卫星导航信号码跟踪精度研究
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摘要
全球导航卫星系统（GNSS）已成为一个国家的重要基础设施之一，对一个国家具有举足轻重的意义，世界主要航天大国都不惜巨资发展属于自己的卫星导航系统。目前，已建成和在建的GNSS有GPS、GLONASS、GALILEO和COMPASS。由这四大GNSS的信号体制参数可知，BOC（包括衍生的ALTBOC和MBOC信号）调制信号在GNSS中已被广泛地采用，而传统的PSK-R调制信号依然保留下来，因此，PSK-R和BOC调制信号同时存在的局面不可避免。伪距是卫星导航系统的基本观测量，伪距观测量的提取是通过码和载波的精确跟踪来实现的，因而，码和载波跟踪精度直接决定了伪距观测精度。码跟踪精度是导航信号体制设计中所必须考虑的关键指标，对码跟踪精度及其影响因素的研究具有重要意义，可为卫星导航系统接收终端的研发提供理论指导。
本论文以GNSS的PSK-R与BOC调制信号为对象，结合经典的功率谱密度、自相关函数及伪码跟踪等相关理论，对伪码跟踪精度及影响跟踪精度的外部因素和内在因素进行了深入地研究。分析的外部因素主要包括白噪声、高斯干扰、多径干扰及接收系统；而内在因素则主要从信号体制入手，着重研究子载波相位及恒包络互复用对码跟踪精度的影响。主要的研究内容包括：
(1)系统地论述了信号功率谱密度及相关函数求解的通用理论。详细分析了PSK-R、BOC、ALTBOC和MBOC调制信号的功率谱密度和自相关函数，总结得到PSK-R与BOC调制信号的功率谱密度和自相关函数的特点。
(2)从定性和定量两个方面对伪码跟踪精度进行分析。定性分析主要是根据导航信号S曲线理论来判断码跟踪性能。定量分析是基于码跟踪处理的规范模型，利用导航信号的复基带表示，推导出白噪声及高斯干扰环境下的相干、非相干超前减滞后相关处理的SNIR和码跟踪均方根误差的解析表达式，SNIR和码跟踪均方根误差均可反映噪声、干扰对码跟踪精度的影响。基于码跟踪精度的理论成果，对白噪声、窄带干扰、高斯带限干扰以及匹配谱干扰的码跟踪精度进行了详细地研究。
(3)基于标准相关器，推导出伪码及载波相位多径误差的显式解析表达式，弥补了传统隐函数数值分析方法的不足，且显式解析表达式引入的误差足够小。考虑到多径环境与卫星仰角的变化对多径误差带来影响，在对统计信道模型进行详尽分析的基础上，提出了基于统计信道模型的显式解析表达式的多径误差分析方法，包括滑动平均多径误差包络、加权多径误差包络及加权多径误差包络的滑动平均三种评价方法，使得多径误差分析更加真实有效。
(4)提出了GNSS接收系统的载噪比计算模型，并对天线噪声温度、电缆插入损耗、噪声系数与等效噪声温度等进行了分析研究，提出了电缆插入损耗的线性化简化计算方法；在组件及各模块噪声系数与功率增益已知的情况下，依据噪声系数与等效噪声温度的定义，分析了整个接收系统的载噪比计算方法。文中主要从ADC量化、CIC抽取滤波、码时延与多普勒残留误差这四个方面来详细分析载噪比损失对码跟踪精度和误码率的影响。
(5)采用功率谱密度定义的方法，选取合适的任意相位子载波扩频符号波形分段形式的参数表示，在此基础上经过严格建模和推导，得到了任意相位子载波BOC调制信号的通用解析表达式。并选取两种典型的BOC调制信号进行分析，验证了通用解析表达式的正确性，总结得到一些重要结论。基于任意相位子载波功率谱密度解析表达式，对任意相位子载波调制信号所对应的Gabor带宽及所能达到的码跟踪误差下界进行了深入地研究。
(6)系统地阐述了Interplex与CASM这两种恒包络互复用方法的原理，并对其合成损耗进行定义。对恒包络互复用的实现及合成的功率谱密度进行了论述，给出了三信号与四信号互复用的实例。对恒包络互复用效率进行了分析，根据互复用效率可选择最佳的恒包络复用功率分配参数。提出了码跟踪误差相对信号载噪比变化率方法，可实现将恒包络互复用合成损耗归算到码跟踪均方根误差增量。
Global Navigation Satellite System has become one of the most important infrastructures and ofvital significance for a country. Major space powers of the world have not hesitated to developtheir own satellite navigation system. Currently, Global Navigation Satellite Systems have beenbuilt and are being built include GPS, GLONASS, GALILEO and COMPASS. BOC (includingALTBOC and MBOC signals) modulated signals have been widely adopted, while thetraditional PSK-R modulation signal is still preserved via the four GNSS signal systemparameters. Therefore, the coexistence situation for PSK-R and BOC modulation signal isinevitable. Pseudo-range is a basic observed quantity of satellite navigation system. Theextraction of pseudo-range observed quantity is achieved through the code and carrier tracking,therefore, the code and carrier tracking accuracy directly determines the accuracy of thepseudo-range observations. Code tracking accuracy is a key indicator which must be consideredduring the design of navigation signal system. The study on impact factors for code trackingaccuracy is of great significance, which can provide theoretical guidance for research anddevelopment of satellite navigation system receiver.
Pseudo-code tracking accuracy and external factors and internal factors on tracking accuracyare studied in depth combined with relevant theory including classic power spectral density,auto-correlation function, pseudo-code tracking and others in this paper. External factorsanalyzed include white noise, Gaussian interference, multipath interference and the receivingsystem; while the influence of internal factors including arbitrary sub-carrier phase and constantenvelope composite technology which both belonging to signal system on code trackingaccuracy is analyzed. The main research contents will be shown as followings.
(1) General theory for solving signal power spectral density and correlation function iselaborated systematically. According to the characteristics of the navigation signals, the powerspectral density and autocorrelation function for PSK-R, BOC, ALTBOC and MBOCmodulation signals are analyzed in detail and their characteristics are summarized.
(2) Pseudo-code tracking accuracy is analyzed from two aspects of qualitative andquantitative.S curve which stems from autocorrelation function can be used for qualitativejudging the performance of code tracking loop. It is not enough for us to make a qualitativeanalysis on code tracking loop error via S curve, next, under canonical model framework ofTOA error estimation, using no-coherent delay lock loop, through modeling and derivation canget a quantitative formula between code tracking error and SNIR calculated theoretically and the RF front-end bandwidth, early code and late code space, carrier to noise ratio, integrationtime and code loop bandwidth, which leading to a quantitative analysis of the non-coherentdelay lock loop for code tracking error. SNIR and root mean square error of code tracking canreflect the effect on code tracking accuracy of noise, interference. Based on theoretical resultsof the pseudo-code tracking accuracy, the code tracking under white noise, narrowbandinterference, bandlimited white interference with fixed centre frequency and differentbandwidths, and matched spectrum interference are studied in detail.
(3) Explicit analytical expression for pseudo-code and carrier phase multipath error is deducedbased on standard correlator, which to make up for the deficiencies of the traditional implicitfunction numerical analysis method, and the error introduced by the explicit analyticalexpression is negligible. A more practical and reliable way for multipath error analysis based onexplicit analytical expression of statistical channel model is advanced considering the effect ofmultipath scenario and elevation of satellite. This includes three kinds of evaluation methodscontaining running average multipath error envelope, weighted multipath error envelope andrunning weighted multipath error envelope, which make a more realistic analysis of themultipath error.
(4) The calculation model about the GNSS receiving system is proposed, and the antenna noisetemperature, the cable insertion loss, the noise figure and the equivalent noise temperature areanalyzed, the linear simplified calculation method is proposed; In the condition of the powergain coefficient of the component and the modules is known, according to the definition ofnoise coefficient and equivalent noise temperature, the calculation method of carrier to noiseratio for whole receiving system is proposed. This paper mainly detailed analyze the effect ofcarrier to noise ratio loss on tracking accuracy and bit error rate from the ADC quantization,CIC decimation filter, code delay and doppler residual error.
(5) Common explicit expression for BOC signal power spectral density of arbitrary phasesub-carrier is derived through rigorous modeling and derivation which based on a commonapproach for solving the navigation signal power spectral density and representation for spreadspectrum symbols of segmental waveform by selection of arbitrary phase subcarrier. Formula isverified correct by analyzing two kinds of typical BOC signals, and some important conclusionsare drawn. Gabor bandwidth and code tracking lower bound error for modulation signals ofarbitrary phase sub-carrier are studied in depth based on the analytical expression of any phasesub-carrier power spectral density.
(6) The principle about the Interplex and CASM constant envelope and mutual multiplexingmethods is systematically elaborated, and the combining loss is defined. The power spectraldensity of constant envelope synthesis and realization is discussed, and the examples about the multiplexing of three and four signals are given. The efficiency of constant envelope andmutual multiplexing are analyzed, and the power distribution parameters are chosen accordingto the best constant envelope multiplexing. The tracking error code in relative signal to noiseratio variation method are put forward, which can realize constant envelope and mutualmultiplexing power spectrum and combining loss count to the code tracking RMS error.
本论文以GNSS的PSK-R与BOC调制信号为对象，结合经典的功率谱密度、自相关函数及伪码跟踪等相关理论，对伪码跟踪精度及影响跟踪精度的外部因素和内在因素进行了深入地研究。分析的外部因素主要包括白噪声、高斯干扰、多径干扰及接收系统；而内在因素则主要从信号体制入手，着重研究子载波相位及恒包络互复用对码跟踪精度的影响。主要的研究内容包括：
(1)系统地论述了信号功率谱密度及相关函数求解的通用理论。详细分析了PSK-R、BOC、ALTBOC和MBOC调制信号的功率谱密度和自相关函数，总结得到PSK-R与BOC调制信号的功率谱密度和自相关函数的特点。
(2)从定性和定量两个方面对伪码跟踪精度进行分析。定性分析主要是根据导航信号S曲线理论来判断码跟踪性能。定量分析是基于码跟踪处理的规范模型，利用导航信号的复基带表示，推导出白噪声及高斯干扰环境下的相干、非相干超前减滞后相关处理的SNIR和码跟踪均方根误差的解析表达式，SNIR和码跟踪均方根误差均可反映噪声、干扰对码跟踪精度的影响。基于码跟踪精度的理论成果，对白噪声、窄带干扰、高斯带限干扰以及匹配谱干扰的码跟踪精度进行了详细地研究。
(3)基于标准相关器，推导出伪码及载波相位多径误差的显式解析表达式，弥补了传统隐函数数值分析方法的不足，且显式解析表达式引入的误差足够小。考虑到多径环境与卫星仰角的变化对多径误差带来影响，在对统计信道模型进行详尽分析的基础上，提出了基于统计信道模型的显式解析表达式的多径误差分析方法，包括滑动平均多径误差包络、加权多径误差包络及加权多径误差包络的滑动平均三种评价方法，使得多径误差分析更加真实有效。
(4)提出了GNSS接收系统的载噪比计算模型，并对天线噪声温度、电缆插入损耗、噪声系数与等效噪声温度等进行了分析研究，提出了电缆插入损耗的线性化简化计算方法；在组件及各模块噪声系数与功率增益已知的情况下，依据噪声系数与等效噪声温度的定义，分析了整个接收系统的载噪比计算方法。文中主要从ADC量化、CIC抽取滤波、码时延与多普勒残留误差这四个方面来详细分析载噪比损失对码跟踪精度和误码率的影响。
(5)采用功率谱密度定义的方法，选取合适的任意相位子载波扩频符号波形分段形式的参数表示，在此基础上经过严格建模和推导，得到了任意相位子载波BOC调制信号的通用解析表达式。并选取两种典型的BOC调制信号进行分析，验证了通用解析表达式的正确性，总结得到一些重要结论。基于任意相位子载波功率谱密度解析表达式，对任意相位子载波调制信号所对应的Gabor带宽及所能达到的码跟踪误差下界进行了深入地研究。
(6)系统地阐述了Interplex与CASM这两种恒包络互复用方法的原理，并对其合成损耗进行定义。对恒包络互复用的实现及合成的功率谱密度进行了论述，给出了三信号与四信号互复用的实例。对恒包络互复用效率进行了分析，根据互复用效率可选择最佳的恒包络复用功率分配参数。提出了码跟踪误差相对信号载噪比变化率方法，可实现将恒包络互复用合成损耗归算到码跟踪均方根误差增量。
Global Navigation Satellite System has become one of the most important infrastructures and ofvital significance for a country. Major space powers of the world have not hesitated to developtheir own satellite navigation system. Currently, Global Navigation Satellite Systems have beenbuilt and are being built include GPS, GLONASS, GALILEO and COMPASS. BOC (includingALTBOC and MBOC signals) modulated signals have been widely adopted, while thetraditional PSK-R modulation signal is still preserved via the four GNSS signal systemparameters. Therefore, the coexistence situation for PSK-R and BOC modulation signal isinevitable. Pseudo-range is a basic observed quantity of satellite navigation system. Theextraction of pseudo-range observed quantity is achieved through the code and carrier tracking,therefore, the code and carrier tracking accuracy directly determines the accuracy of thepseudo-range observations. Code tracking accuracy is a key indicator which must be consideredduring the design of navigation signal system. The study on impact factors for code trackingaccuracy is of great significance, which can provide theoretical guidance for research anddevelopment of satellite navigation system receiver.
Pseudo-code tracking accuracy and external factors and internal factors on tracking accuracyare studied in depth combined with relevant theory including classic power spectral density,auto-correlation function, pseudo-code tracking and others in this paper. External factorsanalyzed include white noise, Gaussian interference, multipath interference and the receivingsystem; while the influence of internal factors including arbitrary sub-carrier phase and constantenvelope composite technology which both belonging to signal system on code trackingaccuracy is analyzed. The main research contents will be shown as followings.
(1) General theory for solving signal power spectral density and correlation function iselaborated systematically. According to the characteristics of the navigation signals, the powerspectral density and autocorrelation function for PSK-R, BOC, ALTBOC and MBOCmodulation signals are analyzed in detail and their characteristics are summarized.
(2) Pseudo-code tracking accuracy is analyzed from two aspects of qualitative andquantitative.S curve which stems from autocorrelation function can be used for qualitativejudging the performance of code tracking loop. It is not enough for us to make a qualitativeanalysis on code tracking loop error via S curve, next, under canonical model framework ofTOA error estimation, using no-coherent delay lock loop, through modeling and derivation canget a quantitative formula between code tracking error and SNIR calculated theoretically and the RF front-end bandwidth, early code and late code space, carrier to noise ratio, integrationtime and code loop bandwidth, which leading to a quantitative analysis of the non-coherentdelay lock loop for code tracking error. SNIR and root mean square error of code tracking canreflect the effect on code tracking accuracy of noise, interference. Based on theoretical resultsof the pseudo-code tracking accuracy, the code tracking under white noise, narrowbandinterference, bandlimited white interference with fixed centre frequency and differentbandwidths, and matched spectrum interference are studied in detail.
(3) Explicit analytical expression for pseudo-code and carrier phase multipath error is deducedbased on standard correlator, which to make up for the deficiencies of the traditional implicitfunction numerical analysis method, and the error introduced by the explicit analyticalexpression is negligible. A more practical and reliable way for multipath error analysis based onexplicit analytical expression of statistical channel model is advanced considering the effect ofmultipath scenario and elevation of satellite. This includes three kinds of evaluation methodscontaining running average multipath error envelope, weighted multipath error envelope andrunning weighted multipath error envelope, which make a more realistic analysis of themultipath error.
(4) The calculation model about the GNSS receiving system is proposed, and the antenna noisetemperature, the cable insertion loss, the noise figure and the equivalent noise temperature areanalyzed, the linear simplified calculation method is proposed; In the condition of the powergain coefficient of the component and the modules is known, according to the definition ofnoise coefficient and equivalent noise temperature, the calculation method of carrier to noiseratio for whole receiving system is proposed. This paper mainly detailed analyze the effect ofcarrier to noise ratio loss on tracking accuracy and bit error rate from the ADC quantization,CIC decimation filter, code delay and doppler residual error.
(5) Common explicit expression for BOC signal power spectral density of arbitrary phasesub-carrier is derived through rigorous modeling and derivation which based on a commonapproach for solving the navigation signal power spectral density and representation for spreadspectrum symbols of segmental waveform by selection of arbitrary phase subcarrier. Formula isverified correct by analyzing two kinds of typical BOC signals, and some important conclusionsare drawn. Gabor bandwidth and code tracking lower bound error for modulation signals ofarbitrary phase sub-carrier are studied in depth based on the analytical expression of any phasesub-carrier power spectral density.
(6) The principle about the Interplex and CASM constant envelope and mutual multiplexingmethods is systematically elaborated, and the combining loss is defined. The power spectraldensity of constant envelope synthesis and realization is discussed, and the examples about the multiplexing of three and four signals are given. The efficiency of constant envelope andmutual multiplexing are analyzed, and the power distribution parameters are chosen accordingto the best constant envelope multiplexing. The tracking error code in relative signal to noiseratio variation method are put forward, which can realize constant envelope and mutualmultiplexing power spectrum and combining loss count to the code tracking RMS error.
引文
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