Parameter estimation of the 2D‐GTD model and RCS reconstruction based on an improved 2D‐ESPRIT algorithm

The two‐dimensional estimating signal parameter via rotational invariance techniques (2D‐ESPRIT) algorithm is a classical method to estimate parameters of the two‐dimensional geometric theory of diffraction (2D‐GTD) model. While as signal‐to‐noise‐ratio (SNR) decreases, the parameter estimation performance of 2D‐ESPRIT algorithm is severely influenced. To solve this problem, a performance‐enhanced 2D‐ESPRIT algorithm is proposed in this article. The improved 2D‐ESPRIT algorithm combines the conjugate data with the original back‐scattered data and obtains a novel covariance matrix by squaring the original total covariance matrix. Simulation results indicate that the improved algorithm has a better noise robustness and a more stable parameter estimation performance than the classical ESPRIT algorithm and the classical TLS‐2D‐ESPRIT algorithm. To further validate the superiority of the improved 2D‐ESPRIT algorithm, reconstructed radar cross section (RCS) is presented in this article. Compared with the classical 2D‐ESPRIT algorithm, the proposed algorithm presents higher RCS fitting precision. Furthermore, the impacts of other factors on parameter estimation, such as matrix pencil parameters and paring parameters, are also studied in this article.     

图像统计模型参数估计中的期望最大值算法

期望最大值算法是近年来图像统计模型参数估计技术领域的研究热点之一。在对期望最大值算法分析的基础上,结合其在图像统计模型参数估计中的应用研究,对改变标准期望最大值算法的3种方式进行比较分析。结合图像恢复、分割、目标跟踪以及与其他优化算法的融合应用,从丢失数据集的选取、丢失数据集和不完全数据集统计模型的建立,以及统计模型参数估计3个方面,评述期望最大值算法优缺点。丢失数据的选取和不完全数据的描述形式直接决定期望最大值算法的结构和计算复杂度,以致算法的成败。最后,讨论期望最大值算法目前存在的问题及未来的发展方向,指出其在具有丢失数据统计模型参数估计中广泛应用。     

基于统计学理论的参数模型运动估计方法

运动估计对视频编码十分重要,基于参数模型的运动估计方法也越来越受到人们的关注,参数模型的选择是该方法的关键。基于此,提出了基于统计学原理的模型选择方法,它以少量的图像数据流为基础,通过参数估计,并分析各近似模型的预测风险和误差,选出最优模型,它最符合预测对象的实际发展变化规律,进而利用该模型对未知对象进行运动估计。试验结果表明,在对实际图像序列进行运动估计时,这种方法是可靠并且实用的。     

Recursive methods for estimating the radial basis function‐based state‐dependent autoregressive model

Identifying a nonlinear radial basis function‐based state‐dependent autoregressive (RBF‐AR) time series model is the basis for solving the corresponding prediction and control problems. This paper studies some recursive parameter estimation algorithms for the RBF‐AR model. Considering the difficulty of the nonlinear optimal problem arising in estimating the RBF‐AR model, an overall forgetting gradient algorithm is deduced based on the negative gradient search. A numerical method with a forgetting factor is provided to solve the problem of determining the optimal convergence factor. In order to improve the parameter estimation accuracy, the multi‐innovation identification theory is applied to develop an overall multi‐innovation forgetting gradient (O‐MIFG) algorithm. The simulation results indicate that the estimation model based on the O‐MIFG algorithm can capture the dynamics of the RBF‐AR model very well.     

基于粒子群优化算法的Richards模型参数估计和算法有效性

针对Richards模型参数估计较为困难的实际问题,提出将Richards模型的参数估计问题转化为一个多维无约束函数优化问题。结合谷氨酸菌体的实际生长浓度数据,在Matlab 2012b环境中,利用粒子群优化（PSO）算法建立适应度函数,在最小线性二乘意义下估计Richards模型中的4个参数,并建立了拟合的生长曲线和最优值变化曲线。为进一步验证算法有效性,将PSO算法与该模型传统参数估计法中的四点法和遗传算法(GA)进行了比较,以相关指数和剩余标准差作为评价指标。结果表明,PSO算法对Richards模型的拟合效果良好,对模型的参数估计有着很好的适用性。     

利用自回归模型的平稳时序数据快速辨识算法

由于自回归模型的参数估计可归结为求解一个线性方程组的问题,故其在平稳时序数据的辨识过程中具有广泛的应用场合。提出了一种基于自回归模型的快速辨识算法,首先,以递推的方式对平稳时序数据自相关函数矩阵的秩的下界值进行估计,然后,以该估计值作为自回归模型的起始阶数对系统进行依次的递阶辨识,最后,基于F检验对相邻阶次的拟合误差的变化趋势进行显著性检验,并以检验结果作为算法的结束条件。新算法在保证较高辨识精度的条件下,其计算效能及辨识精度的稳定性均优于现有的自回归模型辨识算法,实验结果验证了新算法的有效性和先进性。     

M-estimator and D-optimality model construction using orthogonal forward regression.

This correspondence introduces a new orthogonal forward regression (OFR) model identification algorithm using D-optimality for model structure selection and is based on an M-estimators of parameter estimates. M-estimator is a classical robust parameter estimation technique to tackle bad data conditions such as outliers. Computationally, The M-estimator can be derived using an iterative reweighted least squares (IRLS) algorithm. D-optimality is a model structure robustness criterion in experimental design to tackle ill-conditioning in model structure. The orthogonal forward regression (OFR), often based on the modified Gram-Schmidt procedure, is an efficient method incorporating structure selection and parameter estimation simultaneously. The basic idea of the proposed approach is to incorporate an IRLS inner loop into the modified Gram-Schmidt procedure. In this manner, the OFR algorithm for parsimonious model structure determination is extended to bad data conditions with improved performance via the derivation of parameter M-estimators with inherent robustness to outliers. Numerical examples are included to demonstrate the effectiveness of the proposed algorithm.     

On a constrained mixture vector autoregressive model

A mixture vector autoregressive model has recently been introduced to the literature. Although this model is a promising candidate for nonlinear multiple time series modeling, high dimensionality of the parameters and lack of method for computing the standard errors of estimates limit its application to real data. The contribution of this paper is threefold. First, a form of parameter constraints is introduced with an efficient EM algorithm for estimation. Second, an accurate method for computing standard errors is presented for the model with and without parameter constraints. Lastly, a hypothesis-testing approach based on likelihood ratio tests is proposed, which aids in the selection of unnecessary parameters and leads to the greater efficiency at the estimation. A case study employing U.S. Treasury constant maturity rates illustrates the applicability of the mixture vector autoregressive model with parameter constraints, and the importance of using a reliable method to compute standard errors.     

基于模糊自适应免疫算法的非线性系统模型参数估计

复杂生产工艺中非线性系统的模型参数估计是系统建模优化问题中的难点, 为避免优化算法过早收敛于错误的参数估计值, 根据生物免疫机理和模糊逻辑原理提出了一种新颖的模糊自适应免疫算法, 该算法采用混沌超变异操作增强算法搜索能力, 并用免疫网络调节策略保持抗体群的多样性, 同时采用模糊逻辑调节算法参数以提高算法的自适应能力. 函数优化仿真结果表明其具有较好的收敛性能, 并能够克服早收敛问题. 最后将其成功应用于重油热解非线性模型参数估计中, 验证了该算法解决实际建模问题的可行性和有效性.     

Learning a mixture model for clustering with the completed likelihood minimum message length criterion

Mixture model based clustering (also simply called model-based clustering hereinafter) consists of fitting a mixture model to data and identifying each cluster with one of its components. This paper tackles the model selection and parameter estimation problems in model-based clustering so as to improve the clustering performance on the data sets whose true kernel distribution functions are not in the family of assumed ones, as well as with inherently overlapped clusters. Being tailored to clustering applications, an effective model selection criterion is first proposed. Unlike most criteria that measure the goodness-of-fit of the model only to generate data, the proposed one also evaluates whether the candidate model provides a reasonable partition for the observed data, which enforces a model with well-separated components. Accordingly, an improved method for the estimation of mixture parameters is derived, which aims to suppress the spurious estimates by the standard expectation maximization (EM) algorithm and enforce well-supported components in the mixture model. Finally, the estimation of mixture parameters and the model selection is integrated in a single algorithm which favors a compact mixture model with both the well-supported and well-separated components. Extensive experiments on synthetic and real-world data sets are carried out to show the effectiveness of the proposed approach to the mixture model based clustering.     

非均匀采样数据系统的一种辨识方法

阐述了非均匀采样方案,推导了非均匀多率采样系统的状态空间模型,进一步获得了对应的传递函数模型.为解决辨识模型信息向量中存在未知变量的问题,使用辅助模型技术,用辅助模型的输出代替系统的未知变量,进而提出了非均匀采样数据系统的辅助模型随机梯度辨识算法.为了提高算法收敛速度和改善参数估计精度,在算法中引入遗忘因子,给出了相应的辅助模型带遗忘因子随机梯度算法.仿真结果表明,引入遗忘因子后,算法的收敛速度加快,参数估计精度提高.     

小波域HMT模型参数的快速估计及其在图像降噪中的应用

小波域隐马尔可夫树(Hidden Markov Tree，HMT)模型可以很好地刻画尺度内与尺度间小波系数的相关性，但模型参数的训练过程复杂，计算量大。针对这个缺点，提出了一种不经训练的HMT模型参数快速估计方法。该算法首先用一种自适应阈值将每个子带小波系数分成不同的类，然后分别对每类进行统计，这种统计是局部的，因而有很好的局部自适应性，最后模型参数可以利用这些局部的统计特性来描述。将估计出的参数模型运用到图像降噪中，实验结果表明这种快速估计的HMT参数模型不仅可以大大提高计算速度，降低计算复杂度，而且从峰值信噪比和主观视觉效果上都不逊于传统的经过迭代训练的HMT模型降噪算法。     

基于组合遗传算法的反应动力学模型参数估计

通过构造一个适当的适应度函数,将渣油加氢精制反应动力学模型的参数估计问题转化为一个多维优化问题,然后提出一种组合遗传算法来求解该优化问题。该算法利用混沌序列初始化种群以保证其均匀分布在搜索空间中。在每次迭代过程中随机组合不同的交叉策略和变异以产生若干个新的子代个体。对四个标准数值优化问题进行了仿真实验,仿真结果表明了组合遗传算法的有效性。以石油炼制工业中典型装置催化裂化为例,对渣油加氢精制反应动力学模型的参数进行了优化,获得了满意的结果。     

一种基于GTD模型和状态空间处理的运动目标超宽带散射中心提取方法

超宽带条件下散射中心的不同运动将对参数提取造成影响.基于GTD模型和状态空间处理,本文提出了一种针对运动目标的超宽带散射中心提取方法.该方法首先将超宽带条件下的目标GTD散射模型转化为状态空间方程,通过奇异值分解提取散射中心的径向距离和径向速度信息;然后由标准正交向量基降维表示散射中心在整个带宽上的类型参数信息,采用遍历方法和最小二范数准则求解出散射中心的类型参数信息;最后基于最小二乘法求解出散射中心的散射强度.文中同时给出了各参数估计的CR界.仿真结果验证了文中方法的有效性,该方法可同时提取散射中心径向距离、径向速度、散射强度和类型参数信息,从而有利于各散射中心的跟踪和整体目标的有效识别.     

Parameter estimation of Poisson mixture with automated model selection through BYY harmony learning

Finite mixture is widely used in the fields of information processing and data analysis. However, its model selection, i.e., the selection of components in the mixture for a given sample data set, has been still a rather difficult task. Recently, the Bayesian Ying-Yang (BYY) harmony learning has provided a new approach to the Gaussian mixture modeling with a favorite feature that model selection can be made automatically during parameter learning. In this paper, based on the same BYY harmony learning framework for finite mixture, we propose an adaptive gradient BYY learning algorithm for Poisson mixture with automated model selection. It is demonstrated well by the simulation experiments that this adaptive gradient BYY learning algorithm can automatically determine the number of actual Poisson components for a sample data set, with a good estimation of the parameters in the original or true mixture where the components are separated in a certain degree. Moreover, the adaptive gradient BYY learning algorithm is successfully applied to texture classification.     

Internet AS幂律建模及其参数估计

为了精确建模Internet自治系统层面上的拓扑结构,提出了基于最小节点度和最大节点度的拓扑幂律模型及其参数估计新算法。针对Internet自治系统层拓扑实际测量数据,利用新算法对拓扑幂律模型中的最小节点度、最大节点度以及标度参数进行计算。实验结果表明,由新算法估计的Internet自治系统层拓扑幂律模型的最小节点度为1,最大节点度随网络规模的增大而增大,标度参数的误差与使用最大然似估计法误差一样均非常小,约为2.25。     

UD分解与偏差补偿结合用于变量带误差模型辨识

本文提出一种基于UD(upper-diagonal)分解与偏差补偿结合的辨识方法,用于变量带误差(errors-in-variables,EIV)模型辨识.考虑单输入单输出(single input and single output,SISO)线性动态系统,当输入和输出含有零均值、方差未知的高斯测量白噪声时,该类系统的模型参数估计是一种典型的EIV模型辨识问题.为了获得这种EIV模型参数的无偏估计,本文先推导出最小二乘模型参数估计偏差量与输入输出噪声方差以及最小二乘损失函数与输入输出噪声方差的关系,然后采用UD分解方法递推获得模型参数估计值,再利用输入输出噪声方差估计值补偿模型参数估计偏差,以此获得模型参数的无偏估计.本文还讨论了算法实现过程中遇到的一些问题及修补方法,并通过仿真例验证了所提辨识方法的有效性.     

On time series model selection involving many candidate ARMA models

We study how to perform model selection for time series data where millions of candidate ARMA models may be eligible for selection. We propose a feasible computing method based on the Gibbs sampler. By this method model selection is performed through a random sample generation algorithm, and given a model of fixed dimension the parameter estimation is done through the maximum likelihood method. Our method takes into account several computing difficulties encountered in estimating ARMA models. The method is found to have probability of 1 in the limit in selecting the best candidate model under some regularity conditions. We then propose several empirical rules to implement our computing method for applications. Finally, a simulation study and an example on modelling China's Consumer Price Index (CPI) data are presented for purpose of illustration and verification.     

基于最大熵方法的统计语言模型

针对现有统计语言模型中存在计算量过大和系统负担过重的问题,该文提出了一种基于最大熵方法的统计语言模型。模型在参数估计阶段,引入约束最优化理论中拉格朗日乘数定理和牛顿迭代算法,以确保模型在多个约束条件中可求出最优化参数值;在特征选择阶段,采用计算近似增益的平行算法,解决模型计算量过大和系统开销问题。将该模型用于汉语句子分析的软件实验中表明:模型具有较高的计算效率和鲁棒性。     

聚类模型参数自动选择的图库索引

提出一种基于模式聚类和混合模型参数自动选择的图库索引方法。因为传统的EM（Expectation Maximization）算法为混合模型聚类问题中的参数估计提供了一个很好的解决方法,但需要事先指定聚类数,影响了高维数据索引的精度和效率。综合利用改进的CEM2（Component-wise EM of Mixture）混合模型自动选择算法、矢量量化和概率近似的索引机制,在保证准确率同时有效提高了检索效率。