基于空频域信息的单星对星无源定轨与跟踪关键技术研究
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摘要
随着电子对抗技术和航空航天技术的不断发展,空间信息获取及对抗在现代化的高技术战争中发挥着越来越重要的作用,从而,对空间信息系统载体——卫星的运动状态确定和跟踪就成了亟待解决的关键问题。鉴于采用天基平台对卫星目标进行观测可以不受大气、时间和国界的影响限制,并且单站无源的观测方式具有隐蔽性强、设备简单、作用距离远和适用范围广等优点,利用单颗卫星平台对卫星目标的无源定轨跟踪(单星对星无源定轨跟踪)技术研究就成为具有重要意义的课题。在总结单站无源定位技术和卫星轨道力学知识的基础上,论文对基于空域和频域观测信息的单星对星无源定轨跟踪所涉及的理论方法及关键问题展开研究。
卫星运动建模是单星对星无源定轨跟踪研究的前提。在定义适当的坐标系统和研究相关卫星轨道理论的基础上,建立了卫星运动的力学模型和基于F/G级数的状态递推F-G模型。该模型以对二体运动的精确描述为特点,具有比其它近似递推模型更高的准确性。根据现有文献,综述了只测角单星对星无源定轨的可观测性研究,并引入完全可观测的结论。卫星运动模型的建立和只测角定轨可观测结论的引入,为后续研究奠定了基础。
论文研究了只测角条件下和联合测角与测频条件下的单星对星无源定轨跟踪方法。基于前面给出的卫星运动模型,对单星对星无源定轨系统进行建模,继而提出基于准确状态模型的只测角单星对星无源定轨跟踪方法。接着,在只测角的基础上引入频率观测量,提出基于准确状态模型的联合测角与测频的单星对星无源定轨跟踪方法,显著提高了只测角定轨方法的精度和收敛速度。与已有的基于泰勒级数展开近似模型的方法相比,由于模型准确性更高,论文的只测角和联合测角与测频两种定轨方法具有更优的性能,且运算复杂度相当。
论文接着研究了基于质点运动学原理的单星对星无源测距和定轨跟踪方法。针对单星对星无源定轨背景的特点,推导无源测距方程并给出具体解法,实现了单星对星无源测距。在此基础上,结合测距分解观测模型,提出一种基于运动学原理的单星对星无源测距定轨跟踪方法,可实现快速定位。进一步将径向速度观测量引入观测量集并直接参与递推滤波计算,提出基于径向运动信息的单星对星无源定轨跟踪方法。除具有收敛速度快的优点外,该方法还具有很高的定轨精度,可用于要求快速和高精度的无源定轨场合。
然后,鉴于单星对星无源定轨跟踪问题的非线性本质和递推滤波算法对定轨的重要作用,论文对非线性滤波问题进行了研究。从函数解析近似的思路出发,分析了EKF(Extended Kalman Filtering)及其改进算法的性能特点,针对其不足,对基于Stirling插值多项式近似的差分滤波算法DDF(Divided Difference Filtering)进行了深入研究。根据单星对星无源定轨背景的加性噪声特点,提出一种适合实时应用的简化差分滤波算法SDDF(Simplified DDF),降低了运算复杂度。针对单星对星无源定轨系统可观测性弱和观测误差大的问题,将最大似然迭代策略与DDF相结合,提出一种迭代差分滤波算法IDDF(Iterated DDF)。该方法迭代过程以似然概率增加为准则,在改善跟踪滤波精度和收敛速度的同时,算法稳定性也得到较大程度提高。
本文系统地研究了基于空频域信息的单星对星无源定轨跟踪涉及的关键理论和技术问题,提出了相应的解决方法和结论,相关研究成果具有较强的理论意义和一定的工程意义。
With the development of the electronic countermeasures technology and the aerospace technology, the spatial information acquisition and confrontation plays an increasingly important role in modern high-tech war. Therefore, it is an urgent crucial task to obtain the motion state of a satellite, carrying the spatial information system. The technology of the passive orbit determination and tracking of a satellite by the single-satellite-borne (single-satellite-to-satellite passive orbit determination and tracking) becomes a very significant subject, as the spaceborne surveillance of the target satellites is not confined to the limits of atmosphere, national boundaries, and time, and the passive observation mode by single observer has many advantages, such as excellent invisibility, simplicity in the facility, large effective radius and wide applicability. Based on the single observer passive location technology and satellite orbit dynamics, this dissertation investigates some crucial theoretical methods and issues concerning the single-satellite-to-satellite passive orbit determination and tracking with observations from the spatial-frequency domain.
Satellite motion modeling is the theoretic premise in single-satellite-to-satellite passive orbit determination and tracking research. After difining the appropriate coordinate system and investigating the concerned orbit theory, a dynamics equation and a state prediction F-G equation of satellite with the F/G series based on precise modeling of two-body motion are established, which is more accurate than other state prediction equations based on approximate modeling of two-body motion. Then, the literature as to the observability of the single-satellite-to-satellite passive orbit determination system using bearings information is reviewed, and the conclusion that the system is entirely observable is introduced. The satellite motion modeling and the conclusion of system observability are theoretical bases of following research. The bearings-only method and the bearings-frequency combination method of the single-satellite-to-satellite passive orbit determination and tracking are investigated successively. Firstly, the single-satellite-to-satellite passive orbit determination system is modeled based on the satellite state prediction equation established above, and a novel bearings-only passive orbit determination and tracking method is proposed.
Subsequently, the frequency is introduced into the observation information group, and a novel single-satellite-to-satellite bearings-frequency combination passive orbit determination method based on an accurate state equation is proposed, thus the accuracy of estimation and the speed of convergence are improved greatly. Compared with the methods using an approximate state prediction equation based on Taylor series, higher estimation accuracy and faster convergence are obtained using the both novel methods, due to the more accurate satellite motion model, while the computational complexity is comparable.
A novel single-satellite-to-satellite passive ranging and orbit determination method is investigated based on the particle kinematics theory. Aimed at the characteristics of single-satellite-to-satellite passive orbit determination, a passive ranging equation and its solution are derived, thus, the single-satellite-to-satellite passive ranging is achieved. Next, combined with the ranging orthogonal decomposition measurement model, a novel single-satellite-to-satellite passive ranging and orbit determination method based on kinematics is proposed, by which fast location can be achieved. Furthermore, by utilizing the radial velocity as observation information for recursive filtering directly, another novel single-satellite-to-satellite passive orbit determination and tracking method is proposed, which is based on the radial motion measurements information. Using this novel method, great fast convergence and high accuracy are obtained, and fast and accurate orbit determination can be also achieved.
Then, considering the nonlinear nature of the single-satellite-to-satellite passive orbit determination and the important role of the recursive filtering algorithm in orbit determination, the nonlinear filtering is investigated also. The performance and potential drawbacks of the EKF (Extended Kalman Filtering) algorithm and its upgrades are discussed from the perspective of analytical approximation to nonlinear functions. To remedy its drawbacks, the DDF (Divided Difference Filtering) algorithms based on polynomial approximation according to Stirling interpolation are fully investigated. Due to the character of the additive noise in the single-satellite-to-satellite passive orbit determination, a simplified DDF (SDDF) is proposed to reduce the computational complexity of the standard DDF. It is more suitable for real-time application. In view of the weak observability and the large observation error of a single-satellite-to-satellite passive orbit determination system, an iterated DDF (IDDF) is proposed by combining the maximum likelihood probability iterated means with the DDF. Since the likelihood probability is always increased in the iterated process, IDDF is more robust than the standard DDF, while its tracking accuracy and convergence speed are improved.
With the observation information of the spatial-frequency domain, some crucial theoretical problems and technological issues in the single-satellite-to-satellite passive orbit determination and tracking are investigated systemically in this dissertation, and, the solutions, methods and conclusions are put forward correspondingly. These research fingdings are very significant in both theory and engineering.
卫星运动建模是单星对星无源定轨跟踪研究的前提。在定义适当的坐标系统和研究相关卫星轨道理论的基础上,建立了卫星运动的力学模型和基于F/G级数的状态递推F-G模型。该模型以对二体运动的精确描述为特点,具有比其它近似递推模型更高的准确性。根据现有文献,综述了只测角单星对星无源定轨的可观测性研究,并引入完全可观测的结论。卫星运动模型的建立和只测角定轨可观测结论的引入,为后续研究奠定了基础。
论文研究了只测角条件下和联合测角与测频条件下的单星对星无源定轨跟踪方法。基于前面给出的卫星运动模型,对单星对星无源定轨系统进行建模,继而提出基于准确状态模型的只测角单星对星无源定轨跟踪方法。接着,在只测角的基础上引入频率观测量,提出基于准确状态模型的联合测角与测频的单星对星无源定轨跟踪方法,显著提高了只测角定轨方法的精度和收敛速度。与已有的基于泰勒级数展开近似模型的方法相比,由于模型准确性更高,论文的只测角和联合测角与测频两种定轨方法具有更优的性能,且运算复杂度相当。
论文接着研究了基于质点运动学原理的单星对星无源测距和定轨跟踪方法。针对单星对星无源定轨背景的特点,推导无源测距方程并给出具体解法,实现了单星对星无源测距。在此基础上,结合测距分解观测模型,提出一种基于运动学原理的单星对星无源测距定轨跟踪方法,可实现快速定位。进一步将径向速度观测量引入观测量集并直接参与递推滤波计算,提出基于径向运动信息的单星对星无源定轨跟踪方法。除具有收敛速度快的优点外,该方法还具有很高的定轨精度,可用于要求快速和高精度的无源定轨场合。
然后,鉴于单星对星无源定轨跟踪问题的非线性本质和递推滤波算法对定轨的重要作用,论文对非线性滤波问题进行了研究。从函数解析近似的思路出发,分析了EKF(Extended Kalman Filtering)及其改进算法的性能特点,针对其不足,对基于Stirling插值多项式近似的差分滤波算法DDF(Divided Difference Filtering)进行了深入研究。根据单星对星无源定轨背景的加性噪声特点,提出一种适合实时应用的简化差分滤波算法SDDF(Simplified DDF),降低了运算复杂度。针对单星对星无源定轨系统可观测性弱和观测误差大的问题,将最大似然迭代策略与DDF相结合,提出一种迭代差分滤波算法IDDF(Iterated DDF)。该方法迭代过程以似然概率增加为准则,在改善跟踪滤波精度和收敛速度的同时,算法稳定性也得到较大程度提高。
本文系统地研究了基于空频域信息的单星对星无源定轨跟踪涉及的关键理论和技术问题,提出了相应的解决方法和结论,相关研究成果具有较强的理论意义和一定的工程意义。
With the development of the electronic countermeasures technology and the aerospace technology, the spatial information acquisition and confrontation plays an increasingly important role in modern high-tech war. Therefore, it is an urgent crucial task to obtain the motion state of a satellite, carrying the spatial information system. The technology of the passive orbit determination and tracking of a satellite by the single-satellite-borne (single-satellite-to-satellite passive orbit determination and tracking) becomes a very significant subject, as the spaceborne surveillance of the target satellites is not confined to the limits of atmosphere, national boundaries, and time, and the passive observation mode by single observer has many advantages, such as excellent invisibility, simplicity in the facility, large effective radius and wide applicability. Based on the single observer passive location technology and satellite orbit dynamics, this dissertation investigates some crucial theoretical methods and issues concerning the single-satellite-to-satellite passive orbit determination and tracking with observations from the spatial-frequency domain.
Satellite motion modeling is the theoretic premise in single-satellite-to-satellite passive orbit determination and tracking research. After difining the appropriate coordinate system and investigating the concerned orbit theory, a dynamics equation and a state prediction F-G equation of satellite with the F/G series based on precise modeling of two-body motion are established, which is more accurate than other state prediction equations based on approximate modeling of two-body motion. Then, the literature as to the observability of the single-satellite-to-satellite passive orbit determination system using bearings information is reviewed, and the conclusion that the system is entirely observable is introduced. The satellite motion modeling and the conclusion of system observability are theoretical bases of following research. The bearings-only method and the bearings-frequency combination method of the single-satellite-to-satellite passive orbit determination and tracking are investigated successively. Firstly, the single-satellite-to-satellite passive orbit determination system is modeled based on the satellite state prediction equation established above, and a novel bearings-only passive orbit determination and tracking method is proposed.
Subsequently, the frequency is introduced into the observation information group, and a novel single-satellite-to-satellite bearings-frequency combination passive orbit determination method based on an accurate state equation is proposed, thus the accuracy of estimation and the speed of convergence are improved greatly. Compared with the methods using an approximate state prediction equation based on Taylor series, higher estimation accuracy and faster convergence are obtained using the both novel methods, due to the more accurate satellite motion model, while the computational complexity is comparable.
A novel single-satellite-to-satellite passive ranging and orbit determination method is investigated based on the particle kinematics theory. Aimed at the characteristics of single-satellite-to-satellite passive orbit determination, a passive ranging equation and its solution are derived, thus, the single-satellite-to-satellite passive ranging is achieved. Next, combined with the ranging orthogonal decomposition measurement model, a novel single-satellite-to-satellite passive ranging and orbit determination method based on kinematics is proposed, by which fast location can be achieved. Furthermore, by utilizing the radial velocity as observation information for recursive filtering directly, another novel single-satellite-to-satellite passive orbit determination and tracking method is proposed, which is based on the radial motion measurements information. Using this novel method, great fast convergence and high accuracy are obtained, and fast and accurate orbit determination can be also achieved.
Then, considering the nonlinear nature of the single-satellite-to-satellite passive orbit determination and the important role of the recursive filtering algorithm in orbit determination, the nonlinear filtering is investigated also. The performance and potential drawbacks of the EKF (Extended Kalman Filtering) algorithm and its upgrades are discussed from the perspective of analytical approximation to nonlinear functions. To remedy its drawbacks, the DDF (Divided Difference Filtering) algorithms based on polynomial approximation according to Stirling interpolation are fully investigated. Due to the character of the additive noise in the single-satellite-to-satellite passive orbit determination, a simplified DDF (SDDF) is proposed to reduce the computational complexity of the standard DDF. It is more suitable for real-time application. In view of the weak observability and the large observation error of a single-satellite-to-satellite passive orbit determination system, an iterated DDF (IDDF) is proposed by combining the maximum likelihood probability iterated means with the DDF. Since the likelihood probability is always increased in the iterated process, IDDF is more robust than the standard DDF, while its tracking accuracy and convergence speed are improved.
With the observation information of the spatial-frequency domain, some crucial theoretical problems and technological issues in the single-satellite-to-satellite passive orbit determination and tracking are investigated systemically in this dissertation, and, the solutions, methods and conclusions are put forward correspondingly. These research fingdings are very significant in both theory and engineering.
引文
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