Gaussian Sum PHD Filtering Algorithm for Nonlinear Non-Gaussian Models

A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.

The retrieval of the nonlinear random waves from the non-Gaussian characteristics of the sea surface elevation distribution

In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.

Effect of Multipoint Heterogeneity on Nonlinear Transformations for Geological Modeling: Porosity-Permeability Relations Revisited

An analysis of statistical expected values for transformations is performed in this study to quantify the effect of heterogeneity on spatial geological modeling and evaluations. Algebraic transformations are frequently applied to data from logging to allow for the modeling of geological properties. Transformations may be powers, products, and exponential operations which are commonly used in well-known relations （e.g., porosity-permeability transforms）. The results of this study show that correct computations must account for residual transformation terms which arise due to lack of independence among heterogeneous geological properties. In the case of an exponential porosity-permeability transform, the values may be positive. This proves that a simple exponential model back-transformed from linear regression underestimates permeability. In the case of transformations involving two or more properties, residual terms may represent the contribution of heterogeneous components which occur when properties vary together, regardless of a pair-wise linear independence. A consequence of power- and product-transform models is that regression equations within those transformations need corrections via residual cumulants. A generalization of this result is that transformations of multivariate spatial attributes require multiple-point random variable relations. This analysis provides practical solutions leading to a methodology for nonlinear modeling using correct back transformations in geology.

State Estimation for Sound Environment System with Nonlinear Observation Characteristics by Introducing Wide-Sense Particle Filter

In this study, a modified particle filter considering non-Gaussian properties of noises is proposed in a form applicable to real situation in sound environment system where the observation data are contaminated by the external noise (i.e., background noise) of arbitrary probability distribution and measured in decibel scale. More specifically, a nonlinear observation model in decibel scale with a quantized level is first paid considered by introducing the additive property of energy variables (i.e., sound intensity) in sound environment system. Next, a wide-sense particle filter of an expansion expression type is derived in a form suitable for the nonlinear observation characteristics and the signal processing considering higher-order correlation information between the specific signal and observation. Furthermore, the effectiveness of the proposed theory is confirmed by applying it to the observed data measured in real sound environment.

RANDOM RESPONSES OF A TWO-DEGREE-OF-FREEDOM STRUCTURE WITH STRONGLY NONLINEAR COUPLING AND PARAMETRIC INTERACTION

This paper investigates the random responses of a TDOF structure with strongly nonlinear coupling and parametric vibration. With the nonlinear cou- pling of inertia in the equations of motion of the system being removed by successive elimination, the non-Gaussian moment equation method (NGM) is applied and 69 moment equations are integrated with central cumulative truncation technique. The stochastic central difference-cum-statistical linearization method(SCD-SL) and the digital simulation method(DSM) are also used. A comparison of results by different methods are given and the SCD-SL method is the most efficient method.

A New Particle Filter for Nonlinear Tracking Problems

A new particle filter is presented for nonlinear tracking problems. Inpractice, maneuvering target-tracking systems are usually nonlinear and incompletely observed, andthe main difficulty of maneuvering target-tracking problem lies in the fact that the maneuverabilityat every step is of high uncertainties. Here a new smoothing particle filter algorithm is proposed,which combines the particle filter to tackle the non-linear and non-Gaussian peculiarities of theproblem, together with smoothing of the PDF of system modes and thus settles the estimate problem ofthe target maneuverability. The simulation comparison with the auxiliary particle filters showsthat the approach has superiority and yields performance improvements in solving nonlinear trackingproblems.

基于IMM-PF的分布式估计融合算法

针对基于扩展卡尔曼滤波的估计融合算法存在线性化误差,且受高斯噪声假设限制的问题,提出一种基于交互式多模型粒子滤波(IMM-PF)的分布式多传感器估计融合算法.各传感器节点采用IMM-PF算法,以便在非线性、非高斯条件下稳健地跟踪机动目标;融合中心则采用基于粒子滤波(PF)的分布式融合方法进行全局估计融合.该算法适用于非线性、非高斯条件下的多传感器状态估计.仿真结果表明,该算法能够提高多传感器系统状态估计的精度.

非高斯噪声下基于U-粒子滤波器和似然比的非线性系统故障诊断

针对普通粒子滤波器在非线性系统随机系统故障诊断中的'退化'现象和估计精度的不足,进而影响诊断准确率的问题,提出应用U-粒子滤波器(Unscented particle filter,UPF)进行改进的方法。在建立正常/异常UPF滤波器模型的基础上,推导基于UPF的似然概率密度函数和似然比(Log likelihood ratio,LLR)计算方法,构造故障的检测律和诊断律,并给出完整的故障诊断算法,不仅能准确预报故障发生的时刻,而且可以诊断出故障的类型。最后在某直升机非线性舵回路上进行了试验验证,结果证明了该方法的有效性和优越性。

适于无源阵列跟踪机动目标的IMM-PF算法

针对无源阵列对机动目标跟踪效果较差的问题,在融合交互式多模型和粒子滤波方法的基础上,提出了一种基于粒子滤波的交互多模型(IMM-PF)算法。该算法采用多模型结构以跟踪目标的任意机动;各模型采用粒子滤波算法,以处理非线性、非高斯问题。各模型中相对固定数目的粒子群经过相互交互、粒子滤波后再进行重抽样以减少滤波退化现象。与典型的交互式多模型算法(IMM-KF)进行了比较,计算机仿真结果证实了新算法的正确性和有效性。

改进邻域保持嵌入-独立元分析的间歇过程故障检测算法

针对间歇过程数据的非线性和高斯与非高斯混合分布特性导致故障检测效果不佳的问题,提出了基于多向差分邻域保持嵌入—加权差分独立元分析(MDNPE-WDICA)的间歇过程故障检测算法。首先采用Jarque-Bera检验方法(J-B test)将原始数据空间划分为高斯和非高斯子空间;然后,在高斯子空间,将差分策略与NPE算法结合提出MDNPE算法,对高斯空间数据进行维数约简,在保持其局部结构不变的同时处理非线性,并克服传统非线性处理方法由于引入核函数带来的计算复杂的问题;在非高斯子空间,将加权差分策略与ICA算法结合提出WDICA算法,在充分提取数据非高斯信息的同时解决其非线性,并有效利用数据的局部信息;最后,通过贝叶斯推断构建一个新的监测统计量,实现整个间歇过程数据的故障检测。通过青霉素生产过程仿真结果验证了所提算法的可行性和有效性。

基于t-分布粒子滤波器的目标跟踪

针对贝叶斯跟踪中目标状态的预测分布和后验分布,利用序列蒙特卡洛方法,基于多变量t-分布提出了一种新的粒子滤波算法,称之为t-分布粒子滤波器.为了根据样本估计目标状态的概率分布,提出了一种新的ECME算法,并嵌入到t-分布粒子滤波器中.理论分析表明,在t-分布条件下,t-分布粒子滤波器是在样本数量上的渐近最优估计器.在机动目标跟踪实验中,比较了t-分布粒子滤波器、无色卡尔曼滤波(Unscented Kalm an filter)及自助式粒子滤波器(Bootstrap partic le filters)的跟踪精度.

D-vine copulas混合模型及其在故障检测中的应用

过程监控技术是保证现代流程工业安全平稳运行及产品质量的有效手段。传统的过程监控方法大多采用维度约简方法提取数据特征,且要求过程数据必须服从高斯分布、线性等限制条件,对复杂工况条件下发生的故障难以取得较好的检测效果。因此,提出了混合D-vine copulas故障诊断模型,在不降维的情况下直接刻画数据中存在的复杂相关关系,构建过程变量的统计模型实现对存在非线性与非高斯性过程的精确描述。通过EM算法和伪极大似然估计优化混合模型参数,然后结合高密度区域(HDR)与密度分位数法等理论,构建广义贝叶斯概率(GBIP)指标实现对过程的实时监测。数值例子及在TE过程上的仿真结果说明了该混合模型的有效性及在故障检测中的良好性能。

基于稀疏D-vine Copula的建模方法及其在过程监测中的应用

针对工业过程中高维数据的非线性非高斯问题,提出了一种基于稀疏D-vine Copula(Sparse D-vine Copula-based,SDVC)的过程监测方法。首先,针对传统的Vine Copula结构优化方法容易引起估计误差在Vine结构中累积,并且计算负担随着数据维数的增加急剧增长的问题,修正了二元Copula的先验概率,使得高层次结构树中的二元Copula更倾向于优化为独立状态,实现了高层次树结构稀疏优化。其次,对Vine结构节点次序确定方法进行改进,根据节点间的相关性总和依次展开,使其更适用于水平结构的D-vine建模。最后,引入高密度区域(HDR)与密度分位数理论,构建适用于任意分布的广义局部概率(GLP)指标,以实现对工业过程的实时监测。通过田纳西-伊斯曼(Tennessee-Eastman,TE)和醋酸脱水工业过程验证了所提出方法的优越性能。

基于模糊C-回归聚类的T-S模糊粒子滤波算法

针对非高斯目标动态模型不确定性粒子滤波问题,提出改进的基于模糊C-回归聚类的T-S模糊模型粒子滤波算法。采用T-S模糊模型语义模糊集表示空间特征信息从而高精度近似动态模型,提出基于熵的模糊C-回归聚类方法从而自适应地识别T-S模糊模型的前提参数,调整模型的权重,并使用卡尔曼滤波识别结论参数。通过T-S模糊模型构造重要性密度函数提高采样粒子的鲁棒性和多样性,进一步改进了算法的计算复杂度。仿真验证结果表明,在运动方向突然改变或目标动态模型的先验信息不准确时,该方法可以准确快速地跟踪机动目标。

基于核密度估计的R-Vine Copula选择及其在故障检测中的应用?

在化工过程监控领域,Vine Copula模型为描述高维复杂变量之间相依关系提供了一种新的思想,在不降维的基础上直接刻画变量之间复杂的相关关系。传统的Copula函数模型选择方法是基于赤池信息准则(Akaikeinformation criterion,AIC),但是在利用AIC准则时不仅要计算Copula的密度函数,而且边缘分布的拟合效果也直接影响了AIC的取值。本文提出了基于核密度估计的R-Vine Copula (kernel estimation-based R-vine Copula, KRVC)选择方法,并将其应用在化工过程监控领域。通过核密度选择原理得到R-Vine模型,然后利用高密度区域(HDR)与密度分位数表等理论,构建非高斯态广义局部概率指标(GLP)。该方法在TE(TennesseeEastman)过程中以及醋酸脱水过程中的应用验证了KRVC方法在过程监控中的良好性能。

Theoretical convergence analysis of complex Gaussian kernel LMS algorithm

With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications.This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics.Then the theoretical convergence behavior of the complex Gaussian kernel least mean square（LMS） algorithm is studied by using the fixed dictionary strategy.The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algonthms using non-circular complex data.The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error（MSE） performance among of complex kernel LMS（KLMS） methods according to the specified kernel bandwidth and the length of dictionary.

基于改进舰尾流模型和多层耦合分析的机载雷达测量建模

为提高复杂海洋环境中无人舰载机(Unmanned carrier-based aircraft, UCA)自动着舰时导航定位的准确性,研究舰尾流对机载雷达测量过程的动态影响问题,建立一种基于多层级耦合性分析的测量影响动态建模分析方法.首先,利用直接分解法和前向差分法建立一种基于离散化状态空间的时变舰尾流模型,以克服传统传递函数方法存在的局限性;其次,基于舰尾流各分量均与飞机飞行速度相关的客观事实,通过在时变系统中考虑舰尾流分量间的相互作用关系来构建一种更符合实际系统特征的分量自耦合舰尾流模型;紧接着,采用UCA姿态角变化能够改变坐标转换矩阵的思想,研究舰尾流与UCA位姿变化间的耦合联系,提出一种准确性更高的舰尾流对UCA位姿的深度影响模型;然后,以航母姿态变化对舰载雷达测量结果的影响模型为基础,通过考虑本研究场景的内在特性,建立UCA姿态变化对雷达测量结果的影响模型分析方法;紧接着,采用示意图方式获得位移变化对机载雷达测量结果的影响模型;最后,针对舰船受海洋大气(风、浪、流)干扰而出现失速这一现象,建立实际海洋环境中舰尾流对机载雷达测量结果的非线性非高斯影响分析模型.仿真实验研究验证了上述模型分析方法的有效性和优越性.

铁道车辆轴箱振动非高斯特征与分布研究

以对铁道车辆轴箱振动非高斯特征与分布为对象开展研究。基于列车线路轴箱实测加速度信号,提取由轨道冲击引起的轴箱振动特征非高斯信号。使用多个概率密度函数(Probability Density Function,PDF)模型对实测信号进行拟合,并与实测特征信号的经验分布进行对比,评估各模型对轴箱特征非高斯信号的拟合精度。基于W-H非线性变换模型,建立一种非高斯信号模拟方法。利用模拟信号分析非高斯特征对各模型拟合精度的影响。结果表明:列车在行驶过程中具有非高斯特征,当列车经过轨道焊接接头、道岔与波磨路段时,由于轮轨冲击,非高斯特征明显增大,车轮多边形对信号非高斯特征几乎没有影响;基于W-H模型的非线性变换法,可以在保证模拟信号功率谱与指定功率谱基本一致的情况下,进行不同非高斯特征的信号模拟;高斯混合模型能够对铁道车辆非高斯信号较为准确地拟合;随着模拟非高斯信号峭度与偏度的增大,各模型与经验分布的相对误差也会增大,其中高斯混合模型拟合精度相对较高。

粒子滤波非线性AVO反演方法

提出一种新的AVO非线性反演方法,即利用粒子滤波器来求解AVO非线性贝叶斯反演问题。利用随机带权样本逼近后验概率.论文首先论述了粒子滤波器的基本原理,包括状态转移模型与观测模型,权值预测与更新,重要性密度采样等粒子滤波器应用中的关键技术.然后建立了适合于AVO反演的粒子滤波器状态转移模型和观测模型.最后,利用该方法分别对模型数据和实际资料进行了反演计算.反演结果表明,该方法具有较好的稳定性,在AVO反演中具有的一定的应用潜力.同时对地球物理反演的其他问题求解也提供了一条新的途径.

基于交互式多模型的粒子滤波算法

融合交互式多模型和粒子滤波,提出了一种新的多模型粒子滤波算法。该算法采用多模型结构以跟踪目标的任意机动。各模型采用粒子滤波算法,以处理非线性、非高斯问题。各模型中相对固定数目的粒子群经过相互交互、粒子滤波后再进行重抽样以减少滤波退化现象。与通用的交互式多模型算法进行了比较,试验仿真结果证实了本文新滤波算法的有效性。