Taylor expansion of the differential range for monostatic SAR

The polar format algorithm (PFA) for spotlight synthetic aperture radar (SAR) is based on a linear approximation for the differential range to a scatterer. We derive a second-order Taylor series approximation of the differential range. We provide a simple and concise derivation of both the far-field linear approximation of the differential range, which forms the basis of the PFA, and the corresponding approximation limits based on the second-order terms of the approximation.     

利用差值定理降低飞行器速度和加速度拟合的截断误差

推导了差值定理及其推论,并以此作为数据拟合的有效点判据,显著降低了飞行器速度和加速度拟合的截断误差;探讨了该判据条件下滤波参数对拟合结果的影响及截断误差的判断条件,并采用实测数据对拟合效果进行了检验。     

Limitations of a Variance Approximation

A common approximation for the variance of a function of two random variables is obtained via a series expansion. It is shown that for some cases the error in the approximation is quite large. This approximation is sometimes used to compare the relative merits of two alternate systems. The comparison might be erroneous if the system differences are comparable to the approximation errors.     

中心刚体-柔性悬臂梁系统的动力特性研究

对中心刚体-柔性悬臂梁系统的动力特性进行研究。首先采用Hamilton原理和有限元离散化方法,给出该系统的一次近似耦合模型以及相应的KED解耦模型,然后通过数值仿真对该系统的动力特性进行研究。研究中考虑了2种情况:中心刚体的转动惯量远大于柔性悬臂梁的转动惯量的情况和中心刚体的转动惯量接近柔性悬臂梁的转动惯量的情况。研究结果显示,传统的零次近似模型在处理大范围运动为未知的刚柔耦合动力学问题时同样存在失效的可能,而一次近似模型能够对系统的动力学行为进行正确的数学描述。当中心刚体的转动惯量远大于柔性悬臂梁的转动惯量时,一次近似模型的结果与零次近似模型的结果之间存在较小偏差;但当中心刚体的转动惯量接近柔性悬臂梁的转动惯量时,零次近似模型将导致错误的结果。     

Reachable set estimation for spacecraft relative motion based on bang-bang principle

For spacecraft formation flight, the information of relative motion reachable set is very important, which can be used to predict the operating boundary of adjacent spacecraft and thus to ensure the safety of spacecraft operation. In this paper, we aim at developing a numerical method to approximate the reachable set for spacecraft relative motion. In particular, we focus on the quality of the approximation and the computational cost. Based on the bang-bang control principle, a polyhedral approximation algorithm is proposed to compute the reachable set of a relative motion spacecraft system. An inner approximation and an outer approximation of the reachable set for the system can be obtained. We prove that the approximation quality measured in Hausdorff distance can be guaranteed. The method is easy to implement and has low computational cost. Finally, the effectiveness of the algorithm is demonstrated by experimental simulation.     

PSO节点寻优的样条逼近微分

样条节点分布对逼近精度的影响很大,样条节点寻优模型的雅可比矩阵求解复杂。利用经典参数的PSO（粒子群算法）解算样条最优节点分布模型,以逼近残差的平方和为目标函数,每步对节点序列排序后再计算目标函数,可以提高样条逼近精度,为样条节点寻优提供了一种较好的实现方法。仿真计算表明,在一定的节点个数情况下,PSO节点寻优的逼近效果比Carl de Boor的NEWNOT程序中的方法要好。     

Highest density gates for target tracking

The problem of forming validation regions or gates for new sensor measurements obtained when tracking targets in clutter is considered. Target dynamics and measurement characteristics are modeled with, possible non-Gaussianities or nonlinearities, so that some degree of approximation is usually required in the computation of the filtering densities for the target position and predictive densities for future measurements. Highest density gates (HDGs) are proposed as summaries of the predictive densities. These gates are constructed numerically, via simulation from the filtering density approximation. The algorithm results in gates that are “exact” (up to numerical accuracy) regardless of the approximation used for the filtering density. That is, given an approximation to the filtering density, the gating procedure accounts for all further nonlinearities and non-Gaussianities. Numerical example show that when the predictive density is markedly non-Gaussian, HDGs offer advantages over the more common rectangular and ellipsoidal gates     

推进剂供应管道的集中参数近似模型研究——模态近似模型

提出了用模态近似法建立分布参数湍流管道的集中参数近似模型的新方法,发展了适用于水力和绝热气体湍流管道的两种模态近似模型：Ｉ－Ｒ－Ｃ模态和等效层流模型。模型中考虑了频率相关摩擦损失。利用单根管道阀门关断问题的仿真计算对本文的模型进行了验证,计算结果与考虑频率相关摩擦损失的特征线方法的计算结果十分吻合。     

阶梯函数逼近阶与若干函数类的特征

利用阶梯函数逼近给出了连续函数类的特征,并在此基础上分别导出阶梯函数逼近李普希兹函数类和狄尼-李普希兹函数类的逼近阶。     

飞控系统实时仿真算法分析

采用改进的双线性变换方法－临界频率预翘曲方法,对双线性变换方法引起的偏差进行预补偿,从而减小飞控系统的实时仿真误差。以频带较宽的典型环节为例,对系统频率特性进行了分析,同时,将其与双线性变换及四阶龙格－库塔法的计算结果进行了比较。结果表明：该方法能较好地补偿双线性变换所引起的误差,满足飞机飞控系统的实时仿真要求。     

一种金融投资模型的数值逼近方法

对一种金融模型，给出了一、二阶的Itoe-Taylor逼近的估计，并对这两种估计证明了其强收敛性，同时给出了收敛的阶数．通过比较得出Itoe-Taylor逼近阶数越高，得到的估计强收敛的阶越高。     

特征值反问题逼近解与极值化解的统一应用

基于矩阵最佳逼近与加权残值理论,本文把求解特征值反问题的矩阵逼近法和极值化方法统一为不同范数定义下的最小二乘问题。这对解决部分特征值和／或特征向量给足情况下的反问题提供了一个有效工具。结合工程实际,本文给出了具体应用的数值例子。     

基于小波变换和不变矩的车标识别方法

形状特征是目标识别的重要参数,小波变换的低频部分代表物体的总体形状特征,而图像中的噪声主要分布于高频部分。根据这一特征,利用小波变换消除噪声提取目标形状,进而利用特征不变矩距离进行分类,实现目标识别,将该方法应用在实测车标图像的识别中,结果表明识别效果较好。     

一种结构优化的准解析法

协同利用数学变换、高精度近似和二级逼近策略,提出了一种求解结构优化问题的准解析法。该方法通用性强,计算效率高,尤其适用于求解大型结构设计问题。方法的有效性通过不同类型的优化算例进行了验证。     

判断矩阵的一个恰当的校正方法

 本文首先证明了成对比较矩阵在相容性矩阵集合中的最佳逼近的存在性和不唯一性。然后通过微分同胚,把原来的非线性逼近转化成一个线性逼近,从而用投影定理获得解决。算例证明该方法简易可行。     

Implementation of the simultaneous perturbation algorithm forstochastic optimization

The need for solving multivariate optimization problems is pervasive in engineering and the physical and social sciences. The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for challenging optimization problems where it is difficult or impossible to directly obtain a gradient of the objective function with respect to the parameters being optimized. SPSA is based on an easily implemented and highly efficient gradient approximation that relies on measurements of the objective function, not on measurements of the gradient of the objective function. The gradient approximation is based on only two function measurements (regardless of the dimension of the gradient vector). This contrasts with standard finite-difference approaches, which require a number of function measurements proportional to the dimension of the gradient vector. This paper presents a simple step-by-step guide to implementation of SPSA in generic optimization problems and offers some practical suggestions for choosing certain algorithm coefficients     

带有自适应参数近似的块控反步飞行控制器设计

针对有翼导弹含有未知气动参数时的飞行控制问题,设计了一种带有自适应参数近似的块控反步飞行控制器.分析了块控反步控制器设计的假设条件,并放宽了对指令信号和输入矩阵的部分限制.将导弹动态模型中的未知气动参数转换为待估计参数矩阵,采用自适应参数近似律对未知参数矩阵进行估计,相比使用神经网络逼近未知函数更为简单,易于实现.将滤...     

单一物质的热力学性能近似计算(英文)

本文介绍针对固定温度点的热力学函数 (如焓、熵、比热 )综合近似计算法。该方法已成功地用来近似计算温度范围为 10 0～ 2 0 0 0 0 K的 150 0个热力学函数表。用内含近似计算程序包的 TD软件系统对混合物参数进行热力计算的结果证明,该多项式在求解多组元系统计算中迭代问题时具有很高的可靠性。      

The Acquisition Probability for a Minimum Distance One-Class Classifier

An approximation for the acquisition probability for a minimumdistance one-class classifier is derived. An exact expression for theacquisition probability is dependent upon the operatingcharacteristics in the distance space, the number of targets detected,and the number of other objects detected. An approximateexpression replaces the operating characteristics curve by a singlepoint. Experimental results are presented to demonstrate thevalidity of the approximation. Combinatorial techniques can be usedwhen only the total number of objects detected is known. All ofthese results can be extended to include the multitarget, multipleshotcase.     

Receiver characteristics of laser altimeters with avalanchephotodiodes

The receiver characteristics of a laser altimeter system containing an avalanche photodiode photodetector are analyzed using the Gaussian approximation, the saddlepoint approximation, and a nearly exact analysis. The last two methods are shown to yield very similar results except when the background noise is extremely low and the probability of false alarm is high. However, the Gaussian approximation method is shown to cause significant errors even under relatively high levels of background noise and received signal energy