非线性卡尔曼滤波器改进与应用

发布时间：2018-03-12 18:55

本文选题：容积卡尔曼滤波器　切入点：单纯型　出处：《西南大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文基于非线性系统,提出了新的非线性卡尔曼滤波器。R.E.Kalman在1960年,提出了著名的卡尔曼滤波器算法,它是一种以最小二乘法为基础的递推最优估计算法,能够处理多维度且非平稳的随机信号。这种算法有着结构简单易于实现的优点,因此在工程界大受欢迎,很快得到广泛应用。但是它有一定的应用局限,即只适合于线性系统,然而大多数实际物理系统是非线性的,因此,针对卡尔曼滤波器的这一局限,科学家提出了一种能够应用于非线性系统的卡尔曼滤波器,即扩展卡尔曼滤波器(extended Kalman filter,EKF)。EKF是将非线性系统线性化,存在着精度不高,易于发散的问题,并且只适用于那些时域更新时近乎是线性的系统。而后提出的无先导卡尔曼滤波器(unscented Kalman filter,UKF)算法结合了无先导变换(unscented transformation,UT)和卡尔曼滤波器(Kalman Filter,KF)算法的思想。UKF和EKF的计算复杂度相当,但是相比较之下,UKF的精度更高,省略了计算系统的雅克比(Jacobi)矩阵和汉森(Hession)矩阵的步骤,不要求系统的非线性程度,其适用范围更广。近年来,非线性卡尔曼滤波器主要朝着高效地近似高斯概率密度函数的方向发展,由此设计出数值精度更高、性能更好的非线性卡尔曼滤波器。文中的新的非线性卡尔曼滤波器设计方法主要有三种,其中之一就是源于这一思想。非线性卡尔曼滤波器算法可以由贝叶斯滤波理论统一描述,基于其设计的关键是计算高斯概率密度函数加权的多维非线性函数的积分。数值积分方法中,最具代表性的方法是一类容积准则,便提出了容积卡尔曼滤波器(cubature Kalman filter,CKF)。然而容积卡尔曼滤波器也存在着一些缺点,其精度只能达到三阶。由此,本文提出新型设计的非线性卡尔曼滤波器。新的非线性卡尔曼滤波器设计方法之二是利用Huber M估计算法实现状态的量测更新,其提出思想,基于采用统计线性回归模型近似非线性量测模型,结合基于高阶球面-径向容积准则的状态预测模块,构成基于Huber的高阶容积卡尔曼滤波器,应用于跟踪模型构成跟踪算法。能够有效改善其滤波精度和鲁棒性。方法之三是在方法二的基础上,将q微分引入到Huber方法中,以UKF为例,构成基于q微分的Huber无先导卡尔曼滤波器。本文在深入理解的基础上,并设计出新的滤波器。首先,从卡尔曼滤波理论的基本原理入手,以常用的估计准则为起点,介绍了最小二乘估计、线性最小方差估计等估计准则、贝叶斯滤波理论,以及新的改进方法。其次,用Matlab对新算法进行仿真验证,实现了新的非线性卡尔曼滤波器设计。最后,进行了总结归纳,并对下一步需要做的工作进行了展望。
[Abstract]:In this paper, a new nonlinear Kalman filter .R.E. Kalman is proposed based on nonlinear systems. In 1960, a famous Kalman filter algorithm is proposed, which is a recursive optimal estimation algorithm based on the least square method. This algorithm has the advantage of simple structure and easy to implement, so it has been widely used in engineering field. However, it has some limitations, that is, it is only suitable for linear systems. However, most practical physical systems are nonlinear. Therefore, in view of this limitation of Kalman filter, a kind of Kalman filter which can be applied to nonlinear system is proposed. That is, extended Kalman filter is linearized by extended Kalman filter. EKF has the problem of low precision and easy divergence. The unscented Kalman filter and the unscented Kalman filter (UKF) algorithm, which combines the unscented transformation (UTT) algorithm and the Kalman filter KF (Kalman filter filter KF) algorithm, have the same computational complexity as the EKF algorithm, which is only applicable to those systems where the time domain update is almost linear, and the proposed unscented Kalman filter algorithm combines the unscented transformation with the unscented transform UTU (unscented transform UTU) and the Kalman filter filter KF (KF). But by comparison, the UKF has higher precision, omitting the steps of Jacobi matrix and Hansen Hessionation matrix of the computing system, which does not require the degree of nonlinearity of the system, and its application scope is wider in recent years. The nonlinear Kalman filter mainly develops towards the direction of efficiently approximating Gao Si's probability density function, so the numerical accuracy is higher. Nonlinear Kalman filter with better performance. There are three main methods for designing nonlinear Kalman filter in this paper. The nonlinear Kalman filter algorithm can be described by Bayesian filtering theory. The key of its design is to calculate the integral of the multi-dimensional nonlinear function weighted by Gao Si's probability density function. In the numerical integration method, the most representative method is a kind of volumetric criterion. The volume Kalman filter (cubature Kalman filter) is proposed. However, the volume Kalman filter has some disadvantages, and its precision can only reach the third order. In this paper, a new nonlinear Kalman filter is proposed. The second method is to use Huber M estimation algorithm to realize the state update. Based on the approximate nonlinear measurement model based on statistical linear regression model and the state prediction module based on higher-order spherical and radial volumetric criteria, a high-order volumetric Kalman filter based on Huber is constructed. It can improve the filtering accuracy and robustness effectively. The third method is to introduce Q differential into the Huber method based on the second method and take UKF as an example. In this paper, a new filter is designed on the basis of deep understanding. Firstly, starting with the basic principle of Kalman filter theory, the paper starts with the common estimation criterion. The least square estimation, linear minimum variance estimation, Bayesian filtering theory and new improved method are introduced. Secondly, the new algorithm is simulated by Matlab, and a new nonlinear Kalman filter is designed. Summarized and summarized, and the need to do the next work is prospected.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN713

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