LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION

In this article, we study a least squares estimator （LSE） of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt＋dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s∈[0,t]} as t tends to infinity.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.

ERRATUM TO： LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION （ACTA MATHEMATICA SCIENTIA 2016,36B （2） ：394-408）

We give a correction of Theorem 2.2 of Shen, Yin and Yan （2016）.

STUDY ON FREQUENCY ESTIMATION BASED ON WEIGHTED LEAST SQUARE METHOD WITH THREE FOURIER COEFFICIENTS

In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered,the Fourier coefficients can be written as three equations about the amplitude,phase,and frequency,and the frequency is estimated by solving equations.Because of the error of measurement,weighted least square method is used to solve the frequency equation and get the signal frequency.It is shown that the proposed estimator can approach the Cramer-Rao Bound(CRB)with a low Signal-to-Noise Ratio(SNR)threshold and has a higher accuracy.

基于WLS-KF的UWB室内定位滤波算法研究

针对室内超宽带(UWB)定位过程中受到非视距误差(NLOS)干扰而导致定位精度下降的问题,提出了基于抗差估计原理的自适应卡尔曼滤波方法,结合加权最小二乘法对测距信息解算得到定位坐标。在通视环境下进行测距,利用测得的数据计算新息向量和协方差,并基于此构建阈值信息,对NLOS环境产生的量测异常值进行判别,在此基础上利用Sage-Husa滤波对系统噪声协方差进行估计。采用加权最小二乘法对测距信息进行处理,得到标签解算坐标的最优估计。通过MATLAB仿真验证算法的可行性和有效性并在室内环境下进行测距、定位试验验证。仿真和实验结果表明,基于抗差估计原理的自适应卡尔曼滤波方法,结合加权最小二乘法能有效识别NLOS误差,且对定位过程中发生的状态突变能有效进行跟踪,解算得到的标签坐标x方向误差1 cm左右,y方向误差2 cm左右,提高了UWB室内定位的精度。

A new method of weighted choice in InSAR Least Squares unwrapping

The decorelation phenomena such as Low-SNR radar signal, shadows and layover caused by topography etc, causes phase data discontinuous and makes the result of unwrapping phase inaccurate or completely wrong. Based on the analysis of influencing factors to the weight selection, this paper develops a new method to choose the weights based on the measurement of confidence in frequency domain. Results show that it is more precise and robust than other methods, and can make up for the defect of sub-estimate to the slope of least squares method.

Visualising data distributions with kernel density estimation and reduced chi-squared statistic

The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data.Two commonly used tools are the kernel density estimation and reduced chi-squared statistic used in combination with a weighted mean.Due to the wide applicability of these tools,we present a Java-based computer application called KDX to facilitate the visualization of data and the utilization of these numerical tools.

结合WLS滤波与还原控制因子的图像去雾

雾天退化图像的复原过程中,针对大气光幕和大气亮度估计不准确导致光晕效应、偏色现象和对比度不足等问题,提出一种结合WLS(weighted least square)滤波与还原控制因子的去雾算法.首先分析WLS滤波器的原理和性能,并用于大气光幕的有效提取;其次利用Sobel算子检测二值化图像边缘,将边缘数目与像素均值同时作为四叉树空间索引的依据,提高大气亮度的估计准确性;最后分析天空出现颜色失衡现象的原因,引入还原控制因子改善视觉效果.实验结果表明,去雾后图像的平均梯度整体提高58.03%,信息熵提高2.88%,运行时间节省50%以上.该方法对含有浓雾、薄雾以及天空等深度复杂的远景图像、近景图像均能得到高对比度、可视度和色彩保真度的恢复效果.

A new method of weight choice in InSAR least squares unwrapping

The de-coherence phenomena such as Low-SNR radar signal, shadows and layover caused by topography, etc. , causing phase data discontinuity, makes the result of unwrapping phase inaccuracy or even completely wrong. Based on the analysis of influencing factors to weight choice, this thesis develops a new method to choose the weights based on the measure of the confidence in the frequency domain. Experiments show that it could overcome the defect of sub-estimate to the slope of least squares method very well, which has a better rationale, stability and performance.

基于多准则分区和WLS-PDIPM算法的有源配电网状态估计

针对复杂有源配电网三相不平衡状态估计计算速度较慢与计算精度较低的问题,提出了一种基于多准则分区和基本加权最小二乘法—原对偶内点法(WLS-PDIPM)混合算法的状态估计方法。基于对有源配电网中实时量测、虚拟量测和伪量测的配置分析,建立了适用于复杂有源配电网状态估计的多准则分区优化模型,该模型综合考虑了分区后各子区域规模均衡、量测冗余度均衡及伪量测平均误差均衡。通过高级量测体系(AMI)全量测点实现各子区域完全解耦,有效减小了系统规模和雅可比矩阵阶数。所提方法将WLS与PDIPM的优点相结合,在提高算法精度的同时减少了计算时间。仿真算例结果表明所提方法可实现对复杂有源配电网的合理分区,有效提高了状态估计的计算速度与求解精度。

基于MPSO-WLS-SVM的矿井瓦斯涌出量预测模型研究

为有效预防瓦斯灾害,以预测矿井瓦斯涌出量为研究目的,提出经改进的粒子群算法(MPSO)优化的加权最小二乘支持向量机(WLS-SVM),并用其预测非线性动态瓦斯涌出量。算法通过对WLS-SVM的正则化参数C和高斯核参数σ寻优,建立基于MPSO优化的WLS-SVM的瓦斯涌出量预测模型,并利用某矿井监测到的各项历史数据进行实例分析。试验结果表明:该预测模型预测的最大相对误差为5.99%,最小相对误差为0.43%,平均相对误差为2.95%,较其他预测模型有更强的泛化能力和更高的预测精度。

基于WLS-SVM回归模型的电力负荷预测

针对电力系统年用电量增长的特点,提出一种基于加权最小二乘支持向量机(LS-SVM)的电力负荷预测模型。与标准LS-SVM的电力预测方法比较,该模型能通过设置训练样本权重比例,实现样本优化选择,达到历史数据"重近轻远"的学习效果,从而能有效提高预测精度。通过具体实例验证,WLS-SVM模型预测精度明显优于标准LS-SVM模型,说明本文模型实现容易,鲁棒性好,预测精度高。

基于WLS-SVM的加速度计动态模型参数辩识

提高加速度计动态模型参数辨识精度,对研究和改善加速度计动态特性有重要作用。针对加速度计的非线性影响其动态模型参数辨识精度的问题,提出了一种基于加权最小二乘(WLS)和支持向量机(SVM)的加速度计动态模型参数辩识方法,该方法针对包含线性部分和非线性项的加速度计二阶非线性动态模型,利用WLS辩识加速度计动态模型的线性部分参数,并采用SVM估计加速度计动态模型的非线性特性,通过迭代和最小化所构建的误差准则函数,实现加速度计动态模型参数最优辨识。仿真实验和加速度计绝对法冲击激励校准实验表明,该方法能够减小加速度计非线性对动态模型参数辩识精度的影响,所得加速度计动态模型参数辨识结果具有较高的精度。

基于WLS-SVM标准差σ预测的产品过程质量控制方法研究

及时、准确地预测加工过程产品质量标准差σ,对于及时判断工序状态、调整加工过程因素,进而提高产品过程质量等具有重要意义。文章提出了一种基于加权最小二乘支持向量机(WLS-SVM)的时间序列预测新方法,该方法采用了结构风险最小化原则,较好地避免了人工神经网络等智能方法在小样本学习、预测过程中存在的过学习、泛化能力弱等缺点;并采用"重近轻远"的权重设置原则,提高了预测的精度。实验表明,采用该方法对产品过程质量标准差σ进行预测切实可行,对于产品过程质量控制具有重要意义。

基于WPA与WLS-SVM方法的化工过程故障诊断

化工过程存在变量多,系统复杂,非线性等特点,这使得常规的故障诊断方法具有模型难以建立、参数难以调整、收敛速度慢、多故障无法正确识别等局限性。以标准化模型TE过程为实验平台,结合模型特点以及在故障诊断中的难点,采用小波包算法(WPA)滤除过程数据噪声,恢复原始信号,数据缩放统一数据量度,最小二乘支持向量机(WLS-SVM)为模型,K聚类方法确定权值系数,交叉验证来选择模型参数,提出了一系列具体的解决方案。通过仿真实验,验证了算法的有效性,以及在过程故障诊断中的可行性,并在最后提出了一些展望。

基于WLSE-KF的传感器融合定位算法研究

多传感器融合在定位中的应用越来越广泛。在利用这些传感器进行定位的过程中,需要对其采集的数据进行融合。射频识别融合定位一般采用最小二乘法,然而,它可能使定位误差较大。文中提出了将最小二乘和卡尔曼滤波相结合的算法。该算法先利用加权最小二乘估计获得移动用户的初步位置,再利用扩展卡尔曼滤波进一步使定位精度得到提高。仿真结果表明该算法相比多种传统定位算法,误差减少,定位精度明显提高。

基于WLS-SVM的变速风力机有效风速估计

控制技术是大型变速恒频风力发电机组安全高效运行的关键。有效风速的精确估计可以提高风力发电机组的控制性能。由于风力机处于三维时变的风场环境中,风速在整个风力机旋转平面上分布不同,风速计测量得到的风速和整个风力机旋转平面所受到的有效风速有很大差别,因此有效风速是不能直接测量的。采用加权最小二乘支持向量机(WLS-SVM)对有效风速进行预估。仿真结果表明,该算法具有很高的估计精度,有效风速估计值能较好地跟踪有效风速的变化趋势。

Ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints

The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

基于APSO–WLS–SVM的含瓦斯煤渗透率预测模型

为了较准确预测含瓦斯煤渗透率,有效预防瓦斯安全事故,提出自适应粒子群算法(APSO)优化的加权最小二乘法支持向量机(WLS–SVM)算法。根据对含瓦斯煤渗透率的相关理论及文献研究分析,选取有效应力、瓦斯压力、温度和抗压强度作为主要特征指标,采用APSO算法对WLS–SVM模型的组合参数(C、σ)寻优,建立APSO–WLS–SVM含瓦斯煤渗透率预测模型。结合现场实测资料中的40组数据作为训练样本,其余10组为预测样本,对该模型进行训练与检验,并将其预测结果与利用PSO–WLS–SVM和WLS–SVM模型的预测结果进行对比。结果表明:APSO-WLS-SVM模型的预测效果优于另外2个模型,提高了煤体渗透率的预测性能与泛化能力。

对基于贝叶斯证据框架下WLS-SVM中期负荷预测的研究

本文提出了一种基于贝叶斯证据框架下加权最小二乘支持向量机(Weighted Least Squares Support Vector Machine,WLS-SVM)的短期负荷预测模型和算法。在对历史负荷数据进行完预处理基础上,分析影响负荷变化的重要因素,然后选择最佳的输入数据作为LS-SVM训练模型的输入向量。通过贝叶斯证据三层推断寻找到模型的最佳参数:第一层推断确定LS-SVM的权向量w和偏置值b,第二层推断确定模型的超参数γ,第三层推断确定核函数的超参数σ。为了提高模型的鲁棒性,赋予了每个样本误差不同的权系数,建立了具有良好泛化性能的WLS-SVM回归模型,从而进一步提高了模型预测的精度。采用上述方法对一固定预测区电网中期负荷进行了预测,结果证明了该方法具有良好的预测效果。