摘 要

针对传统的Kalman滤波器在非线性非高斯环境下对运动目标的跟踪效果较差这一问题，本文提出了一种基于粒子滤波的目标跟踪方法。粒子滤波是采用一些带有权值的随机样本(粒子)来表示所需要的后验概率密度，而不是采用传统的线性变换，从而得到基于物理模型的近似最优数值解，具有精度高、收敛速度快等特点。基于粒子滤波的目标跟踪原理是通过这些粒子的加权来估计目标运动的状态。目标模型的仿真实验表明，在非线性非高斯环境下，粒子滤波的跟踪效果优于扩展卡尔曼滤波器。最后，将粒子滤波运用于视频跟踪，实验结果进一步说明：在非线性非高斯环境下，粒子滤波具有较好的跟踪效果。粒子滤波技术可以广泛于空对空、空对地等各种具有非线性、非高斯特征的被动式跟踪系统中。

关键字：粒子滤波器 卡尔曼滤波器 目标跟踪 重采样

Abstract

Because in non-linear non-Gaussian environment the performance of traditional Kalman Filter in tracking of moving targets is very poor, the paper uses particle filter to track the moving target. Particle filter does not involve linearization around current estimates but rather represent the desired distributions by discrete random measures, which are composed of weighted particles. It has a high accuracy and a rapid convergence. The theory of target tracking based on particle filter is to use these weighted particles to estimate the states of targets. The simulation results of the target model show that in the non-linear non-Gaussian environment, the performance of the particle filter is better than extended Kalman Filter. Finally, we use the particle filter in video tracking, the experimental results further show that in the non-linear non-Gaussian environment the particle filter has a better tracking performance. Particle filter technology can be widely used for air to air, air-ground and other passive tracking systems of non-linear non-Gaussian characteristics.

Key words: particle filter kalman filter tracking resampling

目 录

第1章 绪论 ....................................................................................................................... 1

1.1 研究背景 ............................................................................................................... 1 1.2 目标跟踪方法的发展状况 ................................................................................... 1 1.3 滤波理论的发展状况 ........................................................................................... 2 1.4 本文的主要工作 ................................................................................................... 5 第2章 卡尔曼滤波理论 ................................................................................................... 6

2.1 卡尔曼滤波器 ....................................................................................................... 6 2.2 扩展卡尔曼滤波器 ............................................................................................... 7

2.2.1 被估计的过程信号 ..................................................................................... 7 2.2.2 滤波器的计算原型 ..................................................................................... 8

第3章 粒子滤波器 ......................................................................................................... 10

3.1 蒙特卡罗方法 ..................................................................................................... 10 3.2 粒子滤波算法 ..................................................................................................... 10

3.2.1 粒子滤波器基本原理 ............................................................................... 10 3.2.2 序贯粒子滤波算法 ................................................................................... 11 3.2.3 退化现象 ................................................................................................... 13 3.2.4 再采样原理 ............................................................................................... 14

第4章 基于粒子滤波的视频跟踪 ................................................................................. 16

4.1 卡尔曼滤波器和粒子滤波器性能对比 ............................................................. 16

4.1.1 实验描述 ................................................................................................... 16 4.1.2 实验结果及分析 ....................................................................................... 16 4.2 粒子数和噪声协方差对粒子滤波跟踪的影响 ................................................. 18

4.2.1 实验描述 ................................................................................................... 18 4.2.2 实验结果及分析 ....................................................................................... 18 4.2.3 实验结论 ................................................................................................... 22 4.3 基于粒子滤波的视频跟踪 ................................................................................. 22

4.3.1 基于颜色特征的粒子滤波跟踪算法 ....................................................... 22 4.3.2 初始背景的获取 ....................................................................................... 23 4.3.3 目标颜色直方图的提取 ........................................................................... 28