In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation...In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.展开更多
A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Fu...A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Furthermore,the exact solutions of (2+1)-dimensional BKP equation are obtained through symmetry analysis.展开更多
Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）-...Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）- dimensional dispersive long-wave equations are obtained.展开更多
This paper extends the Non-Circular MUltiple SIgnal Classification(MUSIC)(NC-MUSIC) method for the common array geometries including Uniform Circular Arrays(UCAs) and Uniform Rectangular Arrays(URAs),which enables the...This paper extends the Non-Circular MUltiple SIgnal Classification(MUSIC)(NC-MUSIC) method for the common array geometries including Uniform Circular Arrays(UCAs) and Uniform Rectangular Arrays(URAs),which enables the algorithm to estimate 2-D Direction Of Arrival(DOA).A comparison between UCAs and URAs of NC-MUSIC is made in this paper.The simulations show that the NC-MUSIC method doubles the maximum estimation number of standard MUSIC.Using non-circular signals,the performance of URAs is improved remarkably while the improvement of UCAs is not so significantly.Moreover,the influence of arrays structures on the NC-MUSIC method is discussed.展开更多
The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model. To find some exact solutions of a nonintegrable model with some arbitrary paramete...The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model. To find some exact solutions of a nonintegrable model with some arbitrary parameters is much more difficult than to find the solutions of a model with some special parameters. In this paper, we make a modification for the usual direct method to find some conditional similarity solutions of a (2+1)-dimensional general nonintegrable KdV equation.展开更多
针对传统联合估计方法计算量大、需要多维谱峰搜索的问题,该文提出了一种基于垂直阵列结构的任意初始相位非圆信号2维DOA(Direction Of Arrival)和初相联合估计方法,利用垂直阵列特点,将3维参数估计问题转化为可并行处理的3个2维参数估...针对传统联合估计方法计算量大、需要多维谱峰搜索的问题,该文提出了一种基于垂直阵列结构的任意初始相位非圆信号2维DOA(Direction Of Arrival)和初相联合估计方法,利用垂直阵列特点,将3维参数估计问题转化为可并行处理的3个2维参数估计,在每一个子阵上,同时使用噪声子空间正交性和信号子空间旋转不变性,将2维参数估计进一步转化为1维估计问题,最终只需要对扩展协方差矩阵进行一次特征分解即可实现2维DOA和初相的联合估计及自动配对。该方法适用于空间信源处于过载的情形和低信噪比、短快拍环境,可估计信源数为2(M-1)。数值仿真验证了该算法的有效性。展开更多
为了降低二维MUSIC(Two Dimensional Multiple Signal Classification,2-D MUSIC)算法的计算量,提高算法的实时处理能力,基于噪声子空间映射思想提出了一种适用于任意平面阵列结构的二维波达角(Direction Of Arrival,DOA)快速估计算法....为了降低二维MUSIC(Two Dimensional Multiple Signal Classification,2-D MUSIC)算法的计算量,提高算法的实时处理能力,基于噪声子空间映射思想提出了一种适用于任意平面阵列结构的二维波达角(Direction Of Arrival,DOA)快速估计算法.新算法利用空间角度划分及非线性变换将信号子空间与噪声子空间的正交性等价地压缩至某个角度分片内,使得真实DOA在该角度分片内产生虚拟镜像,通过搜索该角度分片得到虚拟DOA,最后利用数学式直接计算得到真实DOA.理论分析和实验结果表明新算法能够成倍地提高DOA估计的速度,同时具有比MUSIC算法更高的空间分辨率.展开更多
根据均匀圆阵阵列结构的特点,提出一种利用相邻阵元间相位差进行二维波达方向(direction of ar-rival,DOA)估计的方法。分析了均匀圆阵相邻阵元间接收信号相位差的变化规律,得出了其与入射信号的方位角和俯仰角的对应关系,在此基础上推...根据均匀圆阵阵列结构的特点,提出一种利用相邻阵元间相位差进行二维波达方向(direction of ar-rival,DOA)估计的方法。分析了均匀圆阵相邻阵元间接收信号相位差的变化规律,得出了其与入射信号的方位角和俯仰角的对应关系,在此基础上推导出入射信号方位角和俯仰角的闭式解。同时,针对相位差测量中存在相位模糊的问题,提出一种循环搜索算法有效地实现了相位差的解模糊,极大地提高了利用相位差进行DOA估计的稳健性和适用范围。理论分析和仿真结果表明,该二维DOA估计方法可以在存在相位模糊的情况下稳健有效地工作。展开更多
直接将压缩感知(compressed sensing,CS)思想应用到相干信源二维波达方向(direction of arrival,DOA)估计中会带来高计算复杂度的问题。为了解决这一问题,提出了一种基于降维稀疏重构的二维DOA估计方法,该方法利用特殊阵列结构将二维冗...直接将压缩感知(compressed sensing,CS)思想应用到相干信源二维波达方向(direction of arrival,DOA)估计中会带来高计算复杂度的问题。为了解决这一问题,提出了一种基于降维稀疏重构的二维DOA估计方法,该方法利用特殊阵列结构将二维冗余字典构建问题转化为一维冗余字典的构建,同时提出了一种基于子字典空间谱重构的配对算法,从而在极大降低算法计算复杂度的同时,提高了配对成功概率。仿真结果表明,该方法对相干信源具有接近于克拉美罗下界(Cramér-Rao lower bound,CRLB)的估计性能,即使是在低信噪比、少快拍数和小角度间隔的情况下,仍有良好的估计性能。展开更多
针对常规十字阵子阵间互耦不易处理这一问题,设计一种立体十字型阵列,并在该阵列基础上,提出立体十字型互耦阵列传播算子(propagation method for tridimensional cross array in presence of mutual coupling,TCA-MC-PM)算法。该算法...针对常规十字阵子阵间互耦不易处理这一问题,设计一种立体十字型阵列,并在该阵列基础上,提出立体十字型互耦阵列传播算子(propagation method for tridimensional cross array in presence of mutual coupling,TCA-MC-PM)算法。该算法首先分别从子阵中选取部分合适阵元构成阵列,将理想导向向量与互耦系数剥离,利用信号子空间与理想导向向量张成同一空间这一关系估计方位角与俯仰角,接着通过子空间与秩损原理估算互耦系数,最后利用整个阵列的空间谱函数完成方位角和俯仰角的配对。在此过程中涉及的子空间都以阵列的传播算子构建,可避免特征分解,降低运算量。仿真表明,本文提出的算法不涉及空间谱搜索,运算量小,有效抑制互耦影响,测量精度高。展开更多
结合干涉雷达的天线结构和二维波达方向(direction of arrival,DOA)估计方法,提出一种基于二维干涉式幅相估计的分布式相参阵盲DOA估计算法。利用二维干涉式幅相估计算法的空间谱和模型阶数选择准则获得目标个数和目标方向余弦的粗估计...结合干涉雷达的天线结构和二维波达方向(direction of arrival,DOA)估计方法,提出一种基于二维干涉式幅相估计的分布式相参阵盲DOA估计算法。利用二维干涉式幅相估计算法的空间谱和模型阶数选择准则获得目标个数和目标方向余弦的粗估计;使用子阵间的相位中心偏移来获得目标方向余弦的精估计;针对分布孔径带来的测角模糊问题,采用双尺度解模糊算法实现分布式阵列的高精度方向估计。仿真结果验证了分布式相参阵的高精度测角性能及所提算法的有效性,也验证了分布阵DOA估计中存在基线模糊门限。展开更多
针对配对算法中可能出现的配对错误及运算量较大的问题,提出一种基于双L型阵列的三角函数配对法。首先用一维波达方向(direction of arrival,DOA)算法得到由仰角和方位角三角函数组成的向量,而后利用双L型的阵形特点和三角函数之间的关...针对配对算法中可能出现的配对错误及运算量较大的问题,提出一种基于双L型阵列的三角函数配对法。首先用一维波达方向(direction of arrival,DOA)算法得到由仰角和方位角三角函数组成的向量,而后利用双L型的阵形特点和三角函数之间的关系完成配对过程,有效地解决了不同信源之间的仰角和方位角之差较接近时所出现的配对错误。此方法在不依赖于信号形式和一维估计方法的前提下,提高了配对检测概率和估计精度,同时大大降低了运算量。仿真结果证实了算法在配对成功率和估计性能上的提高。展开更多
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.
基金National Natural Science Foundation of China under Grant Nos.90203001,90503006,0475055,and 10647112the Foundation of Donghua University
文摘A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Furthermore,the exact solutions of (2+1)-dimensional BKP equation are obtained through symmetry analysis.
基金supported by the Natural Science Foundation of Shandong Province of China under Grant Nos.Q2005A01
文摘Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）- dimensional dispersive long-wave equations are obtained.
文摘This paper extends the Non-Circular MUltiple SIgnal Classification(MUSIC)(NC-MUSIC) method for the common array geometries including Uniform Circular Arrays(UCAs) and Uniform Rectangular Arrays(URAs),which enables the algorithm to estimate 2-D Direction Of Arrival(DOA).A comparison between UCAs and URAs of NC-MUSIC is made in this paper.The simulations show that the NC-MUSIC method doubles the maximum estimation number of standard MUSIC.Using non-circular signals,the performance of URAs is improved remarkably while the improvement of UCAs is not so significantly.Moreover,the influence of arrays structures on the NC-MUSIC method is discussed.
文摘The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model. To find some exact solutions of a nonintegrable model with some arbitrary parameters is much more difficult than to find the solutions of a model with some special parameters. In this paper, we make a modification for the usual direct method to find some conditional similarity solutions of a (2+1)-dimensional general nonintegrable KdV equation.
文摘针对传统联合估计方法计算量大、需要多维谱峰搜索的问题,该文提出了一种基于垂直阵列结构的任意初始相位非圆信号2维DOA(Direction Of Arrival)和初相联合估计方法,利用垂直阵列特点,将3维参数估计问题转化为可并行处理的3个2维参数估计,在每一个子阵上,同时使用噪声子空间正交性和信号子空间旋转不变性,将2维参数估计进一步转化为1维估计问题,最终只需要对扩展协方差矩阵进行一次特征分解即可实现2维DOA和初相的联合估计及自动配对。该方法适用于空间信源处于过载的情形和低信噪比、短快拍环境,可估计信源数为2(M-1)。数值仿真验证了该算法的有效性。
文摘为了降低二维MUSIC(Two Dimensional Multiple Signal Classification,2-D MUSIC)算法的计算量,提高算法的实时处理能力,基于噪声子空间映射思想提出了一种适用于任意平面阵列结构的二维波达角(Direction Of Arrival,DOA)快速估计算法.新算法利用空间角度划分及非线性变换将信号子空间与噪声子空间的正交性等价地压缩至某个角度分片内,使得真实DOA在该角度分片内产生虚拟镜像,通过搜索该角度分片得到虚拟DOA,最后利用数学式直接计算得到真实DOA.理论分析和实验结果表明新算法能够成倍地提高DOA估计的速度,同时具有比MUSIC算法更高的空间分辨率.
文摘根据均匀圆阵阵列结构的特点,提出一种利用相邻阵元间相位差进行二维波达方向(direction of ar-rival,DOA)估计的方法。分析了均匀圆阵相邻阵元间接收信号相位差的变化规律,得出了其与入射信号的方位角和俯仰角的对应关系,在此基础上推导出入射信号方位角和俯仰角的闭式解。同时,针对相位差测量中存在相位模糊的问题,提出一种循环搜索算法有效地实现了相位差的解模糊,极大地提高了利用相位差进行DOA估计的稳健性和适用范围。理论分析和仿真结果表明,该二维DOA估计方法可以在存在相位模糊的情况下稳健有效地工作。
文摘针对常规十字阵子阵间互耦不易处理这一问题,设计一种立体十字型阵列,并在该阵列基础上,提出立体十字型互耦阵列传播算子(propagation method for tridimensional cross array in presence of mutual coupling,TCA-MC-PM)算法。该算法首先分别从子阵中选取部分合适阵元构成阵列,将理想导向向量与互耦系数剥离,利用信号子空间与理想导向向量张成同一空间这一关系估计方位角与俯仰角,接着通过子空间与秩损原理估算互耦系数,最后利用整个阵列的空间谱函数完成方位角和俯仰角的配对。在此过程中涉及的子空间都以阵列的传播算子构建,可避免特征分解,降低运算量。仿真表明,本文提出的算法不涉及空间谱搜索,运算量小,有效抑制互耦影响,测量精度高。
文摘结合干涉雷达的天线结构和二维波达方向(direction of arrival,DOA)估计方法,提出一种基于二维干涉式幅相估计的分布式相参阵盲DOA估计算法。利用二维干涉式幅相估计算法的空间谱和模型阶数选择准则获得目标个数和目标方向余弦的粗估计;使用子阵间的相位中心偏移来获得目标方向余弦的精估计;针对分布孔径带来的测角模糊问题,采用双尺度解模糊算法实现分布式阵列的高精度方向估计。仿真结果验证了分布式相参阵的高精度测角性能及所提算法的有效性,也验证了分布阵DOA估计中存在基线模糊门限。
文摘针对配对算法中可能出现的配对错误及运算量较大的问题,提出一种基于双L型阵列的三角函数配对法。首先用一维波达方向(direction of arrival,DOA)算法得到由仰角和方位角三角函数组成的向量,而后利用双L型的阵形特点和三角函数之间的关系完成配对过程,有效地解决了不同信源之间的仰角和方位角之差较接近时所出现的配对错误。此方法在不依赖于信号形式和一维估计方法的前提下,提高了配对检测概率和估计精度,同时大大降低了运算量。仿真结果证实了算法在配对成功率和估计性能上的提高。
