带不确定量测和未知虚警概率的粒子滤波器

为了解决带不确定量测和未知虚警概率的非线性非高斯系统状态估计问题,本文提出了一种新的粒子滤波方法,利用随机不确定量测模型来更新粒子和权值,并基于极大似然准则来辨识未知的虚警概率.本文所提出的带不确定量测和已知虚警概率的粒子滤波方法与现有标准的粒子滤波方法具有几乎一致的计算复杂度,但是更适合用于处理带不确定量测的非线性非高斯系统状态估计问题.此外,在状态转移密度函数被选择为建议密度函数时,本文证明了基于所提出的虚警概率辨识方法的极大似然估计唯一,从而为精确辨识虚警概率提供了理论保证.单变量非平稳增长模型和纯方位跟踪的数值仿真验证了所提出粒子滤波方法的有效性和与现有方法相比的优越性.     

有色量测噪声下的HCKF及其应用

针对高阶容积卡尔曼滤波（HCKF）算法在有色量测噪声条件下滤波精度下降的问题,提出了有色量测噪声下的HCKF算法。通过一阶马尔科夫模型将有色量测噪声进行白化,将带有色量测噪声的非线性离散随机系统转化为白噪声下的非线性时滞系统,并给出高斯域内针对非线性时滞系统的贝叶斯滤波框架。利用高阶容积准则对该滤波框架进行近似计算,进而得到有色量测噪声下的HCKF算法。将所提算法应用到机动目标跟踪系统中,仿真实验结果表明,量测噪声为白噪声时,所提算法与标准HCKF算法具有相同的估计性能;在量测噪声为有色噪声时,所提算法相比于标准HCKF具有更优的估计精度和鲁棒性。     

基于极大似然准则和最大期望算法的自适应UKF 算法

针对噪声先验统计特性未知情况下的非线性系统状态估计问题,提出了基于极大似然准则和 最大期望算法的自适应无迹卡尔曼滤波(Unscented Kalman filter, UKF) 算法.利用极大似然准则构造含有噪声统计特性的对数似然函数,通 过最大期望算法将噪声估计问题转化为对数似然函数数学期望极大化问题,最终得到带次优递 推噪声统计估计器的自适应UKF算法.仿真分析表明,与传统UKF算法相比,提出的自适应UKF算法 有效克服了传统UKF算法在系统噪声统计特性未知情况下滤波精度下降的问题,并实现了系统噪 声统计特性的在线估计.     

基于期望最大化与容积卡尔曼平滑器的机载多平台多传感器系统误差配准算法

针对机载多平台多传感器系统误差配准过程中出现的系统误差参数未知问题,本文提出了一种基于期望最大化(EM)与容积卡尔曼平滑器(CKS)的机载多平台多传感器系统误差配准算法.该算法将传感器的量测系统误差视为系统待估计的未知参数,构建了新的传感器量测方程.引入EM算法框架,在期望步(E–step)利用容积卡尔曼滤波器(CKF)和CKS近似计算对数似然函数的数学期望,在最大化步(M–step)对该数学期望进行最大化处理,最后通过解析更新反复迭代的方式获得各传感器系统误差的参数估计.数值仿真验证了本文提出算法的有效性.     

带有色量测噪声的非线性系统 Unscented 卡尔曼滤波器

传统Unscented卡尔曼滤波器(Unscented Kalman filter, UKF)要求噪声必须为高斯白噪声, 无法解 决带有色噪声的非线性系统滤波问题. 为此, 本文提出了一种带有色量测噪声的UKF滤 波新算法. 首先,基于量测信息增广和最小方差估计, 推导出一类带有色量测噪声的非 线性离散系统状态的最优滤波框架, 接着采用Unscented变换(Unscented transformation, UT)来计算最优框架中的 非线性状态后验均值和协方差, 进而得到有色量测噪声下UKF滤波递推公式. 所设 计的UKF新方法能有效地解决传统UKF在量测噪声有色情况下非线性滤波失效的问题, 数 值仿真实例验证了其可行性和有效性.     

高速列车非线性模型的极大似然辨识

提出高速列车非线性模型的极大似然(Maximum likelihood, ML)辨识方法,适合于高速列车在非高斯噪声干扰下的非线性模型的参数估计.首先,构建了描述高速列车单质点力学行为的随机离散非线性状态空间模型,并将高速列车参数的极大似然(ML)估计问题转化为期望极大(Expectation maximization, EM)的优化问题; 然后,给出高速列车状态估计的粒子滤波器和粒子平滑器的设计方法,据此构造列车的条件数学期望,并给出最大化该数学期望的梯度搜索方法,进而得到列车参数的辨识算法,分析了算法的收敛速度; 最后,进行了高速列车阻力系数估计的数值对比实验. 结果表明, 所提出的辨识方法的有效性.     

带有色厚尾量测噪声的鲁棒高斯近似滤波器和平滑器

为了解决带有色厚尾量测噪声的非线性状态估计问题,本文提出了新的鲁棒高斯近似（Gaussian approximate,GA）滤波器和平滑器.首先,基于状态扩展方法将量测差分后带一步延迟状态和白色厚尾量测噪声的非线性状态估计问题,转化成带厚尾量测噪声的标准非线性状态估计问题.其次,针对量测差分后模型中的噪声尺度矩阵和自由度（Degrees of freedom,DOF）参数未知问题,设计了新的高斯近似滤波器和平滑器,通过建立未知参数和待估计状态的共轭先验分布,并利用变分贝叶斯方法同时估计未知的状态、尺度矩阵、自由度参数.最后,利用目标跟踪仿真验证了本文提出的带有色厚尾量测噪声的鲁棒高斯近似滤波器和平滑器的有效性以及与现有方法相比的优越性.     

非线性离散系统偏倚辨识和状态估计的一种自适应算法

本文对带有色系统噪声的非线性离散随机系统的偏倚辨识和状态估计,提出了一种新算法,通过适时地修正系统噪声和量测噪声的均值和协方差来提高估计精度,并可加快偏倚辨识的收敛速度。仿真结果表明,本文提出的算法是有效的。     

粒子滤波的噪声相关下单步延迟无序量测更新算法

在目标跟踪系统中,因通信延迟等原因会出现传感器量测无序地到达融合中心的现象,将这些量测称为无序量测(OOSM).针对过程噪声、量测噪声相关的非线性系统中出现的无序量测问题,在现有算法基础上,提出了一种可处理单步延迟无序量测的新算法.在前向预测滤波框架下,对系统方程去相关化,并利用粒子滤波(PF)进行状态估计.仿真结果验证了算法的有效性.     

有色量测噪声下的改进求容积卡尔曼滤波器

为解决标准求容积卡尔曼滤波器在有色量测噪声条件下滤波精度退化的问题,提出改进求容积卡尔曼滤波器及其平方根形式.首先利用一阶马尔科夫模型白化非线性离散随机系统中有色量测噪声,将有色量测噪声下非线性离散随机系统转化为白噪声下非线性时滞系统.然后根据所得非线性时滞系统推导其高斯域的贝叶斯滤波框架,最后基于3度Spherical-Radial规则将该滤波框架近似为改进的求容积卡尔曼滤波器和其平方根形式.机动目标跟踪仿真试验结果表明两种改进求容积卡尔曼滤波算法在标准白噪声条件下与标准求容积卡尔曼滤波算法的估计精度相同,而在有色量测噪声背景下滤波精度和鲁棒性更优.     

EM‐based adaptive divided difference filter for nonlinear system with multiplicative parameter

This paper is concerned with application of expectation maximization (EM) algorithm for deriving an adaptive version of divided difference filter for joint state estimation and multiplicative parameter identification of nonlinear system with the colored measurement noise. Owing to the fact that there exist a mutual coupling and interaction of state and parameter on each other, it requires a joint or simultaneous estimation of both state and parameter by a mutual iteration, and justly, EM iterates Expectation (E‐)step and Maximization (M‐)step to meet such requirement. Firstly, E‐step involves state filtering and smoothing issues under knowing the previous parameter identification results, which is well solved by resorting to the Gaussian approximation with a trade‐off between accuracy and complexity. Further, such Gaussian approximation estimators are applied for evaluating the condition expectation of complete‐data likelihood function, nonlinearly characterized by the multiplicative parameter needed to be optimized. Secondly, M‐step deals with the maximization of the condition expectation by directly making its derivative as zero to obtain the current general parameter identification equation as the nonlinear integral. Thirdly, by iteratively operating E‐step and M‐step, an adaptive divided difference filter is proposed for joint state estimation and parameter identification by using the second‐order Stirling interpolation to compute the associated nonlinear integral. Finally, the robust performance of the EM‐based adaptive version of divided difference filter to the unknown or time‐varying multiplicative parameter, as compared with the standard augmentation method, is demonstrated by a maneuvering target tracking example. Copyright © 2016 John Wiley & Sons, Ltd.     

Blind Source Separation of Postnonlinear Convolutive Mixture

In this paper, a novel solution is developed to solve blind source separation of postnonlinear convolutive mixtures. The proposed model extends the conventional linear instantaneous mixture model to include both convolutive mixing and postnonlinear distortion. The maximum-likelihood (ML) approach solution based on the expectation-maximization (EM) algorithm is developed to estimate the source signals and the parameters in the proposed nonlinear model. In the proposed solution, the sufficient statistics associated with the source signals are estimated in the E-step, while the model parameters are optimized through these statistics in the M-step. However, the complication resulted from the postnonlinear function associated with the mixture renders these statistics difficult to be formulated in a closed form and hence causes intractability in the parameter optimization. A computationally efficient algorithm is proposed which uses the extended Kalman smoother (EKS) to facilitate the E-step tractable and a set of self-updated polynomials is used as the nonlinearity estimator to facilitate closed form estimations of the parameters in the M-step. The theoretical foundation of the proposed solution has been rigorously developed and discussed in details. Both simulations and recorded speech signals have been carried out to verify the success and efficacy of the proposed algorithm. Remarkable improvement has been obtained when compared with the existing algorithms.     

Maximum likelihood least squares‐based iterative methods for output‐error bilinear‐parameter models with colored noises

This article is concerned with the parameter identification of output‐error bilinear‐parameter models with colored noises from measurement data. An auxiliary model least squares‐based iterative method is developed through the overparameterization model. It examines the difficulty of estimating the overparameterized vector, which usually presents a heavy computational burden in the identification process. To overcome this drawback, a parameter separation technique is introduced and the nonlinear model is reformulated as a refined identification model through eliminating the crossmultiplying terms. In this regard, a parameter separation least squares‐based iterative (PS‐LSI) algorithm is derived by avoiding estimating the redundant parameters. On the basis of the PS‐LSI algorithm, we derive a maximum likelihood least squares‐based iterative method to further improve the numerical accuracy. The identification is dependent on the formulation of a pseudolinear regression relationship, which contains two linear prefilters constructed from the system and noise models. The performance of this proposed method is confirmed by the numerical simulations as well as direct comparisons with other existing algorithms.     

有色噪声干扰下Hammerstein非线性系统两阶段辨识

针对实际工业过程中普遍存在有色噪声,提出了有色噪声干扰下Hammerstein非线性系统两阶段辨识方法。采用设计的组合式信号实现Hammerstein系统各模块参数辨识分离,简化了辨识过程。在第一阶段,基于可分离信号的输入输出数据,利用相关分析算法估计线性模块参数,减少了有色噪声对辨识的干扰。在第二阶段,基于随机信号的输入输出数据,在最小二乘算法中引入滤波技术,推导了滤波递推增广最小二乘算法,提高了非线性模块参数和噪声模型参数的辨识精度。仿真结果表明：提出的两阶段辨识方法提高了辨识精度,有效地抑制了有色噪声的干扰。     

Robust identification for nonlinear errors-in-variables systems using the EM algorithm

This article presents a robust identification approach for nonlinear errors-in-variables (EIV) systems contaminated with outliers. In this work, the measurement noise is modelled using the t-distribution, instead of the traditional Gaussian distribution, to mitigate the effect of the outliers. The heavier tails of the t-distribution, through the adjustable degrees of freedom, is used to account for noise and outliers concomitantly. Further, to avoid the intricacies related to the direct nonlinear identification, we propose to approximate the nonlinear EIV dynamics using multiple local ARX models and aggregating them using an exponential weighting strategy. The parameters of the local models and weighting parameters are estimated using the expectation maximization (EM) algorithm, under the framework of the maximum likelihood estimation (MLE). The studies with simulated numerical examples and an experiment on a multi-tank system demonstrate the superiority of the proposed method.