基于样条逼近分段线性Hammerstein模型的辨识方法

对分段线性Hammerstein系统,讨论了一种样条逼近重构中间输入的信号还原和处理辨识方法。采用三阶B样条近似逼近H模型的非线性输出,线性部分的参数以及样条近似的系数用最小二乘法辨识得到,再结合样条近似结果,利用重构后的多项式回归估计出非线性部分的参数。数字仿真结果表明了该方法的有效性和实用性。     

矩阵方程AX+BY+CZ=F广义中心对称最小二乘解

研究矩阵方程AX+BY+CZ=F广义中心对称解,给出了AX+BY+CZ=F的最小二乘广义中心对称解的表达式,导出了AX+BY+CZ=F有广义中心对称解的条件.讨论了在AX+BY+CZ=F最小二乘广义中心对称解集合中求与给定矩阵最佳逼近解.     

关于插值法与最小二乘拟合的讨论

本文给出了函数拟合的两种不同方法,即多项式插值和最小二乘拟合方法,并对两者的特点和优劣进行了讨论。     

一类广义可对称化矩阵反问题有解的条件

给出了一类广义可对称化矩阵反问题有解的充要条件和解的表达式，得到了最小二乘解和最佳逼近解的一般表达式。     

加权最小二乘估计与线性无偏最小方差估计的比较

在已知的线性模型中,考虑加权最小二乘估计与线性无偏最小方差估计的结果的差异。发现在两种条件下,加权最小二乘估计与线性无偏最小方差估计的结果趋于一致。     

线性回归在经济预测中的应用

本文利用线性回归模型对具体经济问题进行预测,分别采用两种估计方法：最小二乘估计法和LAD估计法对其进行估计,最后得出当存在异常数据时LAD估计法优于最小二乘估计法的结论。     

基于MATLAB的线性最小二乘估计

采用线性最小二乘估计,可以寻求有限测量数据及其伴随误差的变化规律。本文针对具体实例,采用最小二乘估计,并用MATLAB编制程序,对测量数据进行拟合与分析。     

一类广义可对称化矩阵反问题有解的条件

给出了一类广义可对称化矩阵反问题有解的充要条件和解的表达式,得到了最小二乘解和最佳逼近解的一般表达式.     

三种RBF神经网络比较分析

径向基函数（RBF）神经网络广泛应用于模式识别、非线性函数逼近等领域。通过对聚类、梯度、正交最小二乘三种RBF神经网络进行正弦函数逼近的仿真实验,从中比较分析这三种RBF神经网络。得到的对比分析结果表明：正交最小二乘的方式所需的训练时间最短,网络收敛速度最快,并且不需要预先定义隐层节点数。     

非齐次等式约束线性回归模型回归系数的综合条件岭估计

提出非齐次等式约束线性回归模型回归系数的一个新的有偏估计,即综合条件岭估计,讨论了综合条件岭估计的性质,在一定的条件下,综合条件岭估计的样本总方差、均方误差、均方误差矩阵均分别小于约束最小二乘估计的相应误差.在综合条件岭估计下,条件岭估计和条件根方估计为其特例,从而统一了条件岭估计和条件根方估计的理论.     

On the optimality of hysteresis operators in signal processing and communication systems

This paper demonstrates that hysteresis operators are the optimal estimators for a large class of estimation and decision problems. This class of problems arises whenever a cost is associated with actions needed to process changes in the estimates or decisions. A simple example related to least-squares estimation is used to illustrate and motivate the developments in this paper. Subsequently, the problem of mean-square estimation with minimal cost of actions is investigated. These results provide a justification for the use of hysteresis in many practical signal processing and communication applications.     

On Linear Least-Squares Estimators for Continous-Time Stochastic Systems

The problem of least-squares state estimation of stochastic continuous-time linear systems is reconsidered. A concise derivation of the least-squares minimal-order estimator is presented using an innovations approach. An important result is the reinstatement of the problem in a least-squares estimation framework independent of deterministic observer theory. A second result is thus the clarification of previous approaches to the problem, particularly in relation to observer theory.     

Parameter estimation of an unstable system with a PID controller in a closed loop configuration

An essential part of the auto-tuning control involves parameter estimation of a suitable low order model. Since a common way to control an unstable system is via a PID controller, there is a growing interest in the application of new PID-based algorithms for the identification task. In this light the relative advantages of two recently published methods are investigated. The first method is based on typical data of the reaction curve and the time delay is measured directly from the initial portion of the curve. The second method utilizes a least-squares algorithm to get an equivalent time delay together with the values of the other parameters. Thus, the obtained time delay approximates not only the true delay but also part of the nonlinear and the higher order dynamics. This is an advantage when a PID auto-tuning is sought. Two examples are provided to demonstrate and compare between the results of the methods.     

Robust identification of Wiener time-delay system with expectation-maximization algorithm

This paper considers the parameter estimation for Wiener time-delay systems with the output data contaminated with outliers. The time-delay and corrupted output data bring great challenges to the parameter estimation problem. The statistical model of the estimation problem is constructed based on the Laplace distribution and the identification problem is formulated in the scheme of the expectation-maximization (EM) algorithm. The negative effect of outliers imposed on the parameter estimation problem is sufficiently suppressed and the unknown time-delay and model parameters can be estimated simultaneously. The simulation example is given to demonstrate the effectiveness of the proposed algorithm.     

A novel learning algorithm of the neuro-fuzzy based Hammerstein–Wiener model corrupted by process noise

The Hammerstein–Wiener model is a nonlinear system with three blocks where a dynamic linear block is sandwiched between two static nonlinear blocks. For parameter learning of the Hammerstein–Wiener model, the synchronous parameter learning methods are proposed to learn the model parameters by constructing hybrid model of the three series block, such as over parameterization method, subspace method and maximum likelihood method. It should be pointed out that the aforementioned methods appeared the product term of model parameters in the process of parameter learning, and parameter separation method is further adopted to separate hybrid parameters, which increases the complexity of parameter learning. To address this issue, a novel three-stage parameter learning method of the neuro-fuzzy based Hammerstein–Wiener model corrupted by process noise using combined signals is developed in this paper. The combined signals are designed to completely separate the parameter learning issues of the static input nonlinear block, the linear dynamic block and the static output nonlinear block, which effectively simplifies the process of parameter learning of the Hammerstein–Wiener model. Parameter learning of the Hammerstein–Wiener model are summarized into the following three aspects: The first one is to learn the output static nonlinear block parameters using two sets of separable signals with different sizes. The second one is to estimate the linear dynamic block parameters by means of the correlation analysis method, the unmeasurable intermediate variable information problem is effectively handled. The final one is to determine the parameters of the static input nonlinear block and the moving average noise model using recursive extended least square scheme. The simulation results are presented to illustrate that the proposed learning approach yields high learning accuracy and good robustness for the Hammerstein–Wiener model corrupted by process noise.     

洛特卡参数的新估计法

洛特卡定律是文献计量学的重要理论基础,是文献计量学的三大定律之一。借助它人们可以了解作者发文的结构。广义洛特卡定律是含约束条件的模型,它的参数估计较为复杂,帕欧提出了近似估计法,但其法仍较为复杂,且参数估计方法不科学。为了科学地估计参数本文在帕欧估计结果的基础上,通过回归法给出了更为简单、更为科学的估计法。     

On the Computation of Functionals Over Sample Paths of a Randomly Rotating Rigid Body

This paper deals with the computation of the values of two functionals which are defined over the sample paths of a randomly rotating rigid body. It is assumed that the body is subjected to two different kinds of perturbation. The first kind of perturbation is represented by the standard Wiener process and the second kind by a homogeneous process with independent increments, finite second-order moments, mean zero and no continuous sample functions. In order to measure quantitatively the stochastic stability of the body's motion, two functionals are defined over its sample paths. It is shown that each of these functionals is a solution to a corresponding partial integro-differential equation. A numerical procedure for the solution of these equations is suggested, and its efficiency and applicability are demonstrated with examples.     

Identification of Wiener–Hammerstein models based on variational bayesian approach in the presence of process noise

This paper addresses the identification of Wiener–Hammerstein (WH) models in the presence of process and measurement noises, which has not been well studied yet in the existing works. To achieve an unbiased estimation, the model parameters are obtained by maximizing the likelihood function, which is solved in the expectation-maximization framework. Due to the difficulty of computing the posterior distributions of the latent variables of WH models, variational Bayes (VB) is used here, and a method for approximating the posterior distributions based on Monte Carlo integral is proposed in VB framework. To the best of our knowledge, it is the first time to use VB approach for WH model identification. Two simulation examples demonstrate the effectiveness of the proposed method. Moreover, the proposed method is used for a WH benchmark problem, and the results show that it improves the identification performance.     

基于四阶累积量的CSPRIT算法

分析了基于二阶统计的CSPRIT算法在空间相关高斯噪声环境中存在的问题，提出将四阶累积量与CSPRIT算法相结合，处理一维二元相移键控信号（BPSK）和多元幅移键控信号（MASK），实现信号到达角（DOA）的估计和波束形成器的构造。与基于二阶统计的CSPRIT算法相比，基于四阶累积量的改进算法能够有效抑制空间相关的高斯噪声，提高信号估计精度。计算机仿真验证了该算法的有效性。     

一类广义隐马尔科夫模型的建模与参数估计

隐马尔科夫模型在很多方面已有广泛应用.讨论了一类更为一般的模型,这类模型由Wojciech Pieczynski首次提出,并且给出了在图像识别中的应用.这里首次给出在离散观测和离散状态下该模型的精确数学描述,其中包括建模、状态估计和参数估计,这些算法都是首次被提出的.