X射线脉冲星信号检测及位相测量技术研究
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摘要
脉冲星导航概念自提出以来,已经经过了近半个世纪,但直到十多年前利用X射线脉冲星导航定位可行性得到论证后,才逐渐受到重视。得益于其独特的信号辐射方式以及脉冲周期的稳定性,X射线脉冲星已成为目前人们所认识的十分理想的天文导航信源,并在空间航天器自主导航领域表现出了良好的应用前景。目前,国际上已经开展了利用X射线脉冲星的自主导航技术的空间试验研究,但这项新型技术仍处在基础理论研究和可行性验证阶段。特别是在国内,有关脉冲星导航的实质性的研究才刚刚起步,诸如极弱X射线脉冲星信号高精度计时观测、高效高性能位相测量、时间传递误差修正等制约X射线脉冲星导航(XPNAV)精度提高的关键问题仍没有得到很好的解决。本文主要围绕XPNAV中的信号检测、累积轮廓建立和位相测量等问题展开研究,主要工作内容包括：
(1)分析了可用于脉冲星信号检测的多个特征参量,如周期、轮廓和流量强度等。单独利用周期或轮廓频域特征检测和辨识脉冲星信号的方法可行,但对于强度极弱、探测技术较为复杂的X射线脉冲星信号,这些方法并不令人满意。已有研究表明,由于频域方法存在谐波和色噪声等因素的影响,在对X射线脉冲星信号的检测中存在失效的情况,而时域方法有时表现的更好。将累积轮廓、流量和周期三个重要特征应用于X射线脉冲星信号检测中,提出基于Bayesian估计的时域检测方法。利用仿真数据和(?)XTE卫星的实测数据进行实验验证显示,该法性能优于同类的基于高斯分布模型的检测方法,在检测信号的同时能在一定精度下给出信号位相偏移值。
(2)利用累积轮廓进行位相测量是XPNAV导航信息获取的基本途径,轮廓累积的重要性不言而喻。对转化到SSB原点处的X射线脉冲星光子序列,传统的轮廓累积方法是先识别信号周期,然后再按周期折叠累加得到脉冲轮廓。这种方法依赖于周期识别的准确性,对累积轮廓质量也无评价标准。本文分析了脉冲星累积轮廓和周期的强相关性,提出了周期未知时直接进行轮廓累积的最小熵方法,并对其进行证明,在此基础上,讨论了该方法在周期识别中的作用。利用仿真数据和RXTE卫星的实测数据实验验证了该方法的有效性。脉冲星累积轮廓通常被认为是脉冲星辐射区结构一维分布的反映,人们在对大量累积轮廓统计分析中发现这些轮廓均具有核成分,进而提出利用累积轮廓的高斯成分分离方法分析脉冲星辐射区结构。我们将高斯成分分离方法用于脉冲星累积轮廓建模,发现该模型可以很好地逼近标准轮廓,并将该模型用于累积轮廓位相测量的CRLB分析中,以评价累积轮廓成分对位相测量的影响。结果显示轮廓成分间的相关性和轮廓成分宽度是影响测相精度的两个重要因素。
(3)考虑到Taylor FFT等频域位相测量的实质是在投影定理下用各次谐波的线性叠加对原函数拟合,提出了基于最小熵准则的位相测量高斯拟合方法。实验说明,所提方法在相对较低信噪比条件下,性能优于Taylor FFT方法。鉴于该方法对轮廓质量要求较高,在实际应用中可能造成困难,本文建立了一种新的脉冲星信号概率模型,用于描述在观测时间内光子到达频度随采样时间的分布。分析表明该模型可以很好的刻画轮廓形变与周期误差间的关系。进而本文提出基于该模型的位相和位相速率联合测量方法,将多普勒效应视为参量,利用所提概率模型描述信号的直接累积轮廓,然后利用优化方法求解。仿真实验说明该方法对累积轮廓质量要求较低,能进行位相和位相速率联合测量,且位相测量精度优于Taylor FFT方法。
(4)从XPNAV的性能来看,其定位误差不到最小模糊距离的十分之一,因此连续正常工作时,可以不考虑整周期模糊问题。而对于初始位置未知或者因系统故障导致位置记忆丧失的情况,模糊问题是不可避免的。穷举搜索法是XPNAV常用且有效的解模糊方法,其不足之处在于复杂度高。本文提出一种快速空间搜索方法。该方法依据脉冲星的特征周期将搜索空间划分为多个子空间,利用相位投影增量建立基于满二叉树的快速搜索算法遍历子空间解模糊。仿真实验说明,得益于搜索空间约束和快速二叉树搜索,该方法能有效提高模糊空间搜索速率。
(5)尽管XPNAV相对于其它天文导航方法优势明显,但目前为止,它并不算一个成熟的导航方法。传统的天文自主导航方法利用地球等对星光掩蔽作用进行轨道航天器定轨,利用星敏感器观测恒星和地球问的角距等作为信息输入,与XPNAV机理完全不同。为提高导航精度,增强自主性,提出一种将脉冲星位相测量和星敏感器星光角距测量结合的信息融合天文自主导航方法,并基于UKF (Unscented Kalman Filter)使用真轨道参数做了仿真实验,结果表明组合两种导航方法能有效提高位置和速度估计精度。进而我们也对XPNAV与其它导航系统组合的可能性和有效性做了分析讨论。
(6)地面仿真系统研制在导航系统研究中具有重要意义,由于在地面上无法接收脉冲星的空间辐射X射线信号,对XPNAV而言地面仿真尤其重要。本文设计了一种X射线脉冲星导航信号仿真方案,重点讨论了虚拟参考系建立、信号建模以及硬件系统构成。
Since proposal of pulsar navigation, about half a century elapses. But it does not attract much attention until the feasibility was confirmed ten years ago. Due to its special radiation characteristics and periodic stability, X-ray pulsar has been considered as an ideal navigation source, and shows its great application potential in spacecraft autonomous navigation. By now, space experiments have be carried out for autonomous navigation using X-ray pulsars. But this new technology is still on stage of theory exploration and feasibility validation。 Especially, the substantive research about pulsar navigation is infancy, the key issues limited the precision of X-ray Pulsar NAVigation (XPNAV), such as high precision observation for extremely weak signals, high efficiency and performance phase measurement and error correction of time transfer have not been solved well. This dissertation focus on the problems of signals detecting, integrated profile establishing and phase measurement, and the main content can be summarized as:
(1) Several characteristic parameters which can be used in signal detection, such as periodic, profile and flux intensity, have been analyzed. It is feasible to detect or identify the pulsar signal using the periodic or the profile characteristics in frequency domain respectively. But for extremely weak signal which is complex to detect, these methods are not satisfactory. Studies have shown that, due to influence of harmonic and color noise, there are insufficient situations for the frequency domain method in X-ray pulsar signal detecting, and sometimes, the time domain method do better. In this paper, characteristics of integrated profile, flux intensity and periodic are used in X-ray pulsar detecting, and a time domain method based on Bayesian estimation is proposed. The experiments employing simulation data and RXTE data show that this method does better than the same kind of Gaussian distribution model based method, and the phase offset can be estimated simultaneously.
(2) The basic approach to get navigation information of XPNAV is to measure the phase of integrated profile. For the photons series whose arrival time has been transferred to SSB, the traditional method is to fold the data into one period which should be solved firstly. This method depends on the precision of the period, and has not evaluation criterion. The correlation between period and integrated profile is analyzed in this paper. A minimum entropy method for direct profile folding without period is proposed and proved. Consequently, its ability of solving period is discussed. The efficiency is verified experimentally using simulated and RXTE data. The pulsar integrated profile commonly is considered as one dimensional distribution of the radiation region. The statistical analysis of great integrated profiles shows there are kernel components in these profiles, and then the Gaussian component decomposition method (GFSAP) is proposed to explain the radiation region of pulsar. We use the GFSAP to model pulsar integrated profiles. Since it approximates the profiles well, we apply this model to analyze the CRLB of integrated profile phase measurement to evaluate the effect of integrated profile components in phase measurement. The results show that the correlation among the components and width are two important factors relate to precision of phase measurement. In view of that, the frequency phase measurement method as Taylor FFT is essentially fitting of original function using addition of several harmonics. Keep which in mind, this paper propose the Gaussian fitting method based on minimum entropy criterion. The experiments show that the proposed method does better than Taylor FFT method in relatively low SNR condition.
(3) The phase measurement using integrated profile requires high quality of profile, which lead to difficulty in application. This paper establishes a new probability model for pulsar signal to describe distribution of arrival photon frequency with respect to sampling time in observation duration. The analysis shows the good ability of this model in expressing relation between profile deformation and period error. Based on this model, this paper proposed a joint measurement method for phase and phase rate which takes Doppler as a parameter to formulate the directly folded profile. Then, the optimization method is used to resolve the two variables. Simulation experiments show that this method can estimate phase and phase rate without folding out undistorted profile, and its precision is better than Taylor FFT method.
(4) From the performance of XPNAV, its position error is less than one tenth of the minimum ambiguity distance, so the ambiguity problem can be ignored when the system is working normally and continuously. But for the situations without initial position or the position record losing due to system fault, the ambiguity must be handled. The exhaustive search method is an effective method commonly used, whose shortage is high complexity. This paper proposed a kind of fast space search method which divides the ambiguity space to multiple subspaces. Then, the phase project increment is used to establish fast searching method based on full binary tree. Simulation experiments show that benefiting from the diminution of space scale and fast binary tree, the proposed method promoted the space search efficiency a lot.
(5) By now, although the superiority of XPNAV is obvious comparing with other celestial navigation method, it is not a mature method. The traditional method which uses the star occultation of earth to determinate the spacecraft orbit and takes the angle between star and earth as information input is total different from XPNAV. Aiming at increasing navigation precision and autonomy, an information fusion method combined pulsar phase and star angel measurement is proposed. Based on Unscented Kalman Filter (UKF), real orbit parameters are used in experiment, and the results show than position and velocity estimation precision can be enhance efficiency. Further, the feasibility and possibility for the combination with other navigation method are discussed.
(6) The simulation system on ground is very important for navigation system. It is especially significance for XPNAV due to impossibility to receive the X-ray pulsar signal in space. This paper preliminary designs a kind of signal simulation scheme, which focus on the establishing virtual reference frame, signal modeling and main hardware units.
(1)分析了可用于脉冲星信号检测的多个特征参量,如周期、轮廓和流量强度等。单独利用周期或轮廓频域特征检测和辨识脉冲星信号的方法可行,但对于强度极弱、探测技术较为复杂的X射线脉冲星信号,这些方法并不令人满意。已有研究表明,由于频域方法存在谐波和色噪声等因素的影响,在对X射线脉冲星信号的检测中存在失效的情况,而时域方法有时表现的更好。将累积轮廓、流量和周期三个重要特征应用于X射线脉冲星信号检测中,提出基于Bayesian估计的时域检测方法。利用仿真数据和(?)XTE卫星的实测数据进行实验验证显示,该法性能优于同类的基于高斯分布模型的检测方法,在检测信号的同时能在一定精度下给出信号位相偏移值。
(2)利用累积轮廓进行位相测量是XPNAV导航信息获取的基本途径,轮廓累积的重要性不言而喻。对转化到SSB原点处的X射线脉冲星光子序列,传统的轮廓累积方法是先识别信号周期,然后再按周期折叠累加得到脉冲轮廓。这种方法依赖于周期识别的准确性,对累积轮廓质量也无评价标准。本文分析了脉冲星累积轮廓和周期的强相关性,提出了周期未知时直接进行轮廓累积的最小熵方法,并对其进行证明,在此基础上,讨论了该方法在周期识别中的作用。利用仿真数据和RXTE卫星的实测数据实验验证了该方法的有效性。脉冲星累积轮廓通常被认为是脉冲星辐射区结构一维分布的反映,人们在对大量累积轮廓统计分析中发现这些轮廓均具有核成分,进而提出利用累积轮廓的高斯成分分离方法分析脉冲星辐射区结构。我们将高斯成分分离方法用于脉冲星累积轮廓建模,发现该模型可以很好地逼近标准轮廓,并将该模型用于累积轮廓位相测量的CRLB分析中,以评价累积轮廓成分对位相测量的影响。结果显示轮廓成分间的相关性和轮廓成分宽度是影响测相精度的两个重要因素。
(3)考虑到Taylor FFT等频域位相测量的实质是在投影定理下用各次谐波的线性叠加对原函数拟合,提出了基于最小熵准则的位相测量高斯拟合方法。实验说明,所提方法在相对较低信噪比条件下,性能优于Taylor FFT方法。鉴于该方法对轮廓质量要求较高,在实际应用中可能造成困难,本文建立了一种新的脉冲星信号概率模型,用于描述在观测时间内光子到达频度随采样时间的分布。分析表明该模型可以很好的刻画轮廓形变与周期误差间的关系。进而本文提出基于该模型的位相和位相速率联合测量方法,将多普勒效应视为参量,利用所提概率模型描述信号的直接累积轮廓,然后利用优化方法求解。仿真实验说明该方法对累积轮廓质量要求较低,能进行位相和位相速率联合测量,且位相测量精度优于Taylor FFT方法。
(4)从XPNAV的性能来看,其定位误差不到最小模糊距离的十分之一,因此连续正常工作时,可以不考虑整周期模糊问题。而对于初始位置未知或者因系统故障导致位置记忆丧失的情况,模糊问题是不可避免的。穷举搜索法是XPNAV常用且有效的解模糊方法,其不足之处在于复杂度高。本文提出一种快速空间搜索方法。该方法依据脉冲星的特征周期将搜索空间划分为多个子空间,利用相位投影增量建立基于满二叉树的快速搜索算法遍历子空间解模糊。仿真实验说明,得益于搜索空间约束和快速二叉树搜索,该方法能有效提高模糊空间搜索速率。
(5)尽管XPNAV相对于其它天文导航方法优势明显,但目前为止,它并不算一个成熟的导航方法。传统的天文自主导航方法利用地球等对星光掩蔽作用进行轨道航天器定轨,利用星敏感器观测恒星和地球问的角距等作为信息输入,与XPNAV机理完全不同。为提高导航精度,增强自主性,提出一种将脉冲星位相测量和星敏感器星光角距测量结合的信息融合天文自主导航方法,并基于UKF (Unscented Kalman Filter)使用真轨道参数做了仿真实验,结果表明组合两种导航方法能有效提高位置和速度估计精度。进而我们也对XPNAV与其它导航系统组合的可能性和有效性做了分析讨论。
(6)地面仿真系统研制在导航系统研究中具有重要意义,由于在地面上无法接收脉冲星的空间辐射X射线信号,对XPNAV而言地面仿真尤其重要。本文设计了一种X射线脉冲星导航信号仿真方案,重点讨论了虚拟参考系建立、信号建模以及硬件系统构成。
Since proposal of pulsar navigation, about half a century elapses. But it does not attract much attention until the feasibility was confirmed ten years ago. Due to its special radiation characteristics and periodic stability, X-ray pulsar has been considered as an ideal navigation source, and shows its great application potential in spacecraft autonomous navigation. By now, space experiments have be carried out for autonomous navigation using X-ray pulsars. But this new technology is still on stage of theory exploration and feasibility validation。 Especially, the substantive research about pulsar navigation is infancy, the key issues limited the precision of X-ray Pulsar NAVigation (XPNAV), such as high precision observation for extremely weak signals, high efficiency and performance phase measurement and error correction of time transfer have not been solved well. This dissertation focus on the problems of signals detecting, integrated profile establishing and phase measurement, and the main content can be summarized as:
(1) Several characteristic parameters which can be used in signal detection, such as periodic, profile and flux intensity, have been analyzed. It is feasible to detect or identify the pulsar signal using the periodic or the profile characteristics in frequency domain respectively. But for extremely weak signal which is complex to detect, these methods are not satisfactory. Studies have shown that, due to influence of harmonic and color noise, there are insufficient situations for the frequency domain method in X-ray pulsar signal detecting, and sometimes, the time domain method do better. In this paper, characteristics of integrated profile, flux intensity and periodic are used in X-ray pulsar detecting, and a time domain method based on Bayesian estimation is proposed. The experiments employing simulation data and RXTE data show that this method does better than the same kind of Gaussian distribution model based method, and the phase offset can be estimated simultaneously.
(2) The basic approach to get navigation information of XPNAV is to measure the phase of integrated profile. For the photons series whose arrival time has been transferred to SSB, the traditional method is to fold the data into one period which should be solved firstly. This method depends on the precision of the period, and has not evaluation criterion. The correlation between period and integrated profile is analyzed in this paper. A minimum entropy method for direct profile folding without period is proposed and proved. Consequently, its ability of solving period is discussed. The efficiency is verified experimentally using simulated and RXTE data. The pulsar integrated profile commonly is considered as one dimensional distribution of the radiation region. The statistical analysis of great integrated profiles shows there are kernel components in these profiles, and then the Gaussian component decomposition method (GFSAP) is proposed to explain the radiation region of pulsar. We use the GFSAP to model pulsar integrated profiles. Since it approximates the profiles well, we apply this model to analyze the CRLB of integrated profile phase measurement to evaluate the effect of integrated profile components in phase measurement. The results show that the correlation among the components and width are two important factors relate to precision of phase measurement. In view of that, the frequency phase measurement method as Taylor FFT is essentially fitting of original function using addition of several harmonics. Keep which in mind, this paper propose the Gaussian fitting method based on minimum entropy criterion. The experiments show that the proposed method does better than Taylor FFT method in relatively low SNR condition.
(3) The phase measurement using integrated profile requires high quality of profile, which lead to difficulty in application. This paper establishes a new probability model for pulsar signal to describe distribution of arrival photon frequency with respect to sampling time in observation duration. The analysis shows the good ability of this model in expressing relation between profile deformation and period error. Based on this model, this paper proposed a joint measurement method for phase and phase rate which takes Doppler as a parameter to formulate the directly folded profile. Then, the optimization method is used to resolve the two variables. Simulation experiments show that this method can estimate phase and phase rate without folding out undistorted profile, and its precision is better than Taylor FFT method.
(4) From the performance of XPNAV, its position error is less than one tenth of the minimum ambiguity distance, so the ambiguity problem can be ignored when the system is working normally and continuously. But for the situations without initial position or the position record losing due to system fault, the ambiguity must be handled. The exhaustive search method is an effective method commonly used, whose shortage is high complexity. This paper proposed a kind of fast space search method which divides the ambiguity space to multiple subspaces. Then, the phase project increment is used to establish fast searching method based on full binary tree. Simulation experiments show that benefiting from the diminution of space scale and fast binary tree, the proposed method promoted the space search efficiency a lot.
(5) By now, although the superiority of XPNAV is obvious comparing with other celestial navigation method, it is not a mature method. The traditional method which uses the star occultation of earth to determinate the spacecraft orbit and takes the angle between star and earth as information input is total different from XPNAV. Aiming at increasing navigation precision and autonomy, an information fusion method combined pulsar phase and star angel measurement is proposed. Based on Unscented Kalman Filter (UKF), real orbit parameters are used in experiment, and the results show than position and velocity estimation precision can be enhance efficiency. Further, the feasibility and possibility for the combination with other navigation method are discussed.
(6) The simulation system on ground is very important for navigation system. It is especially significance for XPNAV due to impossibility to receive the X-ray pulsar signal in space. This paper preliminary designs a kind of signal simulation scheme, which focus on the establishing virtual reference frame, signal modeling and main hardware units.
引文
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