粒子滤波算法

粒子滤波算法逐渐成为科学领域的研究热点.文章首先阐述了粒子滤波算法的提出背景,根据m阶马尔科夫假设,分析算法基本原理并推导后验概率密度及权值更新公式.分析了基本粒子滤波算法中存在的问题以及解决方法.针对粒子滤波算法重要性采样密度的选择问题,综述了重要性采样密度选择方法.对重采样技术及样本匮乏问题进行了深入的分析,讨论了算法收敛性分析的最新进展.对自适应粒子滤波算法以及粒子滤波算法在各主要应用领域的进展进行了论述.最后对粒子滤波算法的研究前景提出了展望.     

一种新的粒子滤波算法在INS/GPS组合导航系统中的应用

为改善传统粒子滤波中的样本退化和样本枯竭问题, 提出一种新的粒子滤波算法. 在重要性采样中, 利用最新测量值, 结合差分滤波算法产生重要性函数; 在再采样中, 利用高斯混合模型近似状态的后验概率密度, 引入最大期望算法计算该高斯混合模型的参数, 并从该新分布中采样后验粒子集, 取代传统的再采样. 从而通过提高重要性函数对状态后验概率密度的逼近程度来缓解样本退化问题, 通过改进再采样实现过程来缓解样本枯竭问题. 把新算法应用到INS/GPS组合导航系统中, 仿真结果表明新算法的估计性能明显优于粒子滤波.     

求解单通道盲分离问题的一种新方法

近年来,单通道盲分离作为信号处理领域中的重要分支,受到了人们越来越多的关注。粒子滤波和进化算法都是利用一群粒子(个体)进行逼近估计的方法,同时各有各的优势。本文将粒子滤波与进化算法两种方法结合起来,既利用了粒子滤波估计的准确性,又利用了进化算法对收敛性进行保证,提出了一种解决单通道盲分离问题的新方法。文中针对两路同频BPSK混合信号,采用粒子滤波的架构,同时利用赌轮选择方法对粒子进行重要性采样,最后根据最大后验估计的方法对当前时刻的粒子对进行估计。     

基于硬件实现的粒子滤波重采样算法研究

粒子滤波算法用于硬件实现是目前一个新的研究方向,传统的粒子滤波算法计算量大,所需存储空间大,实时性差,所以在硬件实现方面面临着极大的挑战。为使算法更加适合于硬件实现,以粒子滤波中的重采样步骤为研究重点,以典型的序贯重要性重采样滤波算法为例,对典型的几种重采样算法的复杂度、所需存储空间及执行时间上进行分析研究,并在TI DSPTMS320C5402上对采样算法进行仿真,结果表明部分重采样算法(PDR)更适合于硬件实现。     

基于目标跟踪的粒子群粒子滤波算法研究

针对粒子滤波方法在重采样阶段容易造成样本有效性和多样性的损失,导致了样本贫化问题,提出了一种改进的粒子滤波算法.算法将粒子群优化思想引入粒子滤波中,在粒子采样过程前先利用粒子群算法进行优化.粒子群算法将最新观测值融合到粒子进化公式中,大部分粒子经过粒子群优化后,朝着后验概率分布比较密集的区域运动,聚集在最优粒子附近,使粒子的权值被提高,避免了在重新采样过程中被舍弃,进而缓解了样本被贫化问题.目标跟踪系统中的位置估计由于物体运动具有突然性,很难准确估计.采用非线性目标跟踪模型和分时恒定值模型分别研究改进粒子滤波算法对误差均方值的影响.仿真结果表明改进算法与常规粒子滤波算法和扩展卡曼滤波算法相比,更加有效地降低变量的误差均方值,从而提高了滤波性能.     

一种快速准蒙特卡罗粒子滤波算法

针对准蒙特卡罗(Quasi-Monte Carlo, QMC)方法应用于粒子滤波采样时计算复杂度高, 以及粒子滤波中重采样步骤引起样本枯竭的问题, 提出一种结合准蒙特卡罗方法的粒子滤波算法, 在重要性采样后, 将生成的随机化QMC序列分别映射到以大权重粒子为核心的独立子空间上, 避免了直接对采样空间进行预测, 同时又保持了样本多样性. 实验结果表明该方法可以有效抑制样本枯竭现象, 获得了高于蒙特卡罗(Monte Carlo, MC)方法的估计精度, 而计算效率与粒子滤波相近.     

粒子滤波进展与展望

粒子滤波器是基于序贯M onte Carlo仿真方法的非线性滤波算法,本文对粒子滤波器的研究现状和研究进展做了综述,详细论述了粒子滤波原理、收敛性、应用及进展.首先在Bayes框架内分析了序贯重要性采样原理,重要性分布函数的选择,以及重采样方法,总结了粒子滤波器发展过程中的各种改进策略和新变种,讨论了粒子滤波器在各个领域的应用及进展,最后介绍了粒子方法的新发展,新动态,并对未来发展方向做了进一步的展望.     

非高斯噪声中的粒子滤波算法研究

在非线性非高斯动态系统中,粒子滤波已成为解决系统参数估计和状态滤波的主流方法。然而,粒子退化是粒子滤波中不可避免的现象,粒子重采样是解决方法之一。本文针对粒子退化现象,在扩展卡尔曼滤波器的基础上研究了一种基于支持向量机粒子滤波算法,算法实现中扩展卡尔曼粒子滤波器结合支持向量机对当前时刻的重要性采样,再对粒子样本进行重采样。该算法能有效地利用量测值的最新信息,状态估计误差较小,同时避免了粒子匮乏。理论分析和仿真结果表明,新算法在双模噪声非线性系统估计的精度优于标准粒子滤波算法与扩展卡尔曼粒子滤波算法。     

基于MCMC的改进粒子滤波算法

针对传统粒子滤波算法建议分布函数的选取问题和粒子退化现象,提出一种基于马尔可夫蒙特卡洛思想的改进粒子滤波算法.使用基于比例对称采样方法选取Sigma点的无迹卡尔曼滤波,产生粒子滤波并建议分布函数;将似然分布自适应权值调整策略应用于权值选取步骤;采用系统重采样方法,加入了用来保持粒子多样性的马尔科夫链蒙特卡洛步骤.仿真结果表明,该算法的估计状态能够更好地吻合真实轨迹,在非线性、非高斯场合的估计性能较优.     

一种改进的粒子滤波算法及其在GPS/DR组合定位中的应用

针对粒子滤波的重要性密度函数选择问题,提出一种基于集合卡尔曼滤波(Ensemble Kalman Filter,EnKF)的改进粒子滤波算法。该方法利用集合卡尔曼滤波产生粒子滤波在每一时刻各粒子的重要性密度函数,在融合最新观测信息的同时,使重要性密度函数更加符合状态的真实后验概率分布。为消除样本枯竭现象,对重采样后的粒子进行马尔科夫链蒙特卡洛处理。在仿真实验中,将新算法用于GPS/DR组合定位系统,与粒子滤波、扩展卡尔曼粒子滤波以及无迹粒子滤波进行比较。仿真结果表明,该算法的估计精度高于传统粒子滤波算法,同时其能够有效控制计算量,并且在粒子数目较少时仍能保证较好的估计性能。     

On the optimal and suboptimal nonlinear filtering problem for discrete-time systems

This paper examines optimal and suboptimal algorithms for the state filtering problem in discrete-time nonlinear systems. The optimal equations of sequential filtering are analyzed and conditions are obtained which ensure a multimodal character for the a posteriori densities. This analysis is utilized in the discussion of the performance of suboptimal linearized filters, and suggestions are made for their improvement in critical situations.     

SAR图像MAP降噪的精细研究

本文推导出基于最大后验概率(MAP)滤波的一般形式,给出不同噪声分布和真实图像先验分布条件下的MAP滤波方程.从滤波方程在特定区间上解的分布情况以及区域统计特性分类两方面分析了MAP降噪性能,由此给出了MAP滤波的阈值表达形式.最后给出合成孔径雷达(SAR)图像的MAP降噪试验以及噪声滤除能力的量化指标.为了消除噪声强度对试验结果的影响,全面反映MAP降噪性能,本文给出了降噪能力随噪声大小的动态变化关系.结果表明,真实图像的先验分布对MAP滤波性能有着直接的影响,不合理的先验分布假定会严重降低MAP滤波的降噪能力.     

A differential geometric approach to nonlinear filtering: theprojection filter

This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is proposed which allows one to simplify the projection filter equation and to define an a posteriori measure of the local error of the projection filter approximation. Finally, simulation results are discussed for the cubic sensor problem     

Methods of Ellipsoidal Filtration in Nonlinear Stochastic Systems on Manifolds

The theory of analytical design of the modified ellipsoidal conditionally optimal filters was developed. The algorithms of modified ellipsoidal conditionally optimal filters are simpler than the suboptimal algorithms for the normalized a posteriori distributions. The results obtained were used in the problems of designing the vibroprotective equipment of the computer systems.     

On the choice of importance distributions for unconstrained and constrained state estimation using particle filter

Recursive state estimation of constrained nonlinear dynamical system has attracted the attention of many researchers in recent years. For nonlinear/non-Gaussian state estimation problems, particle filters have been widely used (Arulampalam et al. [1]). As pointed out by Daum [2], particle filters require a proposal distribution and the choice of proposal distribution is the key design issue. In this paper, a novel approach for generating the proposal distribution based on a constrained Extended Kalman filter (C-EKF), Constrained Unscented Kalman filter (C-UKF) and constrained Ensemble Kalman filter (C-EnkF) has been proposed. The efficacy of the proposed state estimation algorithms using a particle filter is illustrated via a successful implementation on a simulated gas-phase reactor, involving constraints on estimated state variables and another example problem, which involves constraints on the process noise (Rao et al. [10]). We also propose a state estimation scheme for estimating state variables in an autonomous hybrid system using particle filter with Unscented Kalman filter as a proposal and unconstrained Ensemble Kalman filter (EnKF) as a proposal. The efficacy of the proposed state estimation scheme for an autonomous hybrid system is demonstrated by conducting simulation studies on a three-tank hybrid system. The simulation studies underline the crucial role played by the choice of proposal distribution in formulation of particle filters.     

Recent Advances in Adaptive Sampling and Reconstruction for Monte Carlo Rendering

Monte Carlo integration is firmly established as the basis for most practical realistic image synthesis algorithms because of its flexibility and generality. However, the visual quality of rendered images often suffers from estimator variance, which appears as visually distracting noise. Adaptive sampling and reconstruction algorithms reduce variance by controlling the sampling density and aggregating samples in a reconstruction step, possibly over large image regions. In this paper we survey recent advances in this area. We distinguish between “a priori” methods that analyze the light transport equations and derive sampling rates and reconstruction filters from this analysis, and “a posteriori” methods that apply statistical techniques to sets of samples to drive the adaptive sampling and reconstruction process. They typically estimate the errors of several reconstruction filters, and select the best filter locally to minimize error. We discuss advantages and disadvantages of recent state‐of‐the‐art techniques, and provide visual and quantitative comparisons. Some of these techniques are proving useful in real‐world applications, and we aim to provide an overview for practitioners and researchers to assess these approaches. In addition, we discuss directions for potential further improvements.     

A posteriori error estimates for discontinuous Galerkin approximation of non-stationary convection-diffusion optimal control problems

In this paper, we investigate a discontinuous Galerkin finite element approximation of non-stationary convection dominated diffusion optimal control problems with control constraints. The state variable is approximated by piecewise linear polynomial space and the control variable is discretized by variational discretization concept. Backward Euler method is used for time discretization. With the help of elliptic reconstruction technique residual type a posteriori error estimates are derived for state variable and adjoint state variable, which can be used to guide the mesh refinement in the adaptive algorithm. Numerical experiment is presented, which indicates the good behaviour of the a posteriori error estimators.     

一种高斯过程的带参近似策略迭代算法

在大规模状态空间或者连续状态空间中,将函数近似与强化学习相结合是当前机器学习领域的一个研究热点;同时,在学习过程中如何平衡探索和利用的问题更是强化学习领域的一个研究难点.针对大规模状态空间或者连续状态空间、确定环境问题中的探索和利用的平衡问题,提出了一种基于高斯过程的近似策略迭代算法.该算法利用高斯过程对带参值函数进行建模,结合生成模型,根据贝叶斯推理,求解值函数的后验分布.在学习过程中,根据值函数的概率分布,求解动作的信息价值增益,结合值函数的期望值,选择相应的动作.在一定程度上,该算法可以解决探索和利用的平衡问题,加快算法收敛.将该算法用于经典的Mountain Car 问题,实验结果表明,该算法收敛速度较快,收敛精度较好.     

基于B样条曲线的GHPF轮廓跟踪算法

针对视觉跟踪中粒子滤波算法的建议性分布函数选择问题,提出一种目标轮廓跟踪的高斯厄米特粒子滤波算法(GHPF).该算法采用B样条曲线描述目标轮廓,建立目标运动模型.利用高斯厄米特滤波器产生建议性分布函数,通过实时融入最新的观测数据来逼近系统状态的后验概率,提高了滤波估计的精度.实验仿真结果验证了所提算法的有效性.