非线性卡尔曼滤波算法的改进及精度分析

发布时间：2018-05-28 23:03

本文选题：卡尔曼滤波 + 混合阶　；参考：《西南大学》2017年硕士论文

【摘要】：目标跟踪在现代科技生活中的应用日益普遍,从国家军事方面的航空登月轨道预测追踪到现实生活中的车辆轨迹追踪。从定义上看,目标追踪可简单理解为对目标运动轨迹的估计问题。如何解决这些问题,实时、准确地对目标进行跟踪是技术上的难点。多年来,人类对于目标跟踪的方法理论和实践的研究从未止步。作为目标跟踪的一个重要实现方法,贝叶斯滤波算法的研究是个热点也是难点。其中,以卡尔曼滤波算法最为典型,在实现过程中,该滤波算法需要将未知参数当作随机变量来处理,进而使用先验概率和当前观测到的数据信息来计算后验概率,协调了先验信息和当前数据信息的应用。此外,在线性系统下,卡尔曼滤波算法可以在最小均方误差条件下,通过先验概率与后验概率的递归运算给出信号的最优估计,是一种应用相当广泛的滤波算法。但是在实际中,我们所遇到的系统大都是非线性的,这种常规的线性卡尔曼滤波算法只能局限于线性系统模型的应用中。非线性滤波算法也因此得到了更多的关注并逐渐被人们提出。近年来,被广泛应用的非线性滤波算法主要有无迹卡尔曼滤波算法、容积卡尔曼滤波算法以及球面单纯形容积卡尔曼滤波算法等等。这类滤波算法大都是在高斯假设的前提下,结合贝叶斯滤波理论,通过对概率密度函数进行近似处理,再利用数值积分理论进行近似计算,从而得到一系列采样点以及相应的权重。考虑到这些复杂多变的噪声以及其他一些不确定性因素,人们需要去寻找鲁棒性能好且能适应复杂非线性环境的非线性卡尔曼滤波算法来改善估计性能。此外,科技的日益进步对算法提出的要求也越来越高,这就意味着对滤波器的研究不能仅限于新型算法的设计,而必须意识到算法性能在其应用上的重要性,而衡量不同滤波器性能好坏的一个重要指标就是状态的估计精度。据此,本文在对已有的研究进行了解之后,主要围绕如下几个方面进行了研究工作:(1)对采样准则的改进。这种改进主要针对容积准则,传统的容积卡尔曼滤波算法是基于相同阶数的球面-径向容积准则推导而来的,而本文则是将混合阶的思想应用在球面-径向容积准则上,提出了一种新型的基于混合阶的容积卡尔曼滤波器,并通过MATLAB仿真对所提算法与传统算法在时间复杂度和精度上进行了综合比较,验证了该算法在工程实践中的应用价值。(2)研究了增广算法在复杂环境应用中表现的鲁棒性。本文将一类基于确定性采样的增广非线性卡尔曼滤波算法应用于目标跟踪模型中,通过设置状态的突变干扰和时变干扰来验证该增广非线性卡尔曼滤波算法在复杂环境中能表现出较好的鲁棒性能,证明了其在目标实时跟踪中的实用性和有效性。(3)对混合阶算法进行了精度分析。在传统的球面单纯形-径向容积卡尔曼滤波算法的基础上,同样将混合阶的思想应用在球面单纯形-径向容积准则中,并利用基于泰勒展开式的精度分析方法对所提的混合阶球面单纯形-径向容积卡尔曼滤波算法进行了均值和协方差的分析,仿真分析验证了该算法能够有效地提高滤波精度。
[Abstract]:The application of target tracking is becoming more and more common in modern scientific and technological life. The tracking of vehicle trajectory in real life is traced from the orbit of the air landing orbit of the national military. In terms of definition, the target tracking can be simply understood as the estimation of the trajectory of the target. How to solve these problems in real time and accurately track the target It is a technical difficulty. For many years, the research on the theory and practice of target tracking has never stopped. As an important realization method of target tracking, the research of Bias filtering algorithm is a hot and difficult point. Among them, the Calman filtering algorithm is the most typical. In the process of implementation, the filtering algorithm needs to be unknown parameter. The number is treated as a random variable, and then the posterior probability is calculated using the prior probability and the data information observed at present, and the application of the prior information and the current data information is coordinated. In addition, under the linear system, the Calman filtering algorithm can be given by the recursive operation of the prior probability and the posterior probability under the minimum mean square error condition. The optimal estimation of the output signal is a fairly wide range of filtering algorithms. However, in practice, most of the systems we have encountered are nonlinear. This conventional linear Calman filtering algorithm can only be limited to the application of linear system model. The nonlinear filtering algorithm has also received more attention and is gradually proposed by people. In recent years, the widely used nonlinear filtering algorithms mainly include the Untraced Calman filter algorithm, the volume Calman filter algorithm and the spherical simplex volume Calman filter algorithm and so on. Most of these filtering algorithms are based on the hypothesis of Gauss and approximated the probability density function by combining the Bayesian filtering theory. A series of sampling points and corresponding weights are obtained by using the numerical integration theory to obtain a series of sampling points and corresponding weights. Considering these complex and changeable noises and other uncertain factors, people need to find the nonlinear Calman filtering algorithm with good robust performance and can adapt to the complex nonlinear environment to improve the estimation performance. In addition, the increasing progress of science and technology is becoming more and more demanding for the algorithm, which means that the research of the filter can not be limited to the design of the new algorithm, but must realize the importance of the performance of the algorithm in its application, and the estimation accuracy of the state is an important index to measure the performance of the different filters. After understanding the existing research, we mainly focus on the following aspects: (1) improving the sampling criteria. This improvement is mainly aimed at the volume criterion. The traditional volume Calman filtering algorithm is derived from the spherical radial volume criterion of the same order, and this paper applies the thought of the mixed order. A new type of volume Calman filter based on mixed order is proposed on the spherical radial volume criterion. The time complexity and accuracy of the proposed algorithm are compared with the traditional algorithm by MATLAB simulation. The application value of the algorithm in engineering practice is verified. (2) the application of augmented algorithm in complex environment is studied. In this paper, an augmented nonlinear Calman filtering algorithm based on deterministic sampling is applied to the target tracking model. By setting the state mutation interference and time-varying interference, it is proved that the augmented nonlinear Calman filter algorithm can show good robust performance in the complex environment, and it is proved that it is in the target. The practicability and effectiveness of the real-time tracking. (3) the precision analysis of the mixed order algorithm is carried out. On the basis of the traditional spherical simplex radial volume Calman filtering algorithm, the idea of mixed order is also applied to the spherical simplex radial volume criterion, and the precision analysis method based on the Taylor expansion formula is used for the mixture. The mean and covariance are analyzed by the uniform spherical simplex radial volume Calman filter algorithm. The simulation results show that the algorithm can improve the filtering accuracy effectively.
【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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