We will study the generalized Steklov-Robin eigenproblem (with possibly matrix weights) in which the spectral parameter is both in the system and on the boundary. The weights may be singular on subsets of positive mea...We will study the generalized Steklov-Robin eigenproblem (with possibly matrix weights) in which the spectral parameter is both in the system and on the boundary. The weights may be singular on subsets of positive measure. We prove the existence of an increasing unbounded sequence of eigenvalues. The method of proof makes use of variational arguments.展开更多
针对机动目标状态跟踪问题,认知雷达能够调整发射端波形来获取持续、稳健目标跟踪信息.本文基于矩阵加权多模型融合思想引入一种新的面向机动目标跟踪的认知雷达自适应波形设计方法(Adaptive waveform design method based on Matrix-we...针对机动目标状态跟踪问题,认知雷达能够调整发射端波形来获取持续、稳健目标跟踪信息.本文基于矩阵加权多模型融合思想引入一种新的面向机动目标跟踪的认知雷达自适应波形设计方法(Adaptive waveform design method based on Matrix-weighted Interacting Multiple Model,AMIMM).首先,利用多模型思路对机动目标状态进行建模,并考虑各模型目标状态估计及其误差协方差矩阵中元素间相关性,以矩阵加权融合方式代替传统概率加权方式,进而构造基于矩阵加权多模型信息融合的跟踪算法框架;然后,以多模型状态融合后的状态估计误差协方差矩阵为基准,利用特征值分解(Eigen Value Decomposition,EVD)技术求取融合后状态估计误差协方差矩阵对应椭圆参数;最后,通过分数阶傅里叶变换(fractional Fourier transform,FrFT)来旋转雷达量测误差椭圆,使得量测误差椭圆与融合后目标状态估计误差椭圆正交,从而获得下一时刻认知波形参数,实现波形自适应捷变.仿真实验表明,与当前流行多种算法相比,本文所提算法能够进一步提高机动目标跟踪精度和稳健性.展开更多
文摘We will study the generalized Steklov-Robin eigenproblem (with possibly matrix weights) in which the spectral parameter is both in the system and on the boundary. The weights may be singular on subsets of positive measure. We prove the existence of an increasing unbounded sequence of eigenvalues. The method of proof makes use of variational arguments.
文摘针对机动目标状态跟踪问题,认知雷达能够调整发射端波形来获取持续、稳健目标跟踪信息.本文基于矩阵加权多模型融合思想引入一种新的面向机动目标跟踪的认知雷达自适应波形设计方法(Adaptive waveform design method based on Matrix-weighted Interacting Multiple Model,AMIMM).首先,利用多模型思路对机动目标状态进行建模,并考虑各模型目标状态估计及其误差协方差矩阵中元素间相关性,以矩阵加权融合方式代替传统概率加权方式,进而构造基于矩阵加权多模型信息融合的跟踪算法框架;然后,以多模型状态融合后的状态估计误差协方差矩阵为基准,利用特征值分解(Eigen Value Decomposition,EVD)技术求取融合后状态估计误差协方差矩阵对应椭圆参数;最后,通过分数阶傅里叶变换(fractional Fourier transform,FrFT)来旋转雷达量测误差椭圆,使得量测误差椭圆与融合后目标状态估计误差椭圆正交,从而获得下一时刻认知波形参数,实现波形自适应捷变.仿真实验表明,与当前流行多种算法相比,本文所提算法能够进一步提高机动目标跟踪精度和稳健性.
