组合导航中的鲁棒滤波研究
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摘要
现代导航系统对精度和可靠性的要求越来越高,要求导航系统能够提供全面、精确的导航定位定向信息,而且不受气象条件制约,隐蔽性和自主性强,抗干扰性能好。因此,到目前为止,没有哪一种单一的导航设备能满足这些要求,而是将几种导航设备适当组合构成组合导航系统,相互取长补短,来提高系统的精度和稳健性,组合导航己成为导航发展的主要方向,这也是多传感器信息融合在导航系统中发展的一个方向。
在组合导航算法方面,对这些单传感器进行融合应用最成功的方法就是卡尔曼滤波,然而卡尔曼滤波器需要精确已知系统的动态模型和过程及测量噪声的统计特性,对系统参数和噪声的不确定性比较敏感,容易造成滤波发散。伴随着鲁棒控制理论发展起来的鲁棒滤波理论,尤其是H_∞滤波的理论,为卡尔曼滤波存在的问题在理论上提供了解决途径。
本文以GPS/DR组合导航系统为对象,研究了组合导航中的鲁棒滤波问题。针对不同的滤波模型以及噪声的不确定性,研究了H_∞滤波算法,混合滤波算法和联合滤波算法的适应性和滤波精度。研究工作主要包括以下几个部分:
第一,分析与推导了GPS/DR组合导航系统的几种滤波数学模型。基于矩阵理论,改进了滤波的参数选择算法。基于线性矩阵不等式,推导了稳态滤波算法。将鲁棒卡尔曼滤波和鲁棒滤波算法运用于GPS/DR组合导航系统,是模型参数不确定性算法应用于组合导航的一次尝试。根据当前“统计”模型的非线性,运用扩展卡尔曼滤波和扩展H_∞滤波算法进行了组合导航滤波研究。
第二,基于线性矩阵不等式,分析推导了离散时间约束方差混合滤波算法,证明了传统的混合滤波算法下确界的存在性,指出了其不便于工程实现的弱点,提出了迭代形式的混合滤波算法。
第三,针对集中参数滤波器的弱点以及联邦卡尔曼滤波算法的不足,提出了联合滤波算法,证明了其与联邦卡尔曼滤波的统一性,并进行了算法的对比研究。
第四,构建了GPS/DR组合导航的实验系统,进行了实际导航实验,对实验中采集的导航数据,采用文中研究的有关算法进行了离线滤波计算,实验结果验证了本文所提出的算法与卡尔曼滤波算法相比的优越性以及在实际导航中应用的可行性。
The requirements of precision and reliability for modern navigation systems become higher and higher. It demands that navigation systems can provide overall and precise information of navigation positioning and orientation, which shall not be restricted by climate, and have the properties of strong concealment and independence, and high anti-jamming performance. Up to now, there is no single navigation equipment that can meet these requirements. Alternatively, an appropriate combination of several navigation systems may solve this problem, which can compensate each to other and improve a system’s precision and stability. Such integrated navigation systems turn out to be a development trend in navigation and in navigation systems in multi-sensor data fusion as well.
Among algorithms in integrated navigation systems, Kalman filtering is the most successful method for the application of single sensor data fusion. However, Kalman filtering requires that the dynamic model of systems and statistical characteristics of state and measured noise must be exactly known. Kalman filtering is sensitive to system parameter and noise uncertainty, thus makes it difficult to converge. Developing along with robust control theory, robust filtering theory, especially H_∞filtering theory, primarily resolves the problem occurring in Kalman filtering in theory.
In this thesis, the robust filtering problem of integrated navigation systems in context of GPS/DR is studied. Aiming at existing problems of uncertainty of model and uncertainty of noise, we analyze applicability and precision of filtering algorithm, filtering algorithm, and federated H_∞H 2 /H_∞H_∞filtering algorithm. The main study as follow. Firstly, several mathematic models in GPS/DR integrated navigation system are derived. Priority algorithm of H_∞filtering based on matrix theory is improved. Stable filtering algorithm based on LMI is developed. Robust Kalman filtering algorithm and robust filtering algorithm are applied to GPS/DR integrated navigation system, this is an attempt to develop the application of model uncertainty algorithm in integrated navigation system. Extended Kalman filtering and extended H filtering are applied to integrated navigation system based on current statistical nonlinear model.
Secondly, mixed filtering algorithm under constraint of error covariance is derived. The results confirm the existence of infimum of traditional mixed filtering algorithm, and manifest its weakness inconvenient for engineering implement. Accordingly, we deduce new iterative mixed H 2 /H_∞filtering algorithm.
Thirdly, aiming at the filter weakness of centralized parameter system and federated Kalman filter, we specifically propose federated H_∞filtering algorithm, which can overcome the weakness of federated Kalman filtering algorithm. By comparing it with federated H_∞filtering algorithm, we prove that they are united.
Fourthly, experiment system of GPS/DR integrated navigation is built, practical experiments are done, and those algorithm in this paper are calculated off-line by practical data. The result of experiment proves that the algorithms in this paper are better than kalman filtering algorithm and applicable in practice.
在组合导航算法方面,对这些单传感器进行融合应用最成功的方法就是卡尔曼滤波,然而卡尔曼滤波器需要精确已知系统的动态模型和过程及测量噪声的统计特性,对系统参数和噪声的不确定性比较敏感,容易造成滤波发散。伴随着鲁棒控制理论发展起来的鲁棒滤波理论,尤其是H_∞滤波的理论,为卡尔曼滤波存在的问题在理论上提供了解决途径。
本文以GPS/DR组合导航系统为对象,研究了组合导航中的鲁棒滤波问题。针对不同的滤波模型以及噪声的不确定性,研究了H_∞滤波算法,混合滤波算法和联合滤波算法的适应性和滤波精度。研究工作主要包括以下几个部分:
第一,分析与推导了GPS/DR组合导航系统的几种滤波数学模型。基于矩阵理论,改进了滤波的参数选择算法。基于线性矩阵不等式,推导了稳态滤波算法。将鲁棒卡尔曼滤波和鲁棒滤波算法运用于GPS/DR组合导航系统,是模型参数不确定性算法应用于组合导航的一次尝试。根据当前“统计”模型的非线性,运用扩展卡尔曼滤波和扩展H_∞滤波算法进行了组合导航滤波研究。
第二,基于线性矩阵不等式,分析推导了离散时间约束方差混合滤波算法,证明了传统的混合滤波算法下确界的存在性,指出了其不便于工程实现的弱点,提出了迭代形式的混合滤波算法。
第三,针对集中参数滤波器的弱点以及联邦卡尔曼滤波算法的不足,提出了联合滤波算法,证明了其与联邦卡尔曼滤波的统一性,并进行了算法的对比研究。
第四,构建了GPS/DR组合导航的实验系统,进行了实际导航实验,对实验中采集的导航数据,采用文中研究的有关算法进行了离线滤波计算,实验结果验证了本文所提出的算法与卡尔曼滤波算法相比的优越性以及在实际导航中应用的可行性。
The requirements of precision and reliability for modern navigation systems become higher and higher. It demands that navigation systems can provide overall and precise information of navigation positioning and orientation, which shall not be restricted by climate, and have the properties of strong concealment and independence, and high anti-jamming performance. Up to now, there is no single navigation equipment that can meet these requirements. Alternatively, an appropriate combination of several navigation systems may solve this problem, which can compensate each to other and improve a system’s precision and stability. Such integrated navigation systems turn out to be a development trend in navigation and in navigation systems in multi-sensor data fusion as well.
Among algorithms in integrated navigation systems, Kalman filtering is the most successful method for the application of single sensor data fusion. However, Kalman filtering requires that the dynamic model of systems and statistical characteristics of state and measured noise must be exactly known. Kalman filtering is sensitive to system parameter and noise uncertainty, thus makes it difficult to converge. Developing along with robust control theory, robust filtering theory, especially H_∞filtering theory, primarily resolves the problem occurring in Kalman filtering in theory.
In this thesis, the robust filtering problem of integrated navigation systems in context of GPS/DR is studied. Aiming at existing problems of uncertainty of model and uncertainty of noise, we analyze applicability and precision of filtering algorithm, filtering algorithm, and federated H_∞H 2 /H_∞H_∞filtering algorithm. The main study as follow. Firstly, several mathematic models in GPS/DR integrated navigation system are derived. Priority algorithm of H_∞filtering based on matrix theory is improved. Stable filtering algorithm based on LMI is developed. Robust Kalman filtering algorithm and robust filtering algorithm are applied to GPS/DR integrated navigation system, this is an attempt to develop the application of model uncertainty algorithm in integrated navigation system. Extended Kalman filtering and extended H filtering are applied to integrated navigation system based on current statistical nonlinear model.
Secondly, mixed filtering algorithm under constraint of error covariance is derived. The results confirm the existence of infimum of traditional mixed filtering algorithm, and manifest its weakness inconvenient for engineering implement. Accordingly, we deduce new iterative mixed H 2 /H_∞filtering algorithm.
Thirdly, aiming at the filter weakness of centralized parameter system and federated Kalman filter, we specifically propose federated H_∞filtering algorithm, which can overcome the weakness of federated Kalman filtering algorithm. By comparing it with federated H_∞filtering algorithm, we prove that they are united.
Fourthly, experiment system of GPS/DR integrated navigation is built, practical experiments are done, and those algorithm in this paper are calculated off-line by practical data. The result of experiment proves that the algorithms in this paper are better than kalman filtering algorithm and applicable in practice.
引文
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