基于天基监视的空间目标测向初轨确定研究
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摘要
天基空间目标监视具有重要的军事和民用价值,天基可见光(Space-Based Visible, SBV)在当前并将在以后相当长的时间内成为主要的天基监视手段。当前美国已有在轨运行的天基监视系统,而我国在此方面研究较为薄弱,为了未来建立相应系统,应开展天基轨道确定等相关关键技术研究。
论文基于SBV监视背景,采用理论分析与数值验证相结合研究了天基测向初轨确定,着重研究了初轨确定技术中的方法、模型和解算等相关问题,尤其是传统方法在天基测向定轨中的改进,并研究了地月转移轨道的天基测向初定轨问题与地月转移轨道和卫星编队构形设计等相关问题。主要内容与结论有:
首先,研究了空间目标对单星和星座观测平台的可见性及观测数据的预处理。研究表明,星座平台可以适当降低各种约束对可见性的不利影响;近地空间目标比中高轨道目标的天基可见性差;平滑随机噪声需要根据平滑多项式阶数折衷考虑采样率和采样点数。
其次,重点研究了双r迭代法、Gauss法和Laplace法在天基测向初定轨中的应用及相应改进,包括定轨误差、模型解算和初值问题等等,分析了观测误差对天基测向初定轨的影响,提出了消除误差定轨模型。
通过该部分研究得到如下主要结论:
1.传统地基定轨方法较适合于低轨平台确定中高轨空间目标,在天基测向初定轨上会出现平凡解和多值性问题,其本质在于缺乏距离观测信息,可以通过改进迭代算法和迭代初值等手段进行抑制,但是很难完全消除;
2.论文提出的天基双ρ迭代法及初值求解和解算算法,基本解决了天基稀疏测向初定轨中的迭代发散与平凡解问题,仿真表明解算成功率在90%以上;
3.定轨模型的截断误差对定轨结果影响不大,观测误差是主要的定轨误差因素;
4.如果不进行观测数据的预处理或者预处理失效时,观测系统差的模型对于分析其影响并进行消除相当重要;在观测数据稀疏时,随机噪声有可能造成平凡解。
再次,研究了星座对空间目标的测向初定轨,尤其从解算过程分析了天基测向初定轨模型奇异性和平凡解等问题。
通过该部分研究得到如下主要结论:
1.星座平台较好的观测几何可以消除平凡解,提高定轨成功率,其中星座同步定轨较优;星座定轨可以有效削弱或消除随机噪声的影响,减弱或者部分消除观测系统差的影响;同时,可以极大地缩短定轨所需弧段,但是对高轨目标成功定轨仍需一定长度的弧段;
2.观测采样率对于成功定轨所需弧段影响有限;观测几何对单星定轨影响比对星座定轨影响大;增加弧段长度和采样率有利于克服观测几何的不利影响,提高定轨成功率;
3.改善观测条件以及避开某些特定定轨时刻,均可以从一定程度上降低平凡解概率;模型奇异性是定轨模型固有的问题,不能通过外界手段进行消除,只能在定轨时避免相应时刻。
最后,作为对天基测向初定轨研究的进一步检验和拓展应用,开展了地月转移轨道的天基测向初定轨等研究,除利用单星和星座平台外,尤其研究了利用卫星编队作为观测平台的可行性,同时介绍了卫星编队设计等相关内容。
该部分研究表明,模型误差使得月球探测器的单星定轨误差远大于一般应用卫星,且利用星座双星定轨并非弧段越长越好;编队同步定轨精度明显优于非同步定轨,后者定轨弧长和观测几何影响与单星定轨基本相同;编队构形较小时,构形尺寸对定轨结果影响不大。
论文的研究可为我国建立天基监视系统提供相应的理论和技术支撑,并为我国探月二三期工程以及未来深空探测的天基测定轨提供一定的借鉴。
The space-based surveillance is valued highly on civil and military applications, which would mainly use the SBV, space-based visible, currently and for a fairly long future period. Today, USA has its on-orbit space-based surveillance system(SBSS). However, China is weak on this research. So it is urgent to develop the key technologies including space-based orbit determination(OD) for our own system in the future.
Under the above background, this dissertation studies the space-based initial orbit determination(SBIOD) by combining theoretical analysis and numerical verification, stresses on relative issues including methods, models, algorithms, etc, especially on improvements of tradition methods for the space-based purpose. At the end of the dissertation, the SBIOD of the cislunar transfer trajectory is researched, incidentally designs of the trajectory and the formation flying(FF) configuration.
The main content and conclusions are drawn as follows:
First, visibilities of space targets to satellite and constellation platforms and the data pretreatment are researched. Results show that the constellation platform can restrain adverse impacts of visibility constraints, the visibilities near the earth are worse than the ones of high targets, and smoothing rand error is a tradeoff among fitting polynomial degree, sampling rate and amount.
Second, applications and improvements of the double r iteration method, the Gauss method and the Laplace method for space-based purposes are studied, including OD accuracy, algorithms and initial values. The impact of measure errors on OD is also analyzed and models under error are presented as a result.
Conclusions of this part consist of four points as follows:
1. The traditional methods are fit for low platforms to measure high targets and would bring on phenomena of multivalue and self-solution. The phenomena, which derive from the absence of range measurement, couldn’t be eliminated and only could be decreased by improvements of iteration algorithms and initial values.
2. The space-based doubleρiteration method together with iteration algorithms and initial values brought forward in the dissertation could basically solve the above phenomena with sparse data. The numerical result shows an over 90% success rate.
3. The model error is negligible and measurement errors play an important role.
4. The systemic measurement error model is vital to error analysis and elimination when the data pretreatment is unconsidered or failed. Under the sparse data, the rand errors could result in the self-solution.
Third, using the constellation to determine target orbits is discussed. Based on the solution process, the self-solution and the model singularity are analyzed.
The following conclusions could be achieved :
1. The constellation has a preferable visible geometry and can eliminate the self-solution, whose synchronized model is excellent. Also has the constellation some merits, such as effectively weakening or eliminating impacts of rand errors, lowering or partly eliminating influences of systemic measurement errors, and greatly shortening required measurement arcs. However, it still needs a fair measurement arc for high ODs.
2. The effect of sampling rate on required measurement arcs is limited. The visibility influences the single platform more than the constellation. Increasing arc length and sampling rate is favorable to overcome visibility influences and to gain a high success rate.
3. The self-solution can be reduced at a certain extent by improving measure conditions and by avoiding some particular times. The model singularity is intrinsic and cannot be eliminated by outside resorts. So it should avoid to determinate orbits at that time.
Finally, as the further verification and expanded applications, the SBIOD of the cislunar transfer trajectory is investigated. The platforms consist of a single satellite, a constellation and especially a FF. The FF configuration design is also researched at the last chapter.
According to the studies of the last chapter, model errors make the cislunar OD error far more than common space targets. The long measurement arc is not always preferable for constellation platforms. The FF synchronized model is obviously more favorable than the unsynchronized one which is nearly the same as the single satellite platform on impacts of measurement arcs and visibilities. When the FF is small, the size of formation has tiny impact on the results.
The dissertation could support the foundation of our SBSS theoretically and technically and could be used as a reference of space-based orbit measurement and determination in our future lunar and deep space exploration.
论文基于SBV监视背景,采用理论分析与数值验证相结合研究了天基测向初轨确定,着重研究了初轨确定技术中的方法、模型和解算等相关问题,尤其是传统方法在天基测向定轨中的改进,并研究了地月转移轨道的天基测向初定轨问题与地月转移轨道和卫星编队构形设计等相关问题。主要内容与结论有:
首先,研究了空间目标对单星和星座观测平台的可见性及观测数据的预处理。研究表明,星座平台可以适当降低各种约束对可见性的不利影响;近地空间目标比中高轨道目标的天基可见性差;平滑随机噪声需要根据平滑多项式阶数折衷考虑采样率和采样点数。
其次,重点研究了双r迭代法、Gauss法和Laplace法在天基测向初定轨中的应用及相应改进,包括定轨误差、模型解算和初值问题等等,分析了观测误差对天基测向初定轨的影响,提出了消除误差定轨模型。
通过该部分研究得到如下主要结论:
1.传统地基定轨方法较适合于低轨平台确定中高轨空间目标,在天基测向初定轨上会出现平凡解和多值性问题,其本质在于缺乏距离观测信息,可以通过改进迭代算法和迭代初值等手段进行抑制,但是很难完全消除;
2.论文提出的天基双ρ迭代法及初值求解和解算算法,基本解决了天基稀疏测向初定轨中的迭代发散与平凡解问题,仿真表明解算成功率在90%以上;
3.定轨模型的截断误差对定轨结果影响不大,观测误差是主要的定轨误差因素;
4.如果不进行观测数据的预处理或者预处理失效时,观测系统差的模型对于分析其影响并进行消除相当重要;在观测数据稀疏时,随机噪声有可能造成平凡解。
再次,研究了星座对空间目标的测向初定轨,尤其从解算过程分析了天基测向初定轨模型奇异性和平凡解等问题。
通过该部分研究得到如下主要结论:
1.星座平台较好的观测几何可以消除平凡解,提高定轨成功率,其中星座同步定轨较优;星座定轨可以有效削弱或消除随机噪声的影响,减弱或者部分消除观测系统差的影响;同时,可以极大地缩短定轨所需弧段,但是对高轨目标成功定轨仍需一定长度的弧段;
2.观测采样率对于成功定轨所需弧段影响有限;观测几何对单星定轨影响比对星座定轨影响大;增加弧段长度和采样率有利于克服观测几何的不利影响,提高定轨成功率;
3.改善观测条件以及避开某些特定定轨时刻,均可以从一定程度上降低平凡解概率;模型奇异性是定轨模型固有的问题,不能通过外界手段进行消除,只能在定轨时避免相应时刻。
最后,作为对天基测向初定轨研究的进一步检验和拓展应用,开展了地月转移轨道的天基测向初定轨等研究,除利用单星和星座平台外,尤其研究了利用卫星编队作为观测平台的可行性,同时介绍了卫星编队设计等相关内容。
该部分研究表明,模型误差使得月球探测器的单星定轨误差远大于一般应用卫星,且利用星座双星定轨并非弧段越长越好;编队同步定轨精度明显优于非同步定轨,后者定轨弧长和观测几何影响与单星定轨基本相同;编队构形较小时,构形尺寸对定轨结果影响不大。
论文的研究可为我国建立天基监视系统提供相应的理论和技术支撑,并为我国探月二三期工程以及未来深空探测的天基测定轨提供一定的借鉴。
The space-based surveillance is valued highly on civil and military applications, which would mainly use the SBV, space-based visible, currently and for a fairly long future period. Today, USA has its on-orbit space-based surveillance system(SBSS). However, China is weak on this research. So it is urgent to develop the key technologies including space-based orbit determination(OD) for our own system in the future.
Under the above background, this dissertation studies the space-based initial orbit determination(SBIOD) by combining theoretical analysis and numerical verification, stresses on relative issues including methods, models, algorithms, etc, especially on improvements of tradition methods for the space-based purpose. At the end of the dissertation, the SBIOD of the cislunar transfer trajectory is researched, incidentally designs of the trajectory and the formation flying(FF) configuration.
The main content and conclusions are drawn as follows:
First, visibilities of space targets to satellite and constellation platforms and the data pretreatment are researched. Results show that the constellation platform can restrain adverse impacts of visibility constraints, the visibilities near the earth are worse than the ones of high targets, and smoothing rand error is a tradeoff among fitting polynomial degree, sampling rate and amount.
Second, applications and improvements of the double r iteration method, the Gauss method and the Laplace method for space-based purposes are studied, including OD accuracy, algorithms and initial values. The impact of measure errors on OD is also analyzed and models under error are presented as a result.
Conclusions of this part consist of four points as follows:
1. The traditional methods are fit for low platforms to measure high targets and would bring on phenomena of multivalue and self-solution. The phenomena, which derive from the absence of range measurement, couldn’t be eliminated and only could be decreased by improvements of iteration algorithms and initial values.
2. The space-based doubleρiteration method together with iteration algorithms and initial values brought forward in the dissertation could basically solve the above phenomena with sparse data. The numerical result shows an over 90% success rate.
3. The model error is negligible and measurement errors play an important role.
4. The systemic measurement error model is vital to error analysis and elimination when the data pretreatment is unconsidered or failed. Under the sparse data, the rand errors could result in the self-solution.
Third, using the constellation to determine target orbits is discussed. Based on the solution process, the self-solution and the model singularity are analyzed.
The following conclusions could be achieved :
1. The constellation has a preferable visible geometry and can eliminate the self-solution, whose synchronized model is excellent. Also has the constellation some merits, such as effectively weakening or eliminating impacts of rand errors, lowering or partly eliminating influences of systemic measurement errors, and greatly shortening required measurement arcs. However, it still needs a fair measurement arc for high ODs.
2. The effect of sampling rate on required measurement arcs is limited. The visibility influences the single platform more than the constellation. Increasing arc length and sampling rate is favorable to overcome visibility influences and to gain a high success rate.
3. The self-solution can be reduced at a certain extent by improving measure conditions and by avoiding some particular times. The model singularity is intrinsic and cannot be eliminated by outside resorts. So it should avoid to determinate orbits at that time.
Finally, as the further verification and expanded applications, the SBIOD of the cislunar transfer trajectory is investigated. The platforms consist of a single satellite, a constellation and especially a FF. The FF configuration design is also researched at the last chapter.
According to the studies of the last chapter, model errors make the cislunar OD error far more than common space targets. The long measurement arc is not always preferable for constellation platforms. The FF synchronized model is obviously more favorable than the unsynchronized one which is nearly the same as the single satellite platform on impacts of measurement arcs and visibilities. When the FF is small, the size of formation has tiny impact on the results.
The dissertation could support the foundation of our SBSS theoretically and technically and could be used as a reference of space-based orbit measurement and determination in our future lunar and deep space exploration.
引文
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