高动态条件下伪码相关特性及其应用研究
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摘要
载体高动态运动条件下,卫星导航接收机接收信号与本地信号之间不但存在载波频偏,还存在伪码频偏。现有研究多针对载波频偏,伪码频偏的影响缺乏系统的理论研究,高动态接收机的设计效率和设计性能均存在较大提升空间。载体静止条件下,卫星运动对精度要求优于0.5ns的高精度定轨/测量型接收机伪距测量精度的影响也不可忽略。基于这两大背景,本文理论与实际相结合,着重研究伪码频偏的影响,内容分为四大部分:
第一部分研究动态条件下的伪码信号相关函数。动态条件下码率偏移使伪码相关函数发生动态效应。现有研究仅限于一阶动态即码率偏移恒定的情形,且相关积分长度内码率偏移引起的相对相位滑动不超过1码元。方法上多采用数值计算,仅Unjieng Cheng采用逐码元求和法推导了相关函数及其均值的表达式。
本文首先将逐码元求和法推广到积分时间任意长和二阶动态即码率偏移变化率恒定的情形,推导并仿真验证了伪码相关函数及其均值、方差的表达式,并给出了方差上限。逐码元求和法结果准确,但表达式繁琐,不利于高动态伪码相关函数特点分析与实际应用。为此,本文提出了平稳随机过程积分法,推导并仿真验证了一阶、二阶动态条件下任意长积分时间伪码相关函数及其均值表达式;分析了一阶、二阶动态伪码相关函数特点,结果表明,动态条件下伪码相关函数不再是三角形,发生了主瓣展宽、峰值移位和损耗三种动态效应,二阶动态条件下伪码相关函数还失去了对称性;基于相关峰损耗表达式的二阶动态与一阶动态比较研究得出结论:二阶动态因素码率偏移变化率可引起dB量级的相关峰损耗或增益,并给出了二阶动态简化为一阶动态的判决条件和方法。与逐码元求和法相比,平稳随机过程积分法所得表达式更为简单、实用,当伪随机序列周期L>>1时具有相当高的精度。
第二部分研究高动态对扩频信号捕获的影响。目前研究多集中于载波频偏对捕获的影响,对伪码频偏影响的分析甚少,同时考虑载波和伪码频偏的理论研究尚未见诸文献。本文基于平稳随机过程积分法推导了同时存在恒定载波和伪码频偏条件下的伪码相关输出和载波-伪码多普勒联合损耗表达式,研究表明忽略伪码频偏导致的信噪比计算误差可达dB甚至10dB量级;在此基础上优化设计了常见的“分段相关.视频积累”伪码捕获系统的中频积累时间,与忽略伪码频偏仅考虑载波频偏的比较研究表明,忽略伪码频偏引起的优化设计性能损耗甚微,因此可仅基于载波频偏优化设计。
第三部分研究动态条件下伪码捕获和跟踪阶段的伪码相位测量方法。基于动态条件下的伪码相关函数表达式,研究了捕获和跟踪阶段的一阶、二阶动态伪码相位测量方法及误差,提出了两种动态条件下伪码捕获相位测量方法和两种一阶动态、三种二阶动态伪码跟踪相位测量方法。其中伪码捕获相位测量方法可基本消除常规方法10ns甚至100ns量级的相位测量误差,降低跟踪电路的负担;伪码跟踪相位测量方法可基本消除常规方法0.001m～1m量级的一阶、二阶动态伪距测量误差,提高伪距测量精度。
第四部分研究高动态定位解算中的滞后效应。指出发射机运动条件下观测伪距对发射机运动状态的反映存在滞后效应。在倒GPS遥外测综合测量系统中,观测伪距的动态滞后效应可导致m级的定位误差,其校正方法是统一各测站观测伪距的发射时间。
本文研究成果为高动态条件下扩频信号同步的分析与设计提供了理论依据,为高精度伪码测距以及如何避免主动定位系统动态滞后误差提供了方法上的指导。
In the satellite navigation receiver, there is not only carrier frequency offset but also code frequency offset between the received and the local signals when the host vehicle is in high dynamic motion. The precious studies mostly aimed at carrier frequency offset, while there were very few systemic theoretical studies on the influences of code frequency offset. There is still large space for improving the efficiencies and performance in the designing of high dynamic receivers. Moreover, the influence of satellites' motion on the metering precision of pseudo range in high precision receivers with the precision demand of 0.5ns is yet not neglectable when the host vehicle is static. Based on these two applications, this thesis focuses on the influence of code frequency offset. It contains four sections:
In sectionⅠ, the correlation function of PN codes under dynamic conditions is studied. Under dynamic conditions code frequency offset makes the code correlation function deformed. The precious study was limited to first-order dynamic, i.e., constant code frequency offset and the integration time interval during which the chip slipping due to code frequency offset is less than one chip. And mostly the numerical calculation method was used, except that Unjeng Cheng derived the expressions of correlation function and its mean value.
In the thesis, first the PN code correlation function, its mean and variance are derived by the method of summing chip by chip, with the correlation time interval extended to arbitrary length and the dynamic condition extended to the case of second-order, i.e., constant code frequency offset rate. And also the upper bound of variance is given. This method is accurate. But its shortcoming of very complicated expression disables it from being used to analyze the characteristic of PN code correlation and guide the analyses and devising of code synchronization. So we present a method which is referred to as stationary random process integrating. The PN code correlation function and its mean with arbitrary integration time interval under first-order and second-order dynamic are derived and verified by simulations. The characteristics of PN code correlation function under first-order and second-order dynamic are analyzed. The result shows that under dynamic conditions the code correlation function is no longer triangular and three dynamic effects of main-lobe spreading, correlation peak shifting and decreasing take place, and moreover the code correlation function loses its symmetry under second-order dynamic. By comparison between second-order and first-order dynamic based on the peak value loss expressions it is concluded that the second-order dynamic factor code frequency offset rate can induce loss or gain in the order of dB, and the conditions when second-order dynamic can be simplified to first-order dynamic and the method how to decision are given. Compared with the method of summing chip by chip, the method of stationary random process integrating is simpler and more practical. And its precision is high when the PN code period length L >>1.
In sectionⅡ, the influences of high dynamic on acquisition are investigated. The precious study focused on the influence of carrier frequency offset on acquisition. The influence of code frequency offset has been seldom analyzed, and the theoretical study with both carrier and code frequency offset taking into account has not been seen in the literature. In this thesis the PN code correlation function with both constant carrier and code frequency offset and also carrier Doppler-code Doppler joint loss are derived. The study shows that ignoring the code frequency offset will induce errors in the order of dB or 10dB. Based on it the IF integration time of the common acquisition system called segment correlation-video integration is optimized, the comparison study shows that optimizing with the code frequency offset ignored brings little performance loss, so the IF integration time can be optimized according to the carrier frequency offset only.
In sectionⅢ, the code phase metering methods for code acquisition and tracking under dynamic conditions are investigated. Based on the expressions for code correlation function under dynamic conditions, the phase metering methods and their errors for code acquisition and tracking under first-order and second-order dynamic are studied. Two code phase metering methods for code acquisition under dynamic, two code phase metering methods for first-order dynamic tracking and three code phase metering methods for second-order dynamic tracking are proposed. The presented metering methods for code acquisition can almost remove the common-used method's error of the order of 10ns to 100ns, so that can reduce the burden of code tracking circuit. And the presented code phase metering methods for code acquisition can almost remove the common-used method's error of the order of 0.001m～0.1m, so that can improve the precision of PN code ranging.
In sectionⅣ, the dynamic delay effect in positioning solution under high dynamic is studied. It is pointed out that when the transmitter is moving, there is a delay effect in the reflection of the observed pseudo range on the transmitter motion state. In the telemetry and tracking integrated system with inverse GPS principle, the dynamic delay effect of pseudo range can induce positioning error in the order of m. The revising method is to align the transmitting time of the observed pseudo range at all the observation stations.
The thesis provides with theoretical guidance for the analysis and designing of dynamic spread spectrum code synchronization, and provides with methods for (a) high precision PN code ranging under dynamic conditions and (b) pseudo range observation in the positive positioning systems in order to avoid the dynamic delay errors.
第一部分研究动态条件下的伪码信号相关函数。动态条件下码率偏移使伪码相关函数发生动态效应。现有研究仅限于一阶动态即码率偏移恒定的情形,且相关积分长度内码率偏移引起的相对相位滑动不超过1码元。方法上多采用数值计算,仅Unjieng Cheng采用逐码元求和法推导了相关函数及其均值的表达式。
本文首先将逐码元求和法推广到积分时间任意长和二阶动态即码率偏移变化率恒定的情形,推导并仿真验证了伪码相关函数及其均值、方差的表达式,并给出了方差上限。逐码元求和法结果准确,但表达式繁琐,不利于高动态伪码相关函数特点分析与实际应用。为此,本文提出了平稳随机过程积分法,推导并仿真验证了一阶、二阶动态条件下任意长积分时间伪码相关函数及其均值表达式;分析了一阶、二阶动态伪码相关函数特点,结果表明,动态条件下伪码相关函数不再是三角形,发生了主瓣展宽、峰值移位和损耗三种动态效应,二阶动态条件下伪码相关函数还失去了对称性;基于相关峰损耗表达式的二阶动态与一阶动态比较研究得出结论:二阶动态因素码率偏移变化率可引起dB量级的相关峰损耗或增益,并给出了二阶动态简化为一阶动态的判决条件和方法。与逐码元求和法相比,平稳随机过程积分法所得表达式更为简单、实用,当伪随机序列周期L>>1时具有相当高的精度。
第二部分研究高动态对扩频信号捕获的影响。目前研究多集中于载波频偏对捕获的影响,对伪码频偏影响的分析甚少,同时考虑载波和伪码频偏的理论研究尚未见诸文献。本文基于平稳随机过程积分法推导了同时存在恒定载波和伪码频偏条件下的伪码相关输出和载波-伪码多普勒联合损耗表达式,研究表明忽略伪码频偏导致的信噪比计算误差可达dB甚至10dB量级;在此基础上优化设计了常见的“分段相关.视频积累”伪码捕获系统的中频积累时间,与忽略伪码频偏仅考虑载波频偏的比较研究表明,忽略伪码频偏引起的优化设计性能损耗甚微,因此可仅基于载波频偏优化设计。
第三部分研究动态条件下伪码捕获和跟踪阶段的伪码相位测量方法。基于动态条件下的伪码相关函数表达式,研究了捕获和跟踪阶段的一阶、二阶动态伪码相位测量方法及误差,提出了两种动态条件下伪码捕获相位测量方法和两种一阶动态、三种二阶动态伪码跟踪相位测量方法。其中伪码捕获相位测量方法可基本消除常规方法10ns甚至100ns量级的相位测量误差,降低跟踪电路的负担;伪码跟踪相位测量方法可基本消除常规方法0.001m～1m量级的一阶、二阶动态伪距测量误差,提高伪距测量精度。
第四部分研究高动态定位解算中的滞后效应。指出发射机运动条件下观测伪距对发射机运动状态的反映存在滞后效应。在倒GPS遥外测综合测量系统中,观测伪距的动态滞后效应可导致m级的定位误差,其校正方法是统一各测站观测伪距的发射时间。
本文研究成果为高动态条件下扩频信号同步的分析与设计提供了理论依据,为高精度伪码测距以及如何避免主动定位系统动态滞后误差提供了方法上的指导。
In the satellite navigation receiver, there is not only carrier frequency offset but also code frequency offset between the received and the local signals when the host vehicle is in high dynamic motion. The precious studies mostly aimed at carrier frequency offset, while there were very few systemic theoretical studies on the influences of code frequency offset. There is still large space for improving the efficiencies and performance in the designing of high dynamic receivers. Moreover, the influence of satellites' motion on the metering precision of pseudo range in high precision receivers with the precision demand of 0.5ns is yet not neglectable when the host vehicle is static. Based on these two applications, this thesis focuses on the influence of code frequency offset. It contains four sections:
In sectionⅠ, the correlation function of PN codes under dynamic conditions is studied. Under dynamic conditions code frequency offset makes the code correlation function deformed. The precious study was limited to first-order dynamic, i.e., constant code frequency offset and the integration time interval during which the chip slipping due to code frequency offset is less than one chip. And mostly the numerical calculation method was used, except that Unjeng Cheng derived the expressions of correlation function and its mean value.
In the thesis, first the PN code correlation function, its mean and variance are derived by the method of summing chip by chip, with the correlation time interval extended to arbitrary length and the dynamic condition extended to the case of second-order, i.e., constant code frequency offset rate. And also the upper bound of variance is given. This method is accurate. But its shortcoming of very complicated expression disables it from being used to analyze the characteristic of PN code correlation and guide the analyses and devising of code synchronization. So we present a method which is referred to as stationary random process integrating. The PN code correlation function and its mean with arbitrary integration time interval under first-order and second-order dynamic are derived and verified by simulations. The characteristics of PN code correlation function under first-order and second-order dynamic are analyzed. The result shows that under dynamic conditions the code correlation function is no longer triangular and three dynamic effects of main-lobe spreading, correlation peak shifting and decreasing take place, and moreover the code correlation function loses its symmetry under second-order dynamic. By comparison between second-order and first-order dynamic based on the peak value loss expressions it is concluded that the second-order dynamic factor code frequency offset rate can induce loss or gain in the order of dB, and the conditions when second-order dynamic can be simplified to first-order dynamic and the method how to decision are given. Compared with the method of summing chip by chip, the method of stationary random process integrating is simpler and more practical. And its precision is high when the PN code period length L >>1.
In sectionⅡ, the influences of high dynamic on acquisition are investigated. The precious study focused on the influence of carrier frequency offset on acquisition. The influence of code frequency offset has been seldom analyzed, and the theoretical study with both carrier and code frequency offset taking into account has not been seen in the literature. In this thesis the PN code correlation function with both constant carrier and code frequency offset and also carrier Doppler-code Doppler joint loss are derived. The study shows that ignoring the code frequency offset will induce errors in the order of dB or 10dB. Based on it the IF integration time of the common acquisition system called segment correlation-video integration is optimized, the comparison study shows that optimizing with the code frequency offset ignored brings little performance loss, so the IF integration time can be optimized according to the carrier frequency offset only.
In sectionⅢ, the code phase metering methods for code acquisition and tracking under dynamic conditions are investigated. Based on the expressions for code correlation function under dynamic conditions, the phase metering methods and their errors for code acquisition and tracking under first-order and second-order dynamic are studied. Two code phase metering methods for code acquisition under dynamic, two code phase metering methods for first-order dynamic tracking and three code phase metering methods for second-order dynamic tracking are proposed. The presented metering methods for code acquisition can almost remove the common-used method's error of the order of 10ns to 100ns, so that can reduce the burden of code tracking circuit. And the presented code phase metering methods for code acquisition can almost remove the common-used method's error of the order of 0.001m～0.1m, so that can improve the precision of PN code ranging.
In sectionⅣ, the dynamic delay effect in positioning solution under high dynamic is studied. It is pointed out that when the transmitter is moving, there is a delay effect in the reflection of the observed pseudo range on the transmitter motion state. In the telemetry and tracking integrated system with inverse GPS principle, the dynamic delay effect of pseudo range can induce positioning error in the order of m. The revising method is to align the transmitting time of the observed pseudo range at all the observation stations.
The thesis provides with theoretical guidance for the analysis and designing of dynamic spread spectrum code synchronization, and provides with methods for (a) high precision PN code ranging under dynamic conditions and (b) pseudo range observation in the positive positioning systems in order to avoid the dynamic delay errors.
引文
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