【作者】 陈磊琛；

【导师】 蔡之华；

【作者基本信息】 中国地质大学 ， 计算机应用技术， 2010， 硕士

【摘要】 本世纪90年代中期,基于有限样本的机器学习理论研究得到了长足的发展,形成了一套完善的理论体系——统计学习理论(Statistics Learning Theory,SLT)。支持向量机(Support Vector Machine, SVM)是以此理论中的结构风险最小化原则为基础建立起来的。SVM采用核函数,使算法复杂度与样本维数无关,将“维数灾难”问题得以解决,在处理非线性问题上优于其他机器学习算法,具有良好的泛化能力。支持向量回归(Support Vector Regression, SVR)是SVM算法的扩展,为解决回归问题而提出来的,而且在函数估计问题中具有良好的表现。卡尔曼滤波是实时递推算法,并且所有状态量都是在时域空间内,因此适用于多维随机过程的估计。在过程处理中,系统内各个状态量都无需存储,只需实时地处理估计状态信息,使估计量逐渐趋于实际状态量。卡尔曼滤波用状态方程体现实际状态量的实时动态规律,无需了解实际状态量和观测量在各个时刻的一、二阶方差矩阵,只需通过系统状态方程和观测噪声的统计特性表征实际状态量和噪声的统计特征。系统中状态噪声和观测噪声都是白噪声,是平稳过程,统计特性不随时间改变,系统的状态方程又是已知的,所以卡尔曼滤波能估计平稳和非平稳状态变量。GPS和INS系统都具有全球、全方位、全时间的导航特点,并且都能输出十分完整的导航数据。GPS/INS组合导航系统发挥各自优势,弥补对方缺点,使组合后的导航精度高于两个系统独自工作的精度。对于INS方面,组合导航系统可以校准惯性传感器,提高INS的精度；而对于GPS而言,由于INS系统的辅助,提高了其定位跟踪的能力,并能防止接收机受到干扰。我国组合导航系统的研究起步于上个世纪70年代末,经过二十多年的努力,现在发展很快,已广泛应用于各个领域,并正在赶超世界先进水平。本文在前三章介绍了支持向量机、卡尔曼滤波和GPS/INS组合导航系统的基础知识,在第四章中提出了一种新型重采样支持向量机算法,从GA和SMOTE思想得到启发,采用类似差分演化交叉变异算子对少数类数据进行过采样,产生新的正类样本,使类之间数据量基本相等。然后根据支持向量机算法的特点,提出一种使用聚类的数据清理方法,删去冗余或者噪声样本。这样,通过对数据集的过采样和清理,一些有用的样本被保留下来,可以减小数据集规模,增强SVM训练的执行效率。第五章提出了一种在线实时优化算法——支持向量回归自适应卡尔曼滤波算法。根据实时获取的观测信息,使用支持向量回归在线调整观测协方差矩阵信息,动态地调整噪声信息能够使之接近实际噪声量,从而提高滤波估计精度。具体方法是假设噪声为零均值高斯白噪声,本章利用理论新息方差阵与实际方差阵比值应该在1附近的原理,如果比值偏离1,则显示观测噪声发生变化,需要对噪声协方差矩阵进行调整,使之重新回到比值为1附近。本文的主要创新之处在于：(1)提出了一种新型重采样支持向量机算法应用于不平衡数据问题中,并采用对比实验和UCI标准数据集实验,通过与标准支持向量机、SMOTE过采样支持向量机、遗传算法过采样支持向量机算法的比较,验证该算法的性能；(2)提出了支持向量回归自适应卡尔曼滤波算法应用于车载GPS/INS组合导航系统中,并与扩展卡尔曼滤波和模糊自适应卡尔曼滤波比较,验证该算法的性能。更多还原

【Abstract】 In the 1960s of the last century, SVM arose from statistical learning theory, the aim being to solve only the problem of interest without solving a more difficult problem as an intermediate step. SVM are based on the structural risk minimization principle, closely related to regularization theory. This principle incorporates capacity control to prevent over-fitting and thus is a partial solution to the bias-variance trade-off dilemma. SVM were first suggested by Vapnik for classification and have recently become an area of intense research owing to developments in the techniques and theory coupled with extensions to regression and density estimation, and had good performance.The kalman filter is a real-time recursion algorithm and all the system states are in the time domain space, therefore, it is appropriate for estimating multi-dimensional stochastic process. Moreover, there is no need to save each system state in memory and we deal with the estimates online, making them trend to real states regularly. In addition, the kalman filter uses the statistical property of the system noise and the observation noise to process the signal and the kalman filter applies the system observation as the input of the filter and the estimation (system state or parameter) as the output. Not only it may carry on the process to the steady uni-dimensional stochastic process, but also it can estimate the non-steady multi-dimensional stochastic process, therefore its application is very widespread.The combination of GPS and inertial navigation system (INS) is the best integrated navigation, and both INS and GPS are global, all-round and full-time navigation equipments. They can provide very completed navigation data, and supplement the shortcomings of each other, which can supply higher accuracy than each works alone. As for INS, integrated navigation corrects the inertial sensors for improving the accuracy, and with the help of INS, GPS enhances the ability of positioning and tracking, which protects the GPS receiver from interference.In the first three chapters, we present the basic principal of SVM, kalman filter and GPS/INS integrated navigation. In the chapter four, we propose a novel resampling SVM algorithm, which is inspired by GA and SMOTE. This method is based on using the mutation and crossover operators of DE to over-sample the minority class to lessen the imbalance ratio and then clustering for both classes to delete redundant or noisy samples. Thus, by combining over-sampling and data cleaning technique, the useful samples are remained, improving the computational efficiency.In chapter five, we present an online optimized method named support vector regression self-adaption kalman filter algorithm (SVREKF). This method uses SVR for adjusting the observation covariance matrix online according to the current system observations. Moreover, using the adjustment factor to update the noisy system dynamically in order to make trend to actual noise and improve the accuracy of estimation. Providing system noise is the zero-mean Gaussian white noise, we recognize that the ratio of the theoretical residual covariance matrix and the actual residual covariance matrix is 1. If the ratio is far away from 1, then it illustrates the observation noise changes, which should adjust the noisy covariance matrix so that the ratio returns to 1.The innovation of this thesis can be grouped into two points. (ⅰ) Propose a novel resampling SVM algorithm application in imbalanced datasets problems, and then make experiments on UCI standard datasets. The results show that our method is an efficient way to solve imbalanced datasets problems, compared with standard SVM, SMOTE-SVM and DE-SVM under the criterion of F-measure and ROC Area (AUC). (ⅱ) Present a support vector regression self-adaption kalman filter application in vehicle-mounted GPS/INS integrated navigation, and make comparison with extend kalman filter and fuzzy self-adaption kalman filter for verifying the performance of this algorithm.更多还原