自适应抗差UKF在卫星组合导航中的理论与应用研究
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摘要
鉴于各种单一的导航系统都有缺点,上世纪70年代,随着电子计算机技术特别是微机技术的迅猛发展和现代控制系统理论的进步,组合导航技术开始迅猛发展起来,成为目前导航技术发展的重要方向之一,并在航海、航空与航天等领域有着广泛的应用前景。对于各种不同形式的组合导航系统通常均具有以下功能：(1)超越功能。组合导航系统能够充分利用各个子系统的导航信息,具有单个子系统不具备的功能。(2)互补功能。由于组合导航系统综合利用了各子系统的信息,所以各子系统能够取长补短,扩大使用范围。(3)余度功能。各子系统感测同一信息源,使测量值冗余,提高系统的可靠性。
组合导航系统信息处理的核心是Kalman滤波器,它是在两个或多个导航系统输出的基础上,利用Kalman滤波去估计系统的各种误差,再用误差状态的估计值去校正系统,达到综合的目的。Kalman滤波在卫星导航定位以及卫星组合导航定位中的应用是目前国内外研究的热点,抗差Kalman滤波、自适应Kalman滤波、以及它们的改进算法包括自适应Kalman滤波、抗差自适应Kalman滤波、自适应抗差联邦滤波都有学者进行研究和建模,但是对于抗差无迹Kalman滤波(Unscented Kalman Filter,UKF)和自适应UKF算法的研究尚且存在空缺。
本文重点分析UKF滤波算法在GPS/SINS卫星组合导航系统中的应用现状,研究其定位精度以及滤波算法的性能指标,针对标准UKF滤波算法的主要缺点提出一种改进的抗差UKF滤波算法,即结合自适应估计理论的自适应抗差UKF滤波算法。论文的主要内容及贡献包括：
研究卫星组合导航系统的基本原理,在组合方式的研究方面,提出了以软硬件全组合为基础的紧组合方法,并且将此组合方式应用于GPS/SINS卫星组合导航系统中,作为研究UKF滤波算法的系统平台。此方法能够简化组合系统的硬件设计要求,同时提高软件的应用范围。与此同时,详细分析GPS/INS、GPS/DR、GPS/INS/TAN等几种常用的卫星组合导航系统及其组合原理、组合结构图。
根据卫星组合导航系统的实际应用环境,分析总结以下几种滤波算法的优缺点,包括Kalman滤波及其各种改进算法、粒子滤波、联邦滤波、Sage滤波、自适应滤波、鲁棒滤波(H∞滤波)以及智能滤波等。
深入研究Kalman滤波的基础理论,分析几种改进型Kalman滤波方法,包括扩展Kalman滤波(EKF),无迹Kalman滤波(UKF),联邦Kalman滤波、抗差Kalman滤波以及自适应Kalman滤波。重点分析UKF算法的性能优缺点,其主要优点是直接利用非线性模型,避免引入线性化误差,从而提高了滤波精度,而且不必计算雅可比矩阵,其主要缺点是仍然应用了Kalman滤波的滤波框架,需要先验已知的系统数学模型和噪声统计信息。
针对卫星组合导航系统的数学模型、系统噪声和观测噪声统计特性未知的情况,提出一种基于自适应因子的自适应UKF滤波算法,将新算法应用于GPS/SINS等卫星组合导航系统中,并与标准UKF和抗差UKF进行比较,从定位精度和算法冗余度上详细分析新算法的性能优势。结果显示,由于从多种误差因素进行考虑,新算法能够较大程度的提高卫星组合导航系统的定位精度。
针对卫星组合导航系统的观测粗差引起的定位精度误差,提出一种基于抗差估计理论的抗差UKF滤波算法。标准Kalman滤波应用的是经典的估计模型,它是针对偶然误差的,粗差的存在将不可避免地对估计结果产生影响,甚至个别大粗差就会使结果产生重大偏离。因此,如何使Kalman滤波的平差模型本身具备抗粗差的能力,正是抗差Kalman滤波研究的内容。
综合考虑观测粗差和模型误差两者共同引起的误差因素,提出自适应抗差UKF滤波算法,将此算法应用于北斗/SINS, GPS/SINS等卫星组合导航系统中,并以GPS/SINS组合系统为主要研究对象,通过计算机仿真,证明新算法分别可以减少粗差和动态误差模型不准确性带来的精度影响因素,达到较高的定位精度。由于卫星组合导航系统是目前科学研究的热点之一,其应用领域和应用前景十分广泛,因此研究如何改善滤波算法的性能从而提高组合系统的导航精度具有很好的实际意义。
Recently, the navigation systems often used in the aircrafts include:the inertial navigation systems, the satellite navigation system, the Doppler navigation systems, the celestial navigation systems, and the terrain-aided navigation system, and so on. In the last 70's century, the integrated navigation system has been emerged in view of the shortcomings of the single navigation system. This new kind of navigation system has been used in the fields of the maritime, the aviation and the aerospace. With the development of the computer technology, especially the micro-computer technology and the modern-control theory, the integrated navigation system is becoming an important development direction of the modern navigation system. The main characteristic of the integrated system is that a variety of single navigation systems can be combined together using some algorithms and their advantages can be used to enforce the whole performance of the system. For many different forms of the integrated navigation systems, their typical functions include:Firstly, the surpass capability. The integrated navigation system has many additional functions which a single subsystem does not have, because it is can take full advantage of the sub-systems. Secondly, the complementary function. The integrated system has the expanded scope of the application, because of the combination of the information from the different subsystems. Thirdly, the redundancy capability. More signal information can be obtained from the subsystems to improve the reliability of the integrated system.
The key technology of information processing phase in the integrated navigation system is the Kalman filtering algorithm. This processing algorithm estimates the system errors based on the Kalman filtering algorithm to correct the positioning errors of the integrated system. The main signal information is obtained from two or more subsystems' output to achieve a comprehensive purpose. Currently, many researchers at home and abroad have studied the Kalman filtering algorithm used in the satellite navigation and the satellite integrated navigation. The main research fields include robust Kalman filtering algorithm, adaptive Kalman filtering algorithm, as well as their improved algorithm. However, few or no analysis has been focused on the robust Unscented Kalman filtering (UKF) algorithm and the adaptive UKF algorithm.
This dissertation focuses on the application of the UKF in the GPS/SINS Integrated Navigation System, its positioning accuracy and the advantages and disadvantages of this filtering algorithm. The dissertation puts forward an improved robust-UKF algorithm based on the main disadvantages of the standard-UKF algorithm, which is combining the adaptive-estimation theory into the robust filtering algorithm. The main contributions of the dissertation include:
·Firstly, the principles of the satellite integrated navigation system were studied. An improved system tight-combination method is presented, which is based on a full portfolio of hardware and software combination method. This new method is used in the GPS/SINS navigation system to become the main experimental platform of the filtering algorithm. The advantage of our new combination method is that it can simplify the hardware-designing process, as well as improve the software applications. At the same time, a detailed analysis of GPS/SINS, GPS/DR, GPS/INS/TAN and other integrated systems has been done to study their combination principle and combination chart.
·Secondly, some filtering algorithm currently used in the satellite integrated navigation system are introduced, including the Kalman filtering algorithm and its improved algorithms, the particle filtering algorithm, the Federal filtering algorithm, the Sage filtering algorithm, the adaptive filtering algorithm, the robust filtering algorithm, and the intelligent filtering algorithm. A detailed analysis to the advantages and disadvantages of these filtering algorithms has been done, based on the practical application environment of the satellite navigation system.
·Thirdly, the basic theory of the standard Kalman filtering algorithm is studied deeply. Several improved Kalman filtering algorithms are analyzed, including the Extended Kalman filtering algorithm (EKF), the Unscented Kalman filtering algorithm (UKF), the Federal Kalman filtering algorithm, the robust Kalman filtering algorithm and the adaptive Kalman filtering algorithm. After summarizing the performance advantages and disadvantages of UKF, we can conclude that:the main advantages are the direct use of the non-linear system model, the avoidance of the function linear-error and no need to calculate the Jacobian matrix; the main disadvantage is the requirement of the priori known to the system mathematical model and noise statistics.
·An adaptive UKF algorithm based on the standard UKF algorithm are proposed to solve the problems that the system's mahematic model is non-accuracy and the noise statistics is unknown. This new algorithm is applied to the GPS/SINS integrated navigation system to analyze its performance in detail, like positioning accuracy and calculation redundancy. Comparing with the standard UKF and the Robust UKF, our new adaptive UKF algorithm can improve the positioning accuracy of the satellite navigation system significantly.
·A robust UKF algorithm based on the robust estimation theory is proposed. This new algorithm is mainly used to improve the poor positioning accuracy caused by the observation-rough errors. The classical estimation model of the standard Kalman filtering algorithm is used to reduce the accidental error. The presence of gross errors will impact the estimation results inevitably and even cause a significant positioning departure. Therefore, the main study point of the robust Kalman filtering algorithm is how to make the adjustment Kalman filter model itself has the ability of anti-gross error.
·Last but not least, an adaptive-robust UKF filtering algorithm is presented, after comprehensively considering of the error caused by observing gross error factors and the model error caused by error factors. Our new UKF algorithm is applied to the BD/SINS and GPS/SINS integrated satellite navigation system respectively. The simulation results indicate that this improved algorithm can achieve a high positioning accuracy, while reducing the accuracy influencing factors caused by the gross error and dynamic error model.
Currently, the problem exist in the satellite integrated navigation system is a hot scientific research topic, and the applications and prospects of this system are very broad. Therefore, it is a great practical significance to study how to improve the performance of filtering algorithms to improve the navigation accuracy of the integrated systems.
组合导航系统信息处理的核心是Kalman滤波器,它是在两个或多个导航系统输出的基础上,利用Kalman滤波去估计系统的各种误差,再用误差状态的估计值去校正系统,达到综合的目的。Kalman滤波在卫星导航定位以及卫星组合导航定位中的应用是目前国内外研究的热点,抗差Kalman滤波、自适应Kalman滤波、以及它们的改进算法包括自适应Kalman滤波、抗差自适应Kalman滤波、自适应抗差联邦滤波都有学者进行研究和建模,但是对于抗差无迹Kalman滤波(Unscented Kalman Filter,UKF)和自适应UKF算法的研究尚且存在空缺。
本文重点分析UKF滤波算法在GPS/SINS卫星组合导航系统中的应用现状,研究其定位精度以及滤波算法的性能指标,针对标准UKF滤波算法的主要缺点提出一种改进的抗差UKF滤波算法,即结合自适应估计理论的自适应抗差UKF滤波算法。论文的主要内容及贡献包括：
研究卫星组合导航系统的基本原理,在组合方式的研究方面,提出了以软硬件全组合为基础的紧组合方法,并且将此组合方式应用于GPS/SINS卫星组合导航系统中,作为研究UKF滤波算法的系统平台。此方法能够简化组合系统的硬件设计要求,同时提高软件的应用范围。与此同时,详细分析GPS/INS、GPS/DR、GPS/INS/TAN等几种常用的卫星组合导航系统及其组合原理、组合结构图。
根据卫星组合导航系统的实际应用环境,分析总结以下几种滤波算法的优缺点,包括Kalman滤波及其各种改进算法、粒子滤波、联邦滤波、Sage滤波、自适应滤波、鲁棒滤波(H∞滤波)以及智能滤波等。
深入研究Kalman滤波的基础理论,分析几种改进型Kalman滤波方法,包括扩展Kalman滤波(EKF),无迹Kalman滤波(UKF),联邦Kalman滤波、抗差Kalman滤波以及自适应Kalman滤波。重点分析UKF算法的性能优缺点,其主要优点是直接利用非线性模型,避免引入线性化误差,从而提高了滤波精度,而且不必计算雅可比矩阵,其主要缺点是仍然应用了Kalman滤波的滤波框架,需要先验已知的系统数学模型和噪声统计信息。
针对卫星组合导航系统的数学模型、系统噪声和观测噪声统计特性未知的情况,提出一种基于自适应因子的自适应UKF滤波算法,将新算法应用于GPS/SINS等卫星组合导航系统中,并与标准UKF和抗差UKF进行比较,从定位精度和算法冗余度上详细分析新算法的性能优势。结果显示,由于从多种误差因素进行考虑,新算法能够较大程度的提高卫星组合导航系统的定位精度。
针对卫星组合导航系统的观测粗差引起的定位精度误差,提出一种基于抗差估计理论的抗差UKF滤波算法。标准Kalman滤波应用的是经典的估计模型,它是针对偶然误差的,粗差的存在将不可避免地对估计结果产生影响,甚至个别大粗差就会使结果产生重大偏离。因此,如何使Kalman滤波的平差模型本身具备抗粗差的能力,正是抗差Kalman滤波研究的内容。
综合考虑观测粗差和模型误差两者共同引起的误差因素,提出自适应抗差UKF滤波算法,将此算法应用于北斗/SINS, GPS/SINS等卫星组合导航系统中,并以GPS/SINS组合系统为主要研究对象,通过计算机仿真,证明新算法分别可以减少粗差和动态误差模型不准确性带来的精度影响因素,达到较高的定位精度。由于卫星组合导航系统是目前科学研究的热点之一,其应用领域和应用前景十分广泛,因此研究如何改善滤波算法的性能从而提高组合系统的导航精度具有很好的实际意义。
Recently, the navigation systems often used in the aircrafts include:the inertial navigation systems, the satellite navigation system, the Doppler navigation systems, the celestial navigation systems, and the terrain-aided navigation system, and so on. In the last 70's century, the integrated navigation system has been emerged in view of the shortcomings of the single navigation system. This new kind of navigation system has been used in the fields of the maritime, the aviation and the aerospace. With the development of the computer technology, especially the micro-computer technology and the modern-control theory, the integrated navigation system is becoming an important development direction of the modern navigation system. The main characteristic of the integrated system is that a variety of single navigation systems can be combined together using some algorithms and their advantages can be used to enforce the whole performance of the system. For many different forms of the integrated navigation systems, their typical functions include:Firstly, the surpass capability. The integrated navigation system has many additional functions which a single subsystem does not have, because it is can take full advantage of the sub-systems. Secondly, the complementary function. The integrated system has the expanded scope of the application, because of the combination of the information from the different subsystems. Thirdly, the redundancy capability. More signal information can be obtained from the subsystems to improve the reliability of the integrated system.
The key technology of information processing phase in the integrated navigation system is the Kalman filtering algorithm. This processing algorithm estimates the system errors based on the Kalman filtering algorithm to correct the positioning errors of the integrated system. The main signal information is obtained from two or more subsystems' output to achieve a comprehensive purpose. Currently, many researchers at home and abroad have studied the Kalman filtering algorithm used in the satellite navigation and the satellite integrated navigation. The main research fields include robust Kalman filtering algorithm, adaptive Kalman filtering algorithm, as well as their improved algorithm. However, few or no analysis has been focused on the robust Unscented Kalman filtering (UKF) algorithm and the adaptive UKF algorithm.
This dissertation focuses on the application of the UKF in the GPS/SINS Integrated Navigation System, its positioning accuracy and the advantages and disadvantages of this filtering algorithm. The dissertation puts forward an improved robust-UKF algorithm based on the main disadvantages of the standard-UKF algorithm, which is combining the adaptive-estimation theory into the robust filtering algorithm. The main contributions of the dissertation include:
·Firstly, the principles of the satellite integrated navigation system were studied. An improved system tight-combination method is presented, which is based on a full portfolio of hardware and software combination method. This new method is used in the GPS/SINS navigation system to become the main experimental platform of the filtering algorithm. The advantage of our new combination method is that it can simplify the hardware-designing process, as well as improve the software applications. At the same time, a detailed analysis of GPS/SINS, GPS/DR, GPS/INS/TAN and other integrated systems has been done to study their combination principle and combination chart.
·Secondly, some filtering algorithm currently used in the satellite integrated navigation system are introduced, including the Kalman filtering algorithm and its improved algorithms, the particle filtering algorithm, the Federal filtering algorithm, the Sage filtering algorithm, the adaptive filtering algorithm, the robust filtering algorithm, and the intelligent filtering algorithm. A detailed analysis to the advantages and disadvantages of these filtering algorithms has been done, based on the practical application environment of the satellite navigation system.
·Thirdly, the basic theory of the standard Kalman filtering algorithm is studied deeply. Several improved Kalman filtering algorithms are analyzed, including the Extended Kalman filtering algorithm (EKF), the Unscented Kalman filtering algorithm (UKF), the Federal Kalman filtering algorithm, the robust Kalman filtering algorithm and the adaptive Kalman filtering algorithm. After summarizing the performance advantages and disadvantages of UKF, we can conclude that:the main advantages are the direct use of the non-linear system model, the avoidance of the function linear-error and no need to calculate the Jacobian matrix; the main disadvantage is the requirement of the priori known to the system mathematical model and noise statistics.
·An adaptive UKF algorithm based on the standard UKF algorithm are proposed to solve the problems that the system's mahematic model is non-accuracy and the noise statistics is unknown. This new algorithm is applied to the GPS/SINS integrated navigation system to analyze its performance in detail, like positioning accuracy and calculation redundancy. Comparing with the standard UKF and the Robust UKF, our new adaptive UKF algorithm can improve the positioning accuracy of the satellite navigation system significantly.
·A robust UKF algorithm based on the robust estimation theory is proposed. This new algorithm is mainly used to improve the poor positioning accuracy caused by the observation-rough errors. The classical estimation model of the standard Kalman filtering algorithm is used to reduce the accidental error. The presence of gross errors will impact the estimation results inevitably and even cause a significant positioning departure. Therefore, the main study point of the robust Kalman filtering algorithm is how to make the adjustment Kalman filter model itself has the ability of anti-gross error.
·Last but not least, an adaptive-robust UKF filtering algorithm is presented, after comprehensively considering of the error caused by observing gross error factors and the model error caused by error factors. Our new UKF algorithm is applied to the BD/SINS and GPS/SINS integrated satellite navigation system respectively. The simulation results indicate that this improved algorithm can achieve a high positioning accuracy, while reducing the accuracy influencing factors caused by the gross error and dynamic error model.
Currently, the problem exist in the satellite integrated navigation system is a hot scientific research topic, and the applications and prospects of this system are very broad. Therefore, it is a great practical significance to study how to improve the performance of filtering algorithms to improve the navigation accuracy of the integrated systems.
引文
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