为了提高非线性变换的近似精度,提出了一种高阶无迹变换(High orderUnscented Transform,HUT)机制,利用HUT确定采样点并进行数值积分去近似状态的后验概率密度函数,建立了高阶无迹卡尔曼滤波(High-order UnscentedKalman Filter,HUKF)算...为了提高非线性变换的近似精度,提出了一种高阶无迹变换(High orderUnscented Transform,HUT)机制,利用HUT确定采样点并进行数值积分去近似状态的后验概率密度函数,建立了高阶无迹卡尔曼滤波(High-order UnscentedKalman Filter,HUKF)算法.进一步的为了解决非线性、非高斯系统的状态估计问题,将HUKF与高斯和滤波(Gaussian Sum Filter,GSF)相结合,提出了一种高斯和高阶无迹卡尔曼滤波算法(Gaussian Sum High order Unscented Kalman filter,GS-HUKF),该算法的核心思想是利用一组高斯分布的和去近似状态的后验概率密度,同时针对每一个高斯分布采用高阶无迹卡尔曼滤波算法进行估计.数值仿真实验结果表明,提出的HUT机制与普通的无迹变换(Unscented Transform,UT)相比,具有更高的近似精度;提出的GS-HUKF与传统的GSF以及高斯和粒子滤波器(Gaussian Sum Particle Filter,GS-PF)相比,兼容了二者的优点,即具有计算复杂度低和估计精度高的特性.展开更多
We continue our study on classification learning algorithms generated by Tikhonov regularization schemes associated with Gaussian kernels and general convex loss functions. Our main purpose of this paper is to improve...We continue our study on classification learning algorithms generated by Tikhonov regularization schemes associated with Gaussian kernels and general convex loss functions. Our main purpose of this paper is to improve error bounds by presenting a new comparison theorem associated with general convex loss functions and Tsybakov noise conditions. Some concrete examples are provided to illustrate the improved learning rates which demonstrate the effect of various loss functions for learning algorithms. In our analysis, the convexity of the loss functions plays a central role.展开更多
Several new series of approximately mutually unbiased bases are constructed by using Gauss sums and Jacobi sums over Galois rings GR(p2, r), and the tensor method.
文摘为了提高非线性变换的近似精度,提出了一种高阶无迹变换(High orderUnscented Transform,HUT)机制,利用HUT确定采样点并进行数值积分去近似状态的后验概率密度函数,建立了高阶无迹卡尔曼滤波(High-order UnscentedKalman Filter,HUKF)算法.进一步的为了解决非线性、非高斯系统的状态估计问题,将HUKF与高斯和滤波(Gaussian Sum Filter,GSF)相结合,提出了一种高斯和高阶无迹卡尔曼滤波算法(Gaussian Sum High order Unscented Kalman filter,GS-HUKF),该算法的核心思想是利用一组高斯分布的和去近似状态的后验概率密度,同时针对每一个高斯分布采用高阶无迹卡尔曼滤波算法进行估计.数值仿真实验结果表明,提出的HUT机制与普通的无迹变换(Unscented Transform,UT)相比,具有更高的近似精度;提出的GS-HUKF与传统的GSF以及高斯和粒子滤波器(Gaussian Sum Particle Filter,GS-PF)相比,兼容了二者的优点,即具有计算复杂度低和估计精度高的特性.
文摘We continue our study on classification learning algorithms generated by Tikhonov regularization schemes associated with Gaussian kernels and general convex loss functions. Our main purpose of this paper is to improve error bounds by presenting a new comparison theorem associated with general convex loss functions and Tsybakov noise conditions. Some concrete examples are provided to illustrate the improved learning rates which demonstrate the effect of various loss functions for learning algorithms. In our analysis, the convexity of the loss functions plays a central role.
基金supported by the Natural Science Foundation of China under Grant No.61370089the Tsinghua National Laboratory for Information Science and Technology+1 种基金by the Fundamental Research Funds for the Central Universities under Grant No.JZ2014HGBZ0349by Science and Technology on Information Assurance Lab.KJ-12-01
文摘Several new series of approximately mutually unbiased bases are constructed by using Gauss sums and Jacobi sums over Galois rings GR(p2, r), and the tensor method.
