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
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
In this paper, we consider the following semipaxametric regression model under fixed design： yi = xi′β＋g（xi）＋ei. The estimators of β, g（·） and σ^2 axe obtained by using the least squares and usual nonp...In this paper, we consider the following semipaxametric regression model under fixed design： yi = xi′β＋g（xi）＋ei. The estimators of β, g（·） and σ^2 axe obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.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.
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 Foundation of China(10571008)Supported by the Natural Science Foundation of Henan(0511013300)Supported by the National Science Foundation of Henan Education Department(2006110012)
文摘In this paper, we consider the following semipaxametric regression model under fixed design： yi = xi′β＋g（xi）＋ei. The estimators of β, g（·） and σ^2 axe obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.
