Transformation-based estimation

To alleviate the computational burden of making the relevant estimation algorithms stable for nonlinear and semiparametric regression models with, particularly, high-dimensional data, a transformation-based method combining sufficient dimension reduction approach is proposed. To this end, model-independent transformations are introduced to models under study. This generic methodology can be applied to transformation models; generalized linear models; and their corresponding quantile regression variants. The constructed estimates almost have closed forms in certain sense such that the above goals can be achieved. Simulation results show that, in finite sample cases with high-dimensional predictors and long-tailed distributions of error, the new estimates often exhibit a smaller degree of variance, and have much less computational burden than the classical methods such as the classical least squares and quantile regression estimation.     

Recursive Identification Methods for Multivariate Output-error Moving Average Systems Using the Auxiliary Model

This paper studies the parameter identification problems of multivariate output-error moving average systems. An auxiliary model based extended stochastic gradient algorithm and based recursive extended least squares algorithm are proposed for estimating the parameters of the multivariate output-error moving average systems. By using the multi-innovation identification theory, an auxiliary model based multi-innovation extended stochastic gradient algorithm is derived for improving the parameter estimation accuracy. Finally, the simulation results indicate that the proposed algorithms can work well.     

学习辨识:最小二乘算法及其重复一致性

针对重复时变系统, 提出学习辨识方法用于估计系统的时变参数. 讨论了有限时间作业区间上重复运行的时变系统以及周期时变系统两种情形. 文中给出最小二乘学习算法的推导过程, 并分析了所提算法的收敛性. 结果表明, 当重复持续激励条件成立时, 提出的学习算法具有重复一致性, 能够给出时变参数的完全估计. 通过数值算例进一步验证了学习算法的有效性.     

Hierarchical least squares identification methods for multivariable systems

For multivariable discrete-time systems described by transfer matrices, we develop a hierarchical least squares iterative (HLSI) algorithm and a hierarchical least squares (HLS) algorithm based on a hierarchical identification principle. We show that the parameter estimation error given by the HLSI algorithm converges to zero for the deterministic cases, and that the parameter estimates by the HLS algorithm consistently converge to the true parameters for the stochastic cases. The algorithms proposed have significant computational advantage over existing identification algorithms. Finally, we test the proposed algorithms on an example and show their effectiveness.     

A theoretical analysis of recursive identification methods

In this paper five different recursive identification methods will be analyzed and compared, namely recursive versions of the least squares method, the instrumental variable method, the generalized least squares method, the extended least squares method and the maximum likelihood method. They are shown to be similar in structure and need of computer storage and time. Making use of recently developed theory for asymptotic analysis of recursive stochastic algorithms, these methods are examined from a theoretical viewpoint. Possible convergence points and their global and local convergence properties are studied. The theoretical analysis is illustrated and supplemented by simulations.     

基于支持向量回归的光谱反射率重建方法

提出了一种基于支持向量回归和小框架核的光谱反射率重建方法。光谱反射率重建是光学研究的一个重要问题,其目的是通过各种成像设备所获取的与设备相关的RGB三色值重建出物体本身固有的与设备和光照都无关的光谱反射率。回归方法已经在这一领域取得了广泛应用,如基于多项式模型的正则化最小二乘方法、基于核的正则化最小二乘方法等。提出了一种新的光谱反射率重建方法,这种方法采用了一种可以减弱样本不规则噪音影响的小框架核函数,并将其用于支持向量回归来重建光谱反射率函数。实验表明,新方法可以提高光谱反射率重建的精度和稳定性。     

Least squares parameter estimation of continuous-time ARX modelsfrom discrete-time data

When modeling a system from discrete-time data, a continuous-time parameterization is desirable in some situations, In a direct estimation approach, the derivatives are approximated by appropriate differences. For an ARX model this lead to a linear regression. The well-known least squares method would then be very desirable since it can have good numerical properties and low computational burden, in particular for fast or nonuniform sampling. It is examined under what conditions a least squares fit for this linear regression will give adequate results for an ARX model. The choice of derivative approximation is crucial for this approach to be useful. Standard approximations like Euler backward or Euler forward cannot be used directly. The precise conditions on the derivative approximation are derived and analyzed. It is shown that if the highest order derivative is selected with care, a least squares estimate will be accurate. The theoretical analysis is complemented by some numerical examples which provide further insight into the choice of derivative approximation     

Convergence rates of continuous-time stochastic ELS parameter estimation

Discrete-time convergence rates for extended least squares (ELS) algorithms are generalized to the continuous-time case. An essential difference in the estimation is the appropriate prefiltering, while in the theory, the existence of solutions of the stochastic equations is a concern.     

多模型系统基于黄金分割法的参数估计

利用变点统计学和黄金分割法讨论具有跳变参数的多模型离散线性动态系统的参数估计。提出基于黄金分割法搜索最佳变点估计（参数变化时间）和同时得到参数估计的最小二乘算法。理论分析和计算机仿真结果表明，该算法具有较好的收敛性并能得到良好的变点及参数的估计值。     

时变参数遗忘梯度估计算法的收敛性

提出了时变随机系统的遗忘梯度辨识算法,并运用随机过程理论研究了算法的收敛 性.分析表明,遗忘梯度算法的性能类似于遗忘因子最小二乘法,可以跟踪时变参数,但计算量 要小得多,且数据的平稳性可以减小参数估计误差上界和提高辨识精度.阐述了最佳遗忘因子 的选择方法,以获得最小参数估计上界.对于确定性时不变系统,遗忘梯度算法是指数速度收 敛的;对于时变或时不变随机系统,遗忘梯度算法的参数估计误差一致有上界.     

Fuzzy linear regression model based on fuzzy scalar product

The new concept and method of imposing imprecise (fuzzy) input and output data upon the conventional linear regression model is proposed in this paper. We introduce the fuzzy scalar (inner) product to formulate the fuzzy linear regression model. In order to invoke the conventional approach of linear regression analysis for real-valued data, we transact the α-level linear regression models of the fuzzy linear regression model. We construct the membership functions of fuzzy least squares estimators via the form of “Resolution Identity” which is a well-known formula in fuzzy sets theory. In order to obtain the membership value of any given least squares estimate taken from the fuzzy least squares estimator, we transform the original problem into the optimization problems. We also provide two computational procedures to solve the optimization problems.     

Parameter identification of wiener models by multi-innovation algorithms

An output nonlinear Wiener system is rewritten as a standard least squares form by reconstructing the input-output items of its difference equation. Multi-innovation based stochastic gradient (MISG) algorithm and its derivate algorithms are introduced to formulate identification methods of Wiener models. In order to increase the convergence performance of stochastic gradient (SG) algorithm, the scalar innovation in SG algorithm is expanded to an innovation vector which contains more information about input-output data. Furthermore, a proper forgetting factor for SG algorithm is introduced to get a faster convergence rates. The comparisons of convergence performance and estimation errors of proposed algorithms are illustrated by two numerical simulation examples.     

基于微分麦克风阵列的自适应语音增强算法研究及DSP实现

自适应滤波是语音增强算法中的常用技术, 而算法复杂度与收敛速度是设计各种自适应算法需要首要考虑的问题. 本文提出一种用于片上的语音增强自适应滤波新算法. 该算法分两步实现, 首先, 利用一阶微分麦克风阵列, 获得噪声的实时估计; 其次, 对传统的仿射投影算法(Affine projection algorithm, APA)加以改进, 得到计算误差向量的快速算法, 并根据估计误差动态调整搜索步长以及仿射投影维数, 对带噪语音进行自适应滤波消噪. 在TMS320VC5509 DSP芯片上实现该算法. 实验表明, 算法的自适应滤波过程具有接近递推最小二乘算法(Recursive least squares, RLS)的快速收敛速度, 以及类似最小均方误差算法(Least mean squares, LMS)的低算法复杂度.     

基于最小二乘算法的最优适应控制器

采用"输入匹配"的方法,建立了"一步超前"最小二乘算法,得以参数估计的收敛速度. 证明了闭环适应系统是全局稳定的,且适应控制收敛于"一步超前"最优控制.     

On parameter convergence in least squares identification and adaptive control

Least squares estimation is appealing in performance and robustness improvements of adaptive control. A strict condition termed persistent excitation (PE) needs to be satisfied to achieve parameter convergence in least squares estimation. This paper proposes a least squares identification and adaptive control strategy to achieve parameter convergence without the PE condition. A modified modeling error that utilizes online historical data together with instant data is constructed as additional feedback to update parameter estimates, and an integral transformation is introduced to avoid the time derivation of plant states in the modified modeling error. On the basis of these results, a regressor filtering–free least squares estimation law is proposed to guarantee exponential parameter convergence by an interval excitation condition, which is much weaker than the PE condition. And then, an identification‐based indirect adaptive control law is proposed to establish exponential stability of the closed‐loop system under the interval excitation condition. Illustrative results considering both identification and control problems have verified the effectiveness and superiority of the proposed approach.     

Algorithmic optimization method for effort estimation

This paper presents an improvement of an effort estimation method that can be used to predict the level of effort for software development projects. A new estimation approach based on a two-phase algorithm is used. In the first phase, we apply a calculation based on use case points (UCPs). In the second phase, we add correction values (a ₁, a ₂) obtained via least squares regression. This approach employs historical project data to refine the estimate. By applying the least squares regression approach, the algorithm filters out estimation errors caused by human factors and company practice.     

基于随机共振的基音周期估计方法

基音周期估计是语音处理和分析的最基本步骤。无论是做语音信号处理,语音压缩,还是语音识别,都要用到基音周期这一重要参数。文章基于随机共振的理论,提出了一种新的估计基音周期的方法。     

差分模型参数递推估计的Householder变换法

本文提出了利用Householder变换进行差分模型参数递推估计的新方法.并由该方法导 出了新的递推最小二乘法、递推增广矩阵法、递推广义最小二乘法、递推极大似然法. 文中分单变量、多变量两种情况重点讨论了新递推最小二乘法及其与传统递推最小二乘 法的比较,并给出了计算实例.     

Sampling Minimal Subsets with Large Spans for Robust Estimation

When sampling minimal subsets for robust parameter estimation, it is commonly known that obtaining an all-inlier minimal subset is not sufficient; the points therein should also have a large spatial extent. This paper investigates a theoretical basis behind this principle, based on a little known result which expresses the least squares regression as a weighted linear combination of all possible minimal subset estimates. It turns out that the weight of a minimal subset estimate is directly related to the span of the associated points. We then derive an analogous result for total least squares which, unlike ordinary least squares, corrects for errors in both dependent and independent variables. We establish the relevance of our result to computer vision by relating total least squares to geometric estimation techniques. As practical contributions, we elaborate why naive distance-based sampling fails as a strategy to maximise the span of all-inlier minimal subsets produced. In addition we propose a novel method which, unlike previous methods, can consciously target all-inlier minimal subsets with large spans.     

Frequency estimation of undamped exponential signals using genetic algorithms

In this paper, we consider the problem of frequency estimation of undamped superimposed exponential signals model. We propose two iterative techniques of frequency estimation using genetic algorithms. The proposed methods use an elitism based generational genetic algorithm for obtaining the least squares and the approximate least squares estimates. In the simulation studies, it is observed that the proposed methods give nearly efficient estimates, having mean square error almost attaining the corresponding Cramér-Rao lower bound. The proposed methods significantly do not depend on the initial guess values otherwise required for other iterative methods of frequency estimation. It is also observed that the proposed methods have fairly high breakdown point with respect to different types of outliers present in the data. Outlier robustness and accuracy of the proposed methods are compared with the classical approaches for this problem.