基于信噪特征的X射线脉冲星信号去噪方法研究
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摘要
X射线脉冲星导航是一种新型的自主导航方式，可以为深空、近地轨道、地球同步轨道、椭圆轨道的航天器导航。X射线脉冲信号是导航的基础，客观地反映了脉冲星的辐射特征。事实上，由于多种因素的干扰导致X射线脉冲星的信号质量较差，如脉冲星与探测器距离遥远、宇宙背景复杂、强电磁干扰等因素。这些干扰不仅降低了X射线脉冲星信号的质量，而且严重影响了相位提取和导航参数的估计。因此，有效地滤除各种噪声干扰，提取高质量的X射线脉冲星信号是X射线脉冲星导航非常重要的工作之一，直接决定着X射线脉冲星定位、测速、测姿、计时的效率和精度。
在获取X射线脉冲星信号过程中，受到各种人为或非人为的噪声干扰。由于各类噪声产生的机理不同，其统计特性和分布也有所不同，如X射线脉冲星自身周期的短期不稳定性引起的高斯噪声，光子到达的随机特性引起的泊松噪声，太阳风暴和X射线爆等现象引起的脉冲噪声等。显然，使用同一种噪声滤除方法难以滤除多种噪声的干扰。针对不同类型的噪声，利用各自不同的产生机理和分布特性分别滤除，才能达到抑制噪声干扰和提高信号质量的目的。X射线脉冲星信号的峰值、波形、脉宽等有其自身特点，X射线脉冲星的噪声滤除方法就是寻找信号和噪声的不同特征，并将其有效分开，从而实现X射线脉冲星信号的降噪。X射线脉冲星信号处理理论是一种涉及多学科的交叉的新型的研究领域，从公开文献来看，还没有利用信号与噪声的特性对X射线脉冲星信号的不同噪声采用不同方法的研究。
本文在深入研究了X射线脉冲星导航原理的基础上，探讨了X射线脉冲星信号处理的必要性，探讨了X射线脉冲星探测系统中噪声源的特性，并根据噪声的机理和分布特性针对性地进行降噪方法的研究。利用RXTE卫星探测系统的实测数据，对降噪理论和方法进行了验证。论文取得的主要研究结果如下：
1在分析了X射线脉冲星探测原理及工作过程的基础上，探讨在获取信号过程中由光子到达随机性和光子探测的随机性引入的泊松噪声、电子读出系统的引入的高斯噪声及电子干扰和特殊现象引入的突发脉冲噪声。通过分析各种噪声来源和特点，建立了相应的数学模型和统计特性。分析了RXTE卫星探测的X射线脉冲星信号的实测数据，深入研究了实测数据的结构、管理、数据处理和信号提取的方法，为降噪理论和方法的验证提供了可靠的数据源。
2针对X射线脉冲星信号系统中产生的高斯噪声的问题，分析了噪声产生的机理和特征，通过对大量的数据分析表明仅依赖周期叠加方法难以快速的获取到高质量的光子脉冲轮廓信号，为此，提出了基于数据优化选择和Daubechies小波对X射线脉冲星信号的降噪方法，该方法针对于X射线脉冲星信号探测系统的复杂性和特殊性，预先滤除强噪声干扰导致信号无效或无意义的时间段，再对X射线脉冲星信号进行Daubechies小波分解，利用阈值策略滤除所含噪声。该方法通过将复杂问题简单化，不仅减轻了算法的负担，而且有效滤除了X射线脉冲星信号中存在的高斯噪声。为了兼顾降噪性能和计算复杂度，提出了提升小波的X射线脉冲星信号降噪方法。通过提升小波将复杂的小波变换简化为基本矩阵的运算,利用阈值化处理方法，滤除高斯噪声的干扰，快速地获取到高质量的光子脉冲轮廓。与传统方法相比，不仅能有效滤除噪声的干扰，还有利于资源受限的航天器的信号的处理。
3针对X射线脉冲星信号探测系统中因光子辐射的随机性和探测器接收的随机性产生泊松噪声的问题，分析了泊松噪声产生的机理，提出了方差稳定性变换(VST)的泊松噪声抑制方法。该方法利用Haar-Fisz变换将含泊松噪声的信号进行VST变换，使得泊松噪声“漂白”为高斯白噪声，对变换后的信号阈值化处理，反变换即得到降噪后的信号。该方法间接地滤除了泊松噪声的干扰，扩展了X射线脉冲星信号的研究空间。另外，针对于方差稳定性变换不利于低强度的X射线脉冲星信号的问题，提出了一种利用Bayesian多尺度模型对X射线脉冲星信号估计的方法，该方法不需做变换直接地X射线脉冲星信号进行估计达到抑制噪声的目的。
4针对X射线脉冲星探测系统中存在突发的脉冲噪声的问题，提出了一种基于局部的小波包变换去除脉冲噪声的新方法。根据脉冲噪声的非连续性、幅度大、不规则的特点，检测出受污染的脉冲噪声信号。在小波包域内对不同的脉冲噪声区间分别计算阈值进行降噪处理，而没被检测出脉冲噪声的信号则不做任何处理。针对在滤除脉冲噪声过程中丢失了部分X射线光子的时刻信息的问题，提出了对降噪后的脉冲噪声信号进行插值来增加各区间内光子到达的时间分辨率方法，从而实现了高质量的X射线脉冲轮廓的恢复。
X-ray Pulsar-based Navigation is a new kind of autonomous navigation technology,which has a huge potential for development of the spacecrafts in deep-space, near-earth,Geostationary orbit, and elliptic-orbit. X-ray pulsar signal is the basis of pulsar-basednavigation, which must objectively express the characteristic of pulsar. In fact, thesignal quality of X-ray pulsar is not ideal due to many reasons, such as the long distancebetween pulsars and earth, the complexity of cosmic background noise, the strongelectromagnetic interference, etc. These interferences not only decrease the quality ofsignal but also impact on the signal extraction and the estimation of navigationparameters. Therefore, extracting high-quality signal of X-ray pulsar is a very importantpre-propressing, and directly determines the efficiency and precision of position,velocity, attitude and timing.
During the acquisition of X-ray pulsar signal, there are many kinds of artificialand non-artificial interference factors. The different mechanism of noises has differentstatistical characteristics and probability distribution. The fluctuation of period mayintroduce Gaussian noise, the stochastic of photon arrival may produce the Poissonnoise, the solar storm and X-ray storm may introduce impulsive noise. Obviously, it isdifficult to filter all kinds of noise using the same denoising method. Therefore, eachnoise properties mechanisms must be researched individually to obtain good denoisingresults. According to the characteristic of X-ray pulsar, pulse peak, pulse width, pulseprofile, the denoising method is trying to find the different characteristics betweenX-ray pulsar signal and noise, and distinguish the signal and noise to accomplish thedenoising. X-ray pulsar signal processing, as a new cross-field research field, has nospecified documents to introduce to filter the noise based on synthetic analysis of thecharacteristics of different kinds of noises.
The importance of the X-ray pulsar signal processing is introduced on the basis ofthe navigation principle of X-ray pulsar. The characteristics of the noise sources inobserving system of X-ray pulsar are discussed. Then several denoising methods areproposed according to the mechanism and distribution of noise. The theories andmethods are verifed by the observing system RXTE. The main works can besummarized as follows.
1Noise source and its character in observation process of X-ray pulsar signal. Theobservation principle and process are analyzed. Noises imported in X-ray pulsar acquisition, including Poisson noise caused by randomness of photon arrival anddetection, Gaussian noise caused by electronic readout and impulsive noise caused byelectrical interference and special astronomical phenomenon, are discussed. Themathematical model and statistical characteristics of the noise are established byanalyzing the source and feature of the noise. And the measured data from RXTE, thestructure, the method of signal extraction, are analyzed, which provides credible datasource for verification of the theory and method.
2Considering Gaussian noise from the observation system of X-ray pulsar signal,the mechanism and feature of noise are analyzed. It is difficult to obtain high-qualitypulsar profile only by epoch folding. A Gaussian noise removal method based on dataoptimization and Daubechies wavelet is proposed. Considering the complexity of theobservation system for the X-ray pulsar signal, Firstly, the method selects out goodinterval from measured data, Secondly decomposes the signal by Daubechies wavelet,then filtering the Gaussian noise by threshold policy. The method, making the complexmatters easier, reduces computational complexity, but also Gaussian noise effectively.The processing platform of X-ray pulsar signal is in a resource-constrained device. Inorder to balance the complexity and performance, a denoising method based liftingscheme wavelet is proposed. The lifting scheme reduced the complex wavelettransformation to the basic matrix calculation. The SNR of pulsar profile based on thelifting scheme is improved by setting a thresholding value to removal the Gaussiannoise. The method is better for engineering implementation than the traditional one.
3The Poisson noise introduced by the randomness of photon arrival and photondetection in observation system of X-ray pulsar signal is analyzed. Considering thePoisson property of X-ray pulsar signal, a Poisson noise suppression method based onVariance Stabilization Transform is proposed. The signal containing Poisson noise istransformed to Gaussian white noise by Haar-Fisz transformation. The noise is reducedby thresholding and inverse transform of Haar-Fisz. The indirect method filters thePoisson noise and extends the research space for X-ray pulsar signal. Besides，a methodbased on Bayesian multi-scale model is proposed by directly suppression the noiseinterference.
4Considering impulsive noise characteristic in X-ray pulsar observation system, animpulsive noise suppression method based on wavelet packet transform is proposed.The detection algorithm named Linear Filtering could find out the peak number ofimpulsive noise by the impulsive noise characteristics, such as discontinuity, large frequency and irregulations. In wavelet packets domain, the impulsive noise overdifferent sections are filtered by thresholding policy. Especially, no noise signals doneed treatment. For the loss of time information in denoised processing, the denoisedsignal is interpolated to obtain high time resolution, which recovers a high-quanlityphoton pulsar profile.
在获取X射线脉冲星信号过程中，受到各种人为或非人为的噪声干扰。由于各类噪声产生的机理不同，其统计特性和分布也有所不同，如X射线脉冲星自身周期的短期不稳定性引起的高斯噪声，光子到达的随机特性引起的泊松噪声，太阳风暴和X射线爆等现象引起的脉冲噪声等。显然，使用同一种噪声滤除方法难以滤除多种噪声的干扰。针对不同类型的噪声，利用各自不同的产生机理和分布特性分别滤除，才能达到抑制噪声干扰和提高信号质量的目的。X射线脉冲星信号的峰值、波形、脉宽等有其自身特点，X射线脉冲星的噪声滤除方法就是寻找信号和噪声的不同特征，并将其有效分开，从而实现X射线脉冲星信号的降噪。X射线脉冲星信号处理理论是一种涉及多学科的交叉的新型的研究领域，从公开文献来看，还没有利用信号与噪声的特性对X射线脉冲星信号的不同噪声采用不同方法的研究。
本文在深入研究了X射线脉冲星导航原理的基础上，探讨了X射线脉冲星信号处理的必要性，探讨了X射线脉冲星探测系统中噪声源的特性，并根据噪声的机理和分布特性针对性地进行降噪方法的研究。利用RXTE卫星探测系统的实测数据，对降噪理论和方法进行了验证。论文取得的主要研究结果如下：
1在分析了X射线脉冲星探测原理及工作过程的基础上，探讨在获取信号过程中由光子到达随机性和光子探测的随机性引入的泊松噪声、电子读出系统的引入的高斯噪声及电子干扰和特殊现象引入的突发脉冲噪声。通过分析各种噪声来源和特点，建立了相应的数学模型和统计特性。分析了RXTE卫星探测的X射线脉冲星信号的实测数据，深入研究了实测数据的结构、管理、数据处理和信号提取的方法，为降噪理论和方法的验证提供了可靠的数据源。
2针对X射线脉冲星信号系统中产生的高斯噪声的问题，分析了噪声产生的机理和特征，通过对大量的数据分析表明仅依赖周期叠加方法难以快速的获取到高质量的光子脉冲轮廓信号，为此，提出了基于数据优化选择和Daubechies小波对X射线脉冲星信号的降噪方法，该方法针对于X射线脉冲星信号探测系统的复杂性和特殊性，预先滤除强噪声干扰导致信号无效或无意义的时间段，再对X射线脉冲星信号进行Daubechies小波分解，利用阈值策略滤除所含噪声。该方法通过将复杂问题简单化，不仅减轻了算法的负担，而且有效滤除了X射线脉冲星信号中存在的高斯噪声。为了兼顾降噪性能和计算复杂度，提出了提升小波的X射线脉冲星信号降噪方法。通过提升小波将复杂的小波变换简化为基本矩阵的运算,利用阈值化处理方法，滤除高斯噪声的干扰，快速地获取到高质量的光子脉冲轮廓。与传统方法相比，不仅能有效滤除噪声的干扰，还有利于资源受限的航天器的信号的处理。
3针对X射线脉冲星信号探测系统中因光子辐射的随机性和探测器接收的随机性产生泊松噪声的问题，分析了泊松噪声产生的机理，提出了方差稳定性变换(VST)的泊松噪声抑制方法。该方法利用Haar-Fisz变换将含泊松噪声的信号进行VST变换，使得泊松噪声“漂白”为高斯白噪声，对变换后的信号阈值化处理，反变换即得到降噪后的信号。该方法间接地滤除了泊松噪声的干扰，扩展了X射线脉冲星信号的研究空间。另外，针对于方差稳定性变换不利于低强度的X射线脉冲星信号的问题，提出了一种利用Bayesian多尺度模型对X射线脉冲星信号估计的方法，该方法不需做变换直接地X射线脉冲星信号进行估计达到抑制噪声的目的。
4针对X射线脉冲星探测系统中存在突发的脉冲噪声的问题，提出了一种基于局部的小波包变换去除脉冲噪声的新方法。根据脉冲噪声的非连续性、幅度大、不规则的特点，检测出受污染的脉冲噪声信号。在小波包域内对不同的脉冲噪声区间分别计算阈值进行降噪处理，而没被检测出脉冲噪声的信号则不做任何处理。针对在滤除脉冲噪声过程中丢失了部分X射线光子的时刻信息的问题，提出了对降噪后的脉冲噪声信号进行插值来增加各区间内光子到达的时间分辨率方法，从而实现了高质量的X射线脉冲轮廓的恢复。
X-ray Pulsar-based Navigation is a new kind of autonomous navigation technology,which has a huge potential for development of the spacecrafts in deep-space, near-earth,Geostationary orbit, and elliptic-orbit. X-ray pulsar signal is the basis of pulsar-basednavigation, which must objectively express the characteristic of pulsar. In fact, thesignal quality of X-ray pulsar is not ideal due to many reasons, such as the long distancebetween pulsars and earth, the complexity of cosmic background noise, the strongelectromagnetic interference, etc. These interferences not only decrease the quality ofsignal but also impact on the signal extraction and the estimation of navigationparameters. Therefore, extracting high-quality signal of X-ray pulsar is a very importantpre-propressing, and directly determines the efficiency and precision of position,velocity, attitude and timing.
During the acquisition of X-ray pulsar signal, there are many kinds of artificialand non-artificial interference factors. The different mechanism of noises has differentstatistical characteristics and probability distribution. The fluctuation of period mayintroduce Gaussian noise, the stochastic of photon arrival may produce the Poissonnoise, the solar storm and X-ray storm may introduce impulsive noise. Obviously, it isdifficult to filter all kinds of noise using the same denoising method. Therefore, eachnoise properties mechanisms must be researched individually to obtain good denoisingresults. According to the characteristic of X-ray pulsar, pulse peak, pulse width, pulseprofile, the denoising method is trying to find the different characteristics betweenX-ray pulsar signal and noise, and distinguish the signal and noise to accomplish thedenoising. X-ray pulsar signal processing, as a new cross-field research field, has nospecified documents to introduce to filter the noise based on synthetic analysis of thecharacteristics of different kinds of noises.
The importance of the X-ray pulsar signal processing is introduced on the basis ofthe navigation principle of X-ray pulsar. The characteristics of the noise sources inobserving system of X-ray pulsar are discussed. Then several denoising methods areproposed according to the mechanism and distribution of noise. The theories andmethods are verifed by the observing system RXTE. The main works can besummarized as follows.
1Noise source and its character in observation process of X-ray pulsar signal. Theobservation principle and process are analyzed. Noises imported in X-ray pulsar acquisition, including Poisson noise caused by randomness of photon arrival anddetection, Gaussian noise caused by electronic readout and impulsive noise caused byelectrical interference and special astronomical phenomenon, are discussed. Themathematical model and statistical characteristics of the noise are established byanalyzing the source and feature of the noise. And the measured data from RXTE, thestructure, the method of signal extraction, are analyzed, which provides credible datasource for verification of the theory and method.
2Considering Gaussian noise from the observation system of X-ray pulsar signal,the mechanism and feature of noise are analyzed. It is difficult to obtain high-qualitypulsar profile only by epoch folding. A Gaussian noise removal method based on dataoptimization and Daubechies wavelet is proposed. Considering the complexity of theobservation system for the X-ray pulsar signal, Firstly, the method selects out goodinterval from measured data, Secondly decomposes the signal by Daubechies wavelet,then filtering the Gaussian noise by threshold policy. The method, making the complexmatters easier, reduces computational complexity, but also Gaussian noise effectively.The processing platform of X-ray pulsar signal is in a resource-constrained device. Inorder to balance the complexity and performance, a denoising method based liftingscheme wavelet is proposed. The lifting scheme reduced the complex wavelettransformation to the basic matrix calculation. The SNR of pulsar profile based on thelifting scheme is improved by setting a thresholding value to removal the Gaussiannoise. The method is better for engineering implementation than the traditional one.
3The Poisson noise introduced by the randomness of photon arrival and photondetection in observation system of X-ray pulsar signal is analyzed. Considering thePoisson property of X-ray pulsar signal, a Poisson noise suppression method based onVariance Stabilization Transform is proposed. The signal containing Poisson noise istransformed to Gaussian white noise by Haar-Fisz transformation. The noise is reducedby thresholding and inverse transform of Haar-Fisz. The indirect method filters thePoisson noise and extends the research space for X-ray pulsar signal. Besides，a methodbased on Bayesian multi-scale model is proposed by directly suppression the noiseinterference.
4Considering impulsive noise characteristic in X-ray pulsar observation system, animpulsive noise suppression method based on wavelet packet transform is proposed.The detection algorithm named Linear Filtering could find out the peak number ofimpulsive noise by the impulsive noise characteristics, such as discontinuity, large frequency and irregulations. In wavelet packets domain, the impulsive noise overdifferent sections are filtered by thresholding policy. Especially, no noise signals doneed treatment. For the loss of time information in denoised processing, the denoisedsignal is interpolated to obtain high time resolution, which recovers a high-quanlityphoton pulsar profile.
引文
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