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...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.展开更多
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 matri...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.展开更多
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 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.展开更多
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...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.展开更多
为提高非视距场景下超宽带(ultra‑wideband,UWB)定位精度,本文提出一种基于误差因子的改进加权最小二乘(weighted least square,WLS)算法.该算法利用测距值和实时信道冲激响应特征训练1维卷积神经网络,实现误差因子的准确预测;基于预测...为提高非视距场景下超宽带(ultra‑wideband,UWB)定位精度,本文提出一种基于误差因子的改进加权最小二乘(weighted least square,WLS)算法.该算法利用测距值和实时信道冲激响应特征训练1维卷积神经网络,实现误差因子的准确预测;基于预测得到的误差因子设计改进WLS算法的加权矩阵,赋予不同基站合理的权重,以改善非视距场景下UWB定位性能.通过实测采集静态和动态定位数据对改进WLS算法进行性能验证.实验结果表明:视距场景下,改进WLS算法与最小二乘(least square,LS)算法、WLS算法定位性能相近;非视距场景下,改进WLS算法明显优于LS算法、WLS算法,能够有效抑制非视距误差.展开更多
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. Bas...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.展开更多
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 c...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.展开更多
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...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。展开更多
基金supported by the National Natural Science Foundation of China(11271020)the Distinguished Young Scholars Foundation of Anhui Province(1608085J06)supported by the National Natural Science Foundation of China(11171062)
文摘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.
基金This work is supported by Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX18_0467)Jiangsu Province,China.During the revision of this paper,the author is supported by China Scholarship Council(No.201906840021)China to continue some research related to data processing.
文摘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.
基金supported by the National Natural Science Foundation(40874001)Key Laboratory of Surveying and Mapping Technology on Island and Reef,State Bureau of Surveying and Mapping(2010A01)
文摘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.
文摘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.
文摘为提高非视距场景下超宽带(ultra‑wideband,UWB)定位精度,本文提出一种基于误差因子的改进加权最小二乘(weighted least square,WLS)算法.该算法利用测距值和实时信道冲激响应特征训练1维卷积神经网络,实现误差因子的准确预测;基于预测得到的误差因子设计改进WLS算法的加权矩阵,赋予不同基站合理的权重,以改善非视距场景下UWB定位性能.通过实测采集静态和动态定位数据对改进WLS算法进行性能验证.实验结果表明:视距场景下,改进WLS算法与最小二乘(least square,LS)算法、WLS算法定位性能相近;非视距场景下,改进WLS算法明显优于LS算法、WLS算法,能够有效抑制非视距误差.
基金supported by the National Natural Science Fundation of China(40874001)Key Laboratory of Surveying and Mapping Technology on Island and Reef,National Administration of Surveying,Mapping and Geoinformation(2010A01)
文摘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.
文摘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.
文摘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。
