【作者】 李甫；

【导师】 石光明；

【作者基本信息】 西安电子科技大学 ， 电路与系统， 2010， 博士

【摘要】 统计信号处理中的非线性滤波问题广泛存在于目标跟踪、红外弱小目标检测、导航、故障检测、金融等相关领域。粒子滤波作为解决非线性、非高斯动态系统滤波问题的一种有效方法,在军事和民用领域已经展现出有效而广阔的理论和应用前景,备受国内外学者的关注。本论文围绕粒子滤波中最为关键的重要性函数采样粒子问题,从算法上展开深入研究,通过补偿、优化的方法来获取新的重要性函数;引入无参估计的方法移动粒子寻找后验概率密度模型,提高了粒子滤波性能和效率。另外,为了解决实际应用中粒子滤波计算量大的问题,设计了粒子滤波电路及其并行运算的电路结构,节省了资源消耗,提高了运算效率。具体的工作概括如下:1.提出了补偿扩展卡尔曼粒子滤波算法。该方法在分析了扩展Kalman滤波器线性化误差的基础上,通过引进调节因子来补偿因线性化引起的误差,据此获取粒子滤波中的重要性概率密度函数,同时该概率密度函数参考了最新的观测量,因此由提议分布产生的粒子更能反映系统状态的后验概率分布。该算法的滤波性能优于标准粒子滤波和Kalman粒子滤波;与Unscented粒子滤波相比,算法降低了计算复杂度。2.提出了基于优化的粒子滤波算法。该算法解决了补偿扩展卡尔曼粒子滤波算法中补偿因子选择比较困难且不够灵活的问题。采用最速下降法对目标代价函数进行无约束优化,获得最优的调节因子;通过迭代逼近,搜索使得代价函数取得最小值的点,以此为参数获取重要性概率密度函数并从中采样高质量的粒子。从该重要性函数中采样得到的粒子更能反映系统状态的后验概率分布,且融入了最新的观测数据。该算法提高了粒子滤波的估计精度和采样效率。3.提出了变窗宽核粒子滤波算法。非线性系统很难得到后验概率的解析表达式,而传统的粒子滤波及改进方法在对后验概率密度分布先验知之甚少的情况下一味的依靠重要性概率密度函数来采样粒子,是具有一定的盲目性。针对此问题,该算法引入核密度估计,将其与粒子滤波相结合,通过优化渐进均方积分误差来获取全局固定核窗宽,然后采用基于粒子的窗宽选择机制,使得从重要性函数中采样后的粒子能够通过变窗宽的核密度估计后朝着后验概率密度的分布移动,新的粒子集更能反映后验概率密度的分布。该方法实质是通过核密度估计来寻找后验概率密度“模型”,因而其在滤波性能和效率上都优于标准的粒子滤波和核粒子滤波。4.提出了基于协方差的变窗宽核粒子滤波。该方法针对所提出的变窗宽核粒子滤波算法复杂度较高的问题,采用粒子集的协方差矩阵估计粒子的粗略核窗宽和其粗略的后验概率密度,通过调节全局核窗宽获得适用于每一个粒子自身的精确核窗宽;迭代达到对后验概率模型的寻找,使得粒子能够在核密度估计后向后验概率密度的分布移动。通过该方法降低了计算复杂度。5.研究了标准粒子滤波算法在纯方位跟踪系统中的电路设计方法。设计了基于冗余存储的高效重采样策略,通过增加冗余存储来解决重采样原位替换所引起的粒子覆盖问题,降低了粒子滤波硬件资源Block RAM的消耗,提高了资源的利用率。设计了冗余存储的并行粒子滤波结构,合理安排了冗余存储的并行化策略,解决了并行粒子滤波中出现的粒子质量不平衡现象,实现了并行处理中各个处理单元之间高质量的粒子交换,节省了资源消耗,减少了算法的运行时间,提高了并行运算的效率。更多还原

【Abstract】 Nonlinear filtering widely exists in the statistical signal processing areas, such as target tracking, infrared dim target detection, navigation, fault detection and finance. As an effective method for Nonlinear/NonGaussian dynamic system, particle filter has shown its application prospect in both military and civil area.This dissertation is an exploration on the critical issue of particle filter about the importance function to sample particles. The new importance sampling methods are proposed to improve the performance of particle filter by compensation and optimization strategy. Nonparametric estimation is also introduced to approximate the posterior by moving particles to seek the posterior model. Otherwise, in order to reduce the computationally intensive in implementation, we also design the circuit of particle filter and its parallel structure. These can reduce the resource utilization and enhance the computation efficiency. The summary of the thesis are as follows:1. A compensated extended Kalman particle filter is proposed. The linearization error of the extended Kalman filter is analyzed firstly. Then a compensation method with adjustable factor is introduced to minimize the linearization error and to improve the generated proposal distribution in particle filtering. Meanwhile, the new proposal distribution integrates the latest observation. Particles sampled from this distribution are closer to the true distribution. The new method performed better than the standard particle filter (PF) and the Kalman particle filter. At the same time, the complexity of the proposed algorithm is lower than the unscented particle filter.2. An optimization-based particle filter is proposed. It is difficult to choose an appropriate adjustable factor in the compensated extended Kalman particle filter. The new algorithm provided an optimization-based method (the steepest descent method) to generate the parameters of the importance function iteratively. High quality particles are sampled form the proposal distribution with the integration of the latest observation. The estimation precision and the sampling efficiency are improved by the method.3. A variable bandwidth kernel particle filter is proposed (VBKPF). It is difficult to find an analytical expression of the posterior. However, the traditional particle filter samples from an importance density function with an unknown prior. The kernel density estimation (KDE) is invoked in the new algorithm with the framework of the particle filter. We adopt the plug-in method to get the global fixed bandwidth by optimizing the asymptotic mean integrated squared error firstly. Then, particle-driven bandwidth selection is introduced in the KDE. To get a more effective allocation of the particles, we use the variable bandwidth KDE to approximate the posterior probability density functions (PDFs) by moving particles toward the posterior. This gives a closed-form expression of the true distribution. The proposed VBKPF performs better than the standard particle filter and the kernel particle filter both in efficiency and estimation precision.4. A covariance based variable bandwidth kernel particle filter is proposed to reduce the complexity of the VBKPF. Firstly, covariance matrix of the particle sets is used to compute the coarse bandwidth and the posterior probability density functions. Then, each particle can acquire its own accurate bandwidth by adjusting the global kernel bandwidth to improve the precision of the KDE estimation. To improve the estimation precision, the iteration strategy is used to seek the posterior model by moving particles toward the posterior.5. The circuit of the standard particle filter in bearing-only tracking system is designed. We present an efficient resampling architecture by redundant storage strategy to deal with the particle coverage problem. The Block RAM resource is reduced greatly with this scheme. By using the redundant storage strategy appropriately, we also design the parallel structure of the particle filter. High quality particles are exchanged between the redundant storage RAMs to eliminate the imbalance phenomenon. The new parallel structure can reduce the resource utilization and the executive time. It also can improve the operation efficiency of the algorithm.更多还原