SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEMS FOR SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS ON INFINITE INTERVAL(Ⅱ)

In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameteris examined, where are constants, and i=0,1 . Moreover, asymptotic estimates of the solutions for the above problems are given.

Some Simple Estimates for the Singular Values of Matrices

We first provide a simple estimate for || A-1||∞and||A-1||1 of a strictly diagonally dominant matrix A. On the Basis of the result, we obtain an estimate for the smallest singular value of A. Secondly, by scaling with a positive diagonal matrix D, we obtain some simple estimates for the smallest singular value of an H-matrix, which is not necessarily positive definite. Finally, we give some examples to show the effectiveness of the new bounds.

奇异值分解五阶容积卡尔曼滤波汽车状态估计

针对三阶滤波对高维汽车非线性模型估计精度有限的问题,以电动汽车为研究对象,提出了一种基于奇异值分解的五阶容积卡尔曼滤波(SVD-FCKF)车辆状态估计器。首先基于Dugoff轮胎模型,构建高维非线性7自由度车辆动力学模型。然后根据三阶球面-径向容积规则将CKF拓展到五阶,使其具有五阶泰勒级数展开精度,同时利用奇异值分解代替传统Cholesky分解,提高估计器的鲁棒性。最后利用Carsim和Matlab/Simulink联合仿真平台对SVD-FCKF进行验证,结果表明:改进的SVD-FCKF估计器能够有效提高电动汽车纵向速度、侧向速度、质心侧偏角和四轮转速的估计精度和稳定性,多工况适应能力强,整体估计效果优于CKF估计器。研究结果为电动汽车主动安全研究提供了理论支撑,具有实际应用价值。

基于SVD的复数UKF及电力系统对称分量估计

电力系统对称分量的检测对于电力系统安全稳定的运行具有很重要的意义。利用复数域无迹卡尔曼滤波算法,对三相电压系统的正负序分量及频率进行了估计。为了提高复数无迹卡尔曼滤波的参数估计精度及算法稳定性,引入最优自适应因子并对预测协方差矩阵进行SVD分解,提出了基于SVD的自适应CUKF算法。为消除零序分量,对三相电压分量进行αβ变换,定义了复数形式的状态变量,建立了非线性状态方程及观测方程,实现了正序、负序对称分量估计。通过与普通复数域无迹卡尔曼滤波算法对比,所提研究方法在估计精度及收敛速度等方面优于传统无迹卡尔曼滤波方法。

基于SVD-K-means算法的软扩频信号伪码序列盲估计

针对通信中软扩频信号伪码序列盲估计困难的问题,提出一种奇异值分解(singular value decomposition,SVD)和K-means聚类相结合的方法。该方法先对接收信号按照一倍伪码周期进行不重叠分段构造数据矩阵。其次对数据矩阵和相似性矩阵分别进行SVD完成对伪码序列集合规模数的估计、数据降噪、粗分类以及初始聚类中心的选取。最后通过K-means算法优化分类结果,得到伪码序列的估计值。该算法在聚类之前事先确定聚类数目,大大减少了迭代次数。同时实验结果表明,该算法在信息码元分组小于5 bit,信噪比大于-10 dB时可以准确估计出软扩频信号的伪码序列,性能较同类算法有所提升。

稀疏阵列的鲁棒矩阵填充DOA估计算法

稀疏阵列布阵灵活,增大阵列孔径的同时还能减少阵元间耦合,但基于稀疏阵列的传统波达方向估计会导致角度模糊混叠,带来估计精度差和稳健性不足的问题。针对以上问题,提出一种适用于稀疏阵列波达方向估计的加权截断奇异值投影(weighted truncated singular value projection,WT-SVP)的鲁棒矩阵填充算法。在填充迭代过程中根据奇异值的大小分配权重,突出大奇异值包含的阵列信息,减少小奇异值中不必要的噪声信息,从而优化传统奇异值投影算法。该算法可以实现稀疏阵列的孔洞信息恢复,对不连续阵元充分利用,同时WT-SVP填充算法实现了稀疏阵列波达方向估计的高精度、高分辨以及在低信噪比、低快拍时的高鲁棒性。

Optimal L_∞ Estimates for Galerkin Methods for Nonlinear Singular Two-point Boundary Value Problems

In this paper, we apply the symmetric Galerkin methods to the numerical solutions of a kind of singular linear two-point boundary value problems. We estimate the error in the maximum norm. For the sake of obtaining full superconvergence uniformly at all nodal points, we introduce local mesh refinements. Then we extend these results to a class of nonlinear problems. Finally, we present some numerical results which confirm our theoretical conclusions.

PCMA系统双同步序列联合盲估计

成对载波多址(Paired Carrier Multiple Access,PCMA)使用同一频率传输通信双方的调制波形,是一种重要的卫星通信多址方式。对PCMA信号进行盲分离是无线电频谱监测的重要内容,高精度的调制参数信息是盲分离的必要基础,同步序列辅助的调制参数估计方法具有精度高、鲁棒性好等特点。然而在PCMA信号的盲接收中,往往无法预知同步序列,且两路同步序列估计需要在无法完成分离解调的条件下得到,因此难度较大。本文针对幅相调制(Amplitude-Phase Modulation,APM)类PCMA信号,利用通信系统数据帧的结构特性,采用子空间分解思想,重点分析了不同条件下的信号相关矩阵奇异值分解(Singular Value Decomposition,SVD)结果,推导了特征值、特征向量与两路信号同步波形间的近似数学关系;提出“先整体后局部”的算法流程,首先对信号按帧长分段做整体SVD分解得到对同步波形及其位置的粗估计,而后对同步波形位置的原始PCMA信号做局部SVD分解,进一步提高估计性能,解决了PCMA信号盲接收中双同步序列估计的难题。仿真结果表明,本文算法可广泛适用于APM类PCMA信号的同步波形和同步序列盲估计问题,在低信噪比条件下算法性能优于最大似然的估计方法,随着信噪比的提升和使用数据量的增加,估计性能不断提高,能够得到对PCMA信号双同步序列的高精度估计,为数据辅助的参数估计方法应用于工程实践提供了先决条件,为PCMA信号调制参数估计和后续的盲分离技术研究提供重要基础。

一种奇异值分解与子空间加权联合的改进MUSIC算法

在低信噪比、小快拍数等非理想条件下,经典DOA估计算法对邻近目标的分辨率严重下降,甚至失去分辨能力。针对这一问题,提出了一种将重构的接收信号协方差矩阵进行奇异值分解并与改进的加权子空间方法相结合的改进算法。该算法充分利用互相关信息构建新的接收信号协方差矩阵,并对噪声子空间信息采用新的校正方法,对噪声特征值进行改造,之后对噪声子空间进行加权,最后与信号子空间加权技术相联合。仿真实验证明,改进算法在低信噪比和小快拍数条件下可以分辨间隔4°的相邻目标,统计分析表明该算法的分辨率明显优于经典MUSIC算法。

基于动态线损与奇异值分解的智能电表误差估计

利用远程数据分析对智能电表进行评估和异常检测,与传统的现场校准相比成本更低、效率更高,在电力行业得到了广泛的关注。基于此,提出一种基于动态线损估计与奇异值分解的智能电表在线误差估计方法。首先考虑负荷类型对线损估计的影响,建立估计误差求解方程;然后结合基于截断奇异值分解的正则化方法进行方程求解,获取智能电表误差估计结果;最后通过仿真及实际数据验证所提方法的有效性。结果表明,与其他方法相比,所提方法能够求解不适定问题,且具有更高的精度。

基于自适应平方根容积卡尔曼滤波算法的分布式驱动车辆状态估计

为了解决分布式驱动电动汽车在实时车辆行驶状态难以获取、估计精度较低的问题,提出了基于奇异值分解(SVD)的平方根容积卡尔曼滤波(SCKF)的分布式驱动车辆状态估计方法。SCKF算法通过奇异值分解优化误差协方差矩阵,以改善CKF在强非线性车辆系统或协方差矩阵非正定时状态估计精度降低甚至发散的问题,利用7自由度车辆动力学模型和Dugoff轮胎模型求得的参数信息准确估计车辆行驶状态。在Matlab/Simulink仿真平台上进行试验验证,并与基于CarSim数据的虚拟值进行了对比分析。结果表明:基于该算法的估计结果更接近真实值,并且响应速度快、实时性强。

一类具有转点的右端不连续奇摄动边值问题

研究了一类具有转点的右端不连续二阶半线性奇摄动边值问题解的渐近性.首先,在间断处将原问题分为左右两个问题,通过修正左问题退化问题的正则化方程,提高了左问题渐近解的精度,并利用Nagumo定理证明了左问题光滑解的存在性.其次,证明了右问题具有空间对照结构的解,并通过在间断点的光滑缝接,得到了原问题的渐近解.最后,通过一个算例验证了结果的正确性.

光纤传感器非周期低频动态信号相位载波解调方法研究

为了提高光纤传感器非周期低频动态信号的相位载波解调效果,提出光纤传感器非周期低频动态信号相位载波解调方法研究。采用自适应波束形成算法增强非周期低频动态信号的细节信息;通过奇异值分解算法提取信号的特征;将提取的特征输入到基于双扩展卡尔曼滤波的CD3S信号解调模型中,通过卡尔曼滤波结构剔除噪声;通过联合估计实现动态信号的扩频码同步,完成光纤传感器非周期低频动态信号相位载波解调。实验结果表明,所提方法在有无噪声干扰下解调误码率均处于1.0%以下,解调后位移误差低至12 pm,提高了解调效果和抗噪声能力。

基于前后向矩阵束方法的线性排布无人机集群目标规模估算

利用前后向矩阵束方法,提出了一种有效的“蜂群”无人机群目标个数估计方法用于目标检测。与传统的参数估算方法相比,所提方法对于稀疏信号也能准确地进行估算。首先,在一定的角度或频率下,获取线阵排列群目标的雷达散射截面;然后,根据已知的雷达回波构造Hankel-Toeplitz矩阵,并对该矩阵进行奇异值分解;最后,通过设置合适的阈值选取比例较大的奇异值,以此准确地估算线阵排列群目标的个数。此外,文中还讨论了不同信噪比对估算结果的影响。为了提高精度,文中采用多组不同方位角度的回波信号来联合估算群目标的个数。仿真结果表明,该方法能够有效、准确地估算线阵排列群目标的个数,而且估计结果不受噪声的影响,具有较好的鲁棒性。

Sylvester-Kac矩阵的奇异值所在区间估计

利用n+1阶置换矩阵,将Sylvester-Kac矩阵化为一个主对角线上2个零块,斜对角线上2个非零块的四分块矩阵,再利用矩阵A的奇异值分解问题等价于矩阵AA^(*)的特征值分解问题的关系,以及矩阵的Gerschgorin圆盘定理、Hermite矩阵、半正定矩阵的性质,获得了这个三对角矩阵的m个奇异值的区间估计,还获得了这个矩阵的谱半径的区间估计.

Approach to blind estimation of the PN sequence in DS-SS signals with residual carrier

This paper presents an approach of singular value de- composition plus digital phase lock loop to solve the difficult problem of blind pseudo-noise （PN） sequence estimation in low signal to noise ratios （SNR） direct sequence spread spectrum （DS-SS） signals with residual carrier. This approach needs some given parameters, such as the period and code rate of PN sequence. The received signal is firstly sampled and divided into non-overlapping signal vectors according to a temporal window, whose duration is two periods of PN sequence. An autocorrelation matrix is then computed and accumulated by those signal vectors one by one. The PN sequence with residual carrier can be estimated by the principal eigenvector of the autocorrelation matrix. Further more, a digital phase lock loop is used to process the estimated PN sequence, it estimates and tracks the residual carrier and removes the residual carrier in the end. Theory analysis and computer simulation results show that this approach can effectively realize the PN sequence blind estimation from the input DS-SS signals with residual carrier in lower SNR.

Angle estimation for bistatic MIMO radar with unknown mutual coupling based on three-way compressive sensing

The problem of angle estimation for bistatic multiple-input multiple-output radar in the present of unknown mutual coupling (MC) is investigated, and a three-way compressive sensing (TWCS) estimation algorithm is developed. To exploit the inherent multi-dimensional structure of received data, a trilinear tensor model is firstly formulated. Then the de-coupling operation is followed. Thereafter, the high-order singular value decomposition is applied to compress the high dimensional tensor to a much smaller one. The estimation of the compressed direction matrices are linked to the compressed trilinear model, and finally two over-complete dictionaries are constructed for angle estimation. Also, Cramer-Rao bounds for angle and MC estimation are derived. The proposed TWCS algorithm is effective from the perspective of estimation accuracy as well as the computational complexity, and it can achieve automatically paired angle estimation. Simulation results show that the proposed method has much better estimation accuracy than the existing algorithms in the low signal-to-noise ratio scenario, and its estimation performance is very close to the parallel factor analysis (PARAFAC) algorithm at the high SNR regions. ? 2017 Beijing Institute of Aerospace Information.

Kalman Filtering for Delayed Singular Systems with Multiplicative Noise

Kalman filtering problem for singular systems is dealt with, where the measurements consist of instantaneous measurements and delayed ones, and the plant includes multiplicative noise. By utilizing standard singular value decomposition, the restricted equivalent delayed system is presented, and the Kalman filters for the restricted equivalent system are given by using the well-known re-organization of innovation analysis lemma. The optimal Kalman filter for the original system is given based on the above Kalman filter by recursive Riccati equations, and a numerical example is presented to show the validity and efficiency of the proposed approach, where the comparison between the filter and predictor is also given.

An algorithm to solve autocorrelation matrix singular value based on SNR estimation

SNR estimation of communication signals is important to improve demodulation performance and channel quality of communication system,thus it is an important research issue of communication field.According to the core problem of autocorrelation matrix singular value in SNR estimation process,through making use of householder transforming autocorrelation matrix into tridiagonal matrix,and by using the relation of corresponding characteristic equation coefficients and singular value,a numerical algorithm is given to obtain autocorrelation matrix singular value,and the algorithm is used for SNR solving process.Theoretical analysis shows that the algorithm can satisfy the requirements in the aspect of constringency speed and stability.

A Class of Biased Estimators Based on SVD in Linear Model

In this paper, a class of new biased estimators for linear model is proposed by modifying the singular values of the design matrix so as to directly overcome the difficulties caused by ill_conditioning in the design matrix. Some important properties of these new estimators are obtained. By appropriate choices of the biased parameters, we construct many useful and important estimators. An application of these new estimators in three_dimensional position adjustment by distance in a spatial coordiate surveys is given. The results show that the proposed biased estimators can effectively overcome ill_conditioning and their numerical stabilities are preferable to ordinary least square estimation.