卫星导航系统多径估计理论与方法研究
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摘要
多径是卫星导航系统（GNSS）的一项重要误差源。在GNSS的高精度应用中，多径是最难以处理的误差源，会对导航与定位结果造成严重危害。多径估计技术是削弱多径影响的一类接收机内部信号处理方法，本文对这一技术进行较为详细的研究，在对已有多径估计方法的性能进行深入分析的基础上，提出了多种不同条件下多径估计的理论与方法。本文的主要工作和创新点可概括如下：
1.分析了多径对卫星导航系统接收机环路的影响以及多径抑制技术的性能，获得了许多重要结论，为多径估计理论与方法的提出奠定了基础。
2.针对多相关器多径估计问题，采用-Deploying法的思想，提出了多径格网化最大似然估计；提出了选取相关器组的合理建议，使方法不受无效多径信号的干扰；提出了一整套多径探测、估计的法则，可以得到直射信号与多径信号的延迟、幅度和载波相位等参数的估计。
3.揭示了格网化最大似然估计受噪声影响强烈和不稳定的根本原因是法矩阵的病态性；依据病态性对参数估计影响的特点，构造了多径岭估计与TSVD正则化估计等一系列多径有偏估计，讨论了其优良性质；结合具体模型中病态性影响的特点给出了合理的偏参数的选取方案。一定程度上解决了噪声对估计影响强烈的问题。
4.基于高度压缩和解析的多径量测模型，研究了多径最大似然估计及其优化算法。采用多种非线性优化方法求解多径最大似然估计，比较了各种求解方法的性能。针对多径信号个数未知的问题，应用模型阶数确定的理论，提出了多径个数确定的准则和方法。
5.针对动态多径模型具有加性Gauss白噪声的特点，建立了无须增广状态向量的平方根无迹Kalman滤波的算法，应用于多径估计。较传统的无迹Kalman滤波方法，能够更为高效准确地估计直射信号与多径信号的各个参数；相比传统多径抑制方法，能够更加有效地抑制多径的影响；与已有的基于边缘化粒子滤波的多径估计方法相比，可以以很小的运算负担实现相近的估计精度。
6.将容积Kalman滤波应用于多径估计。采用平方根容积Kalman滤波可以用小于平方根无迹Kalman滤波的运算负担，达到与平方根无迹Kalman滤波相仿的估计精度，有效抑制多径的影响。
7.针对动态多径估计中多径信号变化复杂，其存在、生灭以及参数的变化规律难以确定的问题，建立了直射信号参数具有动态信息的动态模型，并提出了利用直射信号参数动态模型的粒子滤波。在时间更新中，对直射信号的参数综合利用动态信息和观测信息，而对多径信号的参数仅利用观测信息。给出了合理的建议分布的选取方案及滤波实现方案。方法相比传统的基于粒子滤波的多径估计，一方面，可有效利用直射信号参数含有的动态信息，提高估计的精度；另一方面，可有效处理多径信号存在及生灭的复杂性，避免对多径信号参数误用先验信息，提高估计的可靠性。
Multipath is one of the main error sources in global navigation satellite systems (GNSS). Inapplications of GNSS with high precision, multipath is the most difficult error source to dealwith. Multipath estimation is one of the receiver-internal multipath mitigation approaches. In thisthesis, the multipath estimation technology is researched in details, and several multipathestimation methods are proposed on the basis of in-depth analysis of existing multipathmitigation and estimation methods. The main works and creations are as follows.
1. The effect of multipath on GNSS receiver tracking loops and the performances of somerepresentative multipath mitigation technologies are analyzed, and lots of conclusions are drawnfrom the analysis, which provide a basis for the establishment of multipath estimationtechnology.
2. For multicorrelator multipath estimation, multipath grid maximum likelihood estimation(GMLE) is proposed based on the idea of-deploying method. A proper configuration for thebank of correlators is advised to avoid the interference from ineffective multipath signals. Thesteps of multipath detection and estimation method are established, through which the delay,amplitude, and carrier phase estimations of multipath signals can be estimated.
3. The GMLE is analyzed from two aspects: statistical accuracy and numerical stability,revealing that the ill-conditioning in the normal matrix is the causation of poor performances ofthe GMLE. Several types of biased multipath estimations including ridge estimation andtruncated singular value decomposition (TSVD) estimation are proposed, and the property of theestimations are discussed. The selection methods for the bias parameters of the estimations areadvised based on the characteristics of the ill-conditioning existing in the model. Biasedestimation mitigates the strong effects of noise to a certain extent.
4. Multipath maximum likelihood estimation and the optimization methods to solve theestimation are researched based on the highly compressed and analytic measurement model.Several nonlinear optimization technologies are utilized to solve the multipath maximumlikelihood estimation, and the performances of the different optimization technologies arediscussed. For the problem of the unknown number of the multipath signal components, basedon the theory of model order selection, the rule and method to fix the number of the multipathsignal components are proposed.
5. For the characteristics that the noise in multipath measurement is additive Gaussian whitenoise, square-root unscented Kalman filter using nonaugmented state vectors is proposed andapplied in the multipath estimation problem. Compared with traditional unscented Kalman filter, the new method has lower computational burden, better accuracy of estimation and betterresistance performance to filter dispersion. The new method can mitigate multipath effect moreefficiently than traditional multipath mitigation technology, and can estimate multipathparameters in almost the same precision as marginalized particle filter with much lowercomputational burden.
6. Cubature Kalman filter is applied in the multipath estimation problem. The computationalburden of square-root cubature Kalman filter is lower than square-root unscented Kalman filter,and the estimation precisions of the two filtering methods are at the same level.
7. For the problems that the transformation of multipath signal components is complicatedand it is difficult to characterize how multipath signal components appear and disappear and howthe values of multipath parameters transform, the kinematic model of only the direct signalcomponents is proposed, and multipath estimation based on particle filtering is implementedusing the kinematic information of the direct signal components. In the update steps of theparticle filtering, the parameters of the direct signal component are estimated combiningobservation and kinematic information while the parameters of multipath components areestimated using only observation information. The building of proposals and the implementationof the filtering are given. The method can use the kinematic information of the direct signals toimprove the accuracy and meanwhile avoid misusing of the incorrect kinematic information ofmultipath signals.
1.分析了多径对卫星导航系统接收机环路的影响以及多径抑制技术的性能，获得了许多重要结论，为多径估计理论与方法的提出奠定了基础。
2.针对多相关器多径估计问题，采用-Deploying法的思想，提出了多径格网化最大似然估计；提出了选取相关器组的合理建议，使方法不受无效多径信号的干扰；提出了一整套多径探测、估计的法则，可以得到直射信号与多径信号的延迟、幅度和载波相位等参数的估计。
3.揭示了格网化最大似然估计受噪声影响强烈和不稳定的根本原因是法矩阵的病态性；依据病态性对参数估计影响的特点，构造了多径岭估计与TSVD正则化估计等一系列多径有偏估计，讨论了其优良性质；结合具体模型中病态性影响的特点给出了合理的偏参数的选取方案。一定程度上解决了噪声对估计影响强烈的问题。
4.基于高度压缩和解析的多径量测模型，研究了多径最大似然估计及其优化算法。采用多种非线性优化方法求解多径最大似然估计，比较了各种求解方法的性能。针对多径信号个数未知的问题，应用模型阶数确定的理论，提出了多径个数确定的准则和方法。
5.针对动态多径模型具有加性Gauss白噪声的特点，建立了无须增广状态向量的平方根无迹Kalman滤波的算法，应用于多径估计。较传统的无迹Kalman滤波方法，能够更为高效准确地估计直射信号与多径信号的各个参数；相比传统多径抑制方法，能够更加有效地抑制多径的影响；与已有的基于边缘化粒子滤波的多径估计方法相比，可以以很小的运算负担实现相近的估计精度。
6.将容积Kalman滤波应用于多径估计。采用平方根容积Kalman滤波可以用小于平方根无迹Kalman滤波的运算负担，达到与平方根无迹Kalman滤波相仿的估计精度，有效抑制多径的影响。
7.针对动态多径估计中多径信号变化复杂，其存在、生灭以及参数的变化规律难以确定的问题，建立了直射信号参数具有动态信息的动态模型，并提出了利用直射信号参数动态模型的粒子滤波。在时间更新中，对直射信号的参数综合利用动态信息和观测信息，而对多径信号的参数仅利用观测信息。给出了合理的建议分布的选取方案及滤波实现方案。方法相比传统的基于粒子滤波的多径估计，一方面，可有效利用直射信号参数含有的动态信息，提高估计的精度；另一方面，可有效处理多径信号存在及生灭的复杂性，避免对多径信号参数误用先验信息，提高估计的可靠性。
Multipath is one of the main error sources in global navigation satellite systems (GNSS). Inapplications of GNSS with high precision, multipath is the most difficult error source to dealwith. Multipath estimation is one of the receiver-internal multipath mitigation approaches. In thisthesis, the multipath estimation technology is researched in details, and several multipathestimation methods are proposed on the basis of in-depth analysis of existing multipathmitigation and estimation methods. The main works and creations are as follows.
1. The effect of multipath on GNSS receiver tracking loops and the performances of somerepresentative multipath mitigation technologies are analyzed, and lots of conclusions are drawnfrom the analysis, which provide a basis for the establishment of multipath estimationtechnology.
2. For multicorrelator multipath estimation, multipath grid maximum likelihood estimation(GMLE) is proposed based on the idea of-deploying method. A proper configuration for thebank of correlators is advised to avoid the interference from ineffective multipath signals. Thesteps of multipath detection and estimation method are established, through which the delay,amplitude, and carrier phase estimations of multipath signals can be estimated.
3. The GMLE is analyzed from two aspects: statistical accuracy and numerical stability,revealing that the ill-conditioning in the normal matrix is the causation of poor performances ofthe GMLE. Several types of biased multipath estimations including ridge estimation andtruncated singular value decomposition (TSVD) estimation are proposed, and the property of theestimations are discussed. The selection methods for the bias parameters of the estimations areadvised based on the characteristics of the ill-conditioning existing in the model. Biasedestimation mitigates the strong effects of noise to a certain extent.
4. Multipath maximum likelihood estimation and the optimization methods to solve theestimation are researched based on the highly compressed and analytic measurement model.Several nonlinear optimization technologies are utilized to solve the multipath maximumlikelihood estimation, and the performances of the different optimization technologies arediscussed. For the problem of the unknown number of the multipath signal components, basedon the theory of model order selection, the rule and method to fix the number of the multipathsignal components are proposed.
5. For the characteristics that the noise in multipath measurement is additive Gaussian whitenoise, square-root unscented Kalman filter using nonaugmented state vectors is proposed andapplied in the multipath estimation problem. Compared with traditional unscented Kalman filter, the new method has lower computational burden, better accuracy of estimation and betterresistance performance to filter dispersion. The new method can mitigate multipath effect moreefficiently than traditional multipath mitigation technology, and can estimate multipathparameters in almost the same precision as marginalized particle filter with much lowercomputational burden.
6. Cubature Kalman filter is applied in the multipath estimation problem. The computationalburden of square-root cubature Kalman filter is lower than square-root unscented Kalman filter,and the estimation precisions of the two filtering methods are at the same level.
7. For the problems that the transformation of multipath signal components is complicatedand it is difficult to characterize how multipath signal components appear and disappear and howthe values of multipath parameters transform, the kinematic model of only the direct signalcomponents is proposed, and multipath estimation based on particle filtering is implementedusing the kinematic information of the direct signal components. In the update steps of theparticle filtering, the parameters of the direct signal component are estimated combiningobservation and kinematic information while the parameters of multipath components areestimated using only observation information. The building of proposals and the implementationof the filtering are given. The method can use the kinematic information of the direct signals toimprove the accuracy and meanwhile avoid misusing of the incorrect kinematic information ofmultipath signals.
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