论文总字数：14766字

摘 要

Abstract II

第一章 绪论 1

1.1选题背景与意义 1

1.2目标跟踪的发展与研究现状 1

1.3本文所研究的工作及结构安排 1

第二章 机动目标运动模型 3

2.1 CV模型 3

2.2 CA模型 4

2.3 CT模型 4

2.4 Singer模型 4

2.5 “当前”模型 5

2.6本章小结 5

第三章 卡尔曼滤波算法及非线性系统滤波算法 6

3.1概述 6

3.2卡尔曼滤波算法 6

3.2.1卡尔曼滤波仿真实验 7

3.3非线性滤波算法 10

3.3.1扩展卡尔曼滤波（EKF） 10

3.4无迹卡尔曼滤波（UKF） 11

3.4.1 UT变换 11

3.4.2 UT近似误差分析 12

3.4.2 无迹卡尔曼滤波算法 13

3.5滤波发散及解决方法 14

3.6本章小结 15

第四章 基于UKF滤波算法的单机动目标跟踪 16

4.1 运动模型的推导 16

4.2 机动目标跟踪中的UKF滤波算法 16

4.3 UKF滤波的仿真实验 16

4.4 本章总结 21

第五章 总结与展望 22

5.1总结 22

5.2 展望 22

致谢 23

参考文献 24

无迹卡尔曼滤波在目标跟踪中的应用

摘要

本文针对机动目标模型的建立作了重点研究，深入研究和讨论非线性系统的滤波问题。并以相关理论为基础，进行仿真实验。

在对机动目标进行跟踪之前，首先要对被跟踪目标建立数学模型。本文介绍和分析了多种常用的机动目标运动模型，其中重点介绍了“当前”统计模型。以“当前”统计模型理论为基础来研究机动目标的运动，并建立对应的数学模型。

在对机动目标建立运动模型之后，对模型中的状态向量进行预测和估计需要运用滤波算法。首先，本文引入了卡尔曼滤波的概念，卡尔曼滤波是在线性系统中最常用也是最基础的滤波算法。其次，由于卡尔曼滤波只应用于线性系统，进而介绍了传统的非线性系统算法。在非线性系统滤波中最为常见的要数扩展卡尔曼滤波算法(EKF)。由于扩展卡尔曼滤波在滤波过程中的第一步就是对非线性系统的模型进行线性化处理，这就不可避免的引入了线性误差，另外，扩展卡尔曼滤波只在满足局部线性的条件下能发挥良好的效果，进而介绍了无迹卡尔曼滤波（UKF）。相比扩展卡尔曼滤波的各项不足，无迹卡尔曼滤波具有实现简单，性能稳定，通用性强的特点，它是一种专门针对非线性系统的滤波算法。对比前两者，无迹卡尔曼滤波的进度无疑是较高的，为了保证本次试验结果的准确性，所以重点研究无迹卡尔曼滤波在目标跟踪中的应用。

关键字：机动目标；非线性运动模型；卡尔曼滤波；扩展卡尔曼滤波；无迹卡尔曼滤波

Abstract

In this paper, we focus on the establishment of maneuvering target model, and deeply research and discuss the filtering of nonlinear system, and based on the relevant theory, simulation experiments are carried out.

Before for maneuvering target tracking, the first to the tracked target is to establish the mathematical model. This paper introduces and analyzes several commonly used maneuvering target motion model, which focuses on the "current" statistical model. In the "current" statistical model theory based on maneuvering target motion, and establish corresponding mathematical model.

After the motion model is established, the state vector of the model is predicted and estimated using the filtering algorithm.First of all, this paper introduces the concept of Kalman filter, Kalman filter is in linear systems, the most commonly used is the most basic filtering algorithm. Secondly, due to the Kalman filter applies only to linear system. Then it introduces the traditional algorithms of nonlinear system.In non-linear system filtering is the most common to the extended Kalman filter algorithm (EKF). Due to the extended Kalman filter in the filter process is the first step of the nonlinear system model linearization, which inevitably introduced linear error. In addition, the extended Kalman filter can play a good effect only in the condition of satisfying local linearity, and then the non trace Kalman filter (UKF) is introduced.Compared to the extended Kalman filter to the problem, unscented Kalman filter is simple to implement, stable performance, versatility, it is a specialized filter algorithm for nonlinear system. Compared to the former two, no trace of the progress of Kalman filtering is higher, in order to ensure the accuracy of the results of this test, so focus on the application of non trace Kalman filter in target tracking.

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