(shù)在深空探測中的應(yīng)用,展開對探月飛行器精密定軌、定位的方法研究和精度分析.本文主要做了以下幾個方面的研究和探討:

首先,利用CE-2(Chang’E-2)探測器實時任務(wù)期間的實測數(shù)據(jù),分析在我國現(xiàn)有的測量條件下月球探測器的軌道確定精度,重點討論了CE-2任務(wù)中觀測精度有所提高的VLBI數(shù)據(jù)對提高探測器定軌精度的貢獻.對環(huán)月探測器短弧定軌計算分析表明,聯(lián)合VLBI和測距數(shù)據(jù)15 min短弧定軌精度比單獨3 h測距數(shù)據(jù)定軌精度提高1～1.5個量級.對環(huán)月探測器長弧定軌精度的重疊弧段分析表明,在CE-2實時任務(wù)的測量條件下,當(dāng)環(huán)月探測器處于非通視狀態(tài)時,VLBI數(shù)據(jù)的加入可以在量級上提高軌道精度,提高主要在T和N方向上;對100 km×100 km軌道,18 h弧長聯(lián)合定軌精度3維位置RMS可達30 m;對15 km×100 km軌道,18 h弧長聯(lián)合定軌精度3維位置RMS可達45 m.

我國后續(xù)深空探測任務(wù)將采用X波段測控體制,本論文對CE-2任務(wù)中首次進行的深空探測X波段測控體制試驗數(shù)據(jù)的測量精度和定軌精度進行評定.計算結(jié)果表明,X波段測控體制試驗的ΔDOR時延數(shù)據(jù)噪聲水平相比S波段VLBI時延提高1個量級以上,優(yōu)于0.1 ns,且系統(tǒng)差問題得到顯著改善.

月球引力場精度是影響環(huán)月飛行器定軌精度的主要誤差源,CE-2探測器觀測數(shù)據(jù)可以作為獨立觀測量,對現(xiàn)有的幾種月球引力場模型進行一定程度的外符合精度檢驗.本文的計算結(jié)果表明現(xiàn)有的LP165P和SGM150Q引力場精度相當(dāng).

CE-2探測器在完成既定的環(huán)月探測后,先后開展了對日地系L2點探測的拓展試驗和對4179號小行星探測的再拓展試驗.由于探測器在深空轉(zhuǎn)移軌道飛行階段所受的動力學(xué)約束減弱,且地基測量精度隨著地心距的增加而降低,所以拓展任務(wù)中的探測器定軌精度降低并且對定軌弧長要求變高.本文的定軌分析結(jié)果表明,VLBI數(shù)據(jù)可以大幅度提高定軌精度并縮短定軌所需弧長.

使用基于多項式逼近的動力學(xué)定軌法,用多項式或其他函數(shù)形式替代動力學(xué)模型來描述探測器的運動方程,對探月二期動力落月段的軌道確定方法進行研究.采用此方法對CE-1探測器落月段的實測數(shù)據(jù)進行軌道確定,定軌精度與常規(guī)動力學(xué)統(tǒng)計定軌法相當(dāng);對CE-1探測器硬著陸的落月點進行計算,計算結(jié)果與單點定位以及常規(guī)動力學(xué)定軌法相比較,其值相差在千米量級以內(nèi).

使用運動學(xué)統(tǒng)計定位方法對探月二期月面固定目標(biāo)進行定位,并應(yīng)用月球數(shù)字高程圖提高極端條件下的定位精度.對于只能使用單點定位方法的月面目標(biāo)行走間定位,本文提出通過積分時延率的方法以獲得可以用于月面目標(biāo)行走間定位的高精度時延數(shù)據(jù).仿真分析結(jié)果表明,數(shù)據(jù)采樣率對積分時延率方法的定位精度影響較大,目前的VLBI數(shù)據(jù)采樣率為5秒/點,單步積分(5 s)相對定位精度約為20 m,與傳統(tǒng)單點定位方法只能得到數(shù)千米的定位精度相比,此方法將定位精度提高了2個數(shù)量級.

對于探月三期中的月球軌道交會對接任務(wù),本文利用同波束VLBI觀測量同時對兩顆飛行器進行軌道確定.仿真分析結(jié)果表明,同波束VLBI數(shù)據(jù)可以在量級上提高兩顆探測器的絕對和相對定軌精度;在只有單目標(biāo)的測距觀測數(shù)據(jù)時,聯(lián)合同波束VLBI數(shù)據(jù)可以同時對雙目標(biāo)進行定軌,且定軌精度與使用雙目標(biāo)測距數(shù)據(jù)聯(lián)合同波束VLBI數(shù)據(jù)的定軌精度量級相當(dāng).使用上海天文臺自編軟件對SELELNE任務(wù)中的兩顆小衛(wèi)星Vstar和Rstar的實測數(shù)據(jù)進行軌道確定分析,計算結(jié)果表明同波束VLBI數(shù)據(jù)可以顯著提高兩顆探測器的定軌精度.尤其對測距數(shù)據(jù)較少的Vstar探測器,同波束VLBI數(shù)據(jù)的加入使得其定軌精度相比較測距單獨定軌提高了近1個量級,與Rstar定軌精度相當(dāng).

This dissertation studies the precise orbit determination(POD)and positioning of the Chinese lunar exploration spacecraft,emphasizing the variety of VLBI(very long baseline interferometry)technologies applied for the deep-space exploration,and their contributions to the methods and accuracies of the precise orbit determination and positioning.In summary,the main contents are as following:

In this work,using the real-time data measured by the CE-2(Chang’E-2)detector,the accuracy of orbit determination is analyzed for the domestic lunar probe under the present condition,and the role played by the VLBI tracking data is particularly reassessed through the precision orbit determination experiments for CE-2.The experiments of the short-arc orbit determination for the lunar probe show that the combination of the ranging and VLBI data with the arc of 15 minutes is able to improve the accuracy by 1-1.5 order of magnitude, compared to the cases for only using the ranging data with the arc of 3 hours.The orbital accuracy is assessed through the orbital overlapping analysis,and the results show that the VLBI data is able to contribute to the CE-2’s long-arc POD especially in the along-track and orbital normal directions.For the CE-2’s 100 km×100 km lunar orbit,the position errors are better than 30 meters,and for the CE-2’s 15 km×100 km orbit,the position errors are better than 45 meters.

The observational data with the delta di ff erential one-way ranging(ΔDOR)from the CE-2’s X-band monitoring and control system experimental are analyzed.It is concluded that the accuracy of ΔDOR delay is dramatically improved with the noise level better than 0.1 ns,and the systematic errors are well calibrated.

Although it is unable to support the development of an independent lunar gravity model,the tracking data of CE-2 provided the evaluations of di ff erent lunar gravity models through POD,and the accuracies are examined in terms of orbit-to-orbit solution di ff erences for several gravity models.It is found that for the 100 km×100 km lunar orbit,with a degree and order expansion up to 165,the JPL’s gravity model LP165P does not show noticeable improvement over Japan’s SGM series models(100×100),but for the 15 km×100 km lunar orbit,a higher degree-order model can signi fi cantly improve the orbit accuracy.

After accomplished its nominal mission,CE-2 launched its extended missions,which involving the L2 mission and the 4179 Toutatis mission.During the fl ight of the extended missions,the regime o ff ers very little dynamics thus requires an extensive amount of timeand tracking data in order to attain a solution.The overlap errors are computed,and it is indicated that the use of VLBI measurements is able to increase the accuracy and reduce the total amount of tracking time.

An orbit determination method based on the polynomial fi tting is proposed for the CE-3’s planned lunar soft landing mission.In this method,spacecraft’s dynamic modeling is not necessary,and its noise reduction is expected to be better than that of the point positioning method by making full use of all-arc observational data.The simulation experiments and real data processing showed that the optimal description of the CE-1’s free-fall landing trajectory is a set of fi ve-order polynomial functions for each of the position components as well as velocity components in J2000.0.The combination of the VLBI delay,the delay rate data,and the USB(united S-band)ranging data signi fi cantly improved the accuracy than the use of USB data alone.

In order to determine the position for the CE-3’s Lunar Lander,a kinematic statistical method is proposed.This method uses both ranging and VLBI measurements to the lander for a continuous arc,combing with precise knowledge about the motion of the moon as provided by planetary ephemeris,to estimate the lander’s position on the lunar surface with high accuracy.Application of the lunar digital elevation model(DEM)as constraints in the lander positioning is helpful.The positioning method for the traverse of lunar rover is also investigated.The integration of delay-rate method is able to achieve higher precise positioning results than the point positioning method.This method provides a wide application of the VLBI data.

In the automated sample return mission,the lunar orbit rendezvous and docking are involved.Precise orbit determination using the same-beam VLBI(SBI)measurement for two spacecraft at the same time is analyzed.The simulation results showed that the SBI data is able to improve the absolute and relative orbit accuracy for two targets by 1-2 orders of magnitude.In order to verify the simulation results and test the two-target POD software developed by SHAO(Shanghai Astronomical Observatory),the real SBI data of the SELENE(Selenological and Engineering Explorer)are processed.The POD results for the Rstar and the Vstar showed that the combination of SBI data could signi fi cantly improve the accuracy for the two spacecraft,especially for the Vstar with less ranging data,and the POD accuracy is improved by approximate one order of magnitude to the POD accuracy of the Rstar.

Researches on the Orbit Determination and Positioning of the Chinese Lunar Exploration Program

LI Pei-jia
(Shanghai Astronomical Observatory,Chinese Academy of Sciences,Shanghai 200030)

?2013-07-07獲得博士學(xué)位,導(dǎo)師:上海天文臺胡小工研究員、黃勇研究員;pjli@shao.ac.cn

10.15940/j.cnki.0001-5245.2015.04.012