辛算法应用于Duffing方程的保结构性

讨论了不受外力的Duffing方程在辛算法和非辛算法作用下,相轨线被保持和破坏的性质。证明了当时间步长充分小时,辛算法可以保持原系统的大部分不变闭曲线,而非辛算法却做不到这一点。     

临近空间拦截弹最优弹道跟踪制导律

针对拦截临近空间高超声速飞行器的弹道跟踪过程,基于线性二次型调节器理论和高斯伪谱法设计一种跟踪制导律。为了对标称弹道进行精确跟踪,考虑线性二次型跟踪问题,应用最优控制理论推导最优解的充要条件,得到带时变增益的线性状态反馈控制量的表达式;基于高斯伪谱法,在离散的勒让德-高斯点上利用标称弹道数据计算差分矩阵和系数矩阵,求得状态扰动反馈控制律。仿真结果表明,与基于求解矩阵黎卡提方程的方法相比,该方法选取较少的节点即可获得高精度的反馈控制量,且运算效率大幅提高,满足在线实施要求。     

Aggregating courier deliveries

We consider the problem of efficiently scheduling deliveries by an uncapacitated courier from a central location under online arrivals. We consider both adversary‐controlled and Poisson arrival processes. In the adversarial setting we provide a randomized (3βΔ/2δ ? 1) ‐competitive algorithm, where β is the approximation ratio of the traveling salesman problem, δ is the minimum distance between the central location and any customer, and Δ is the length of the optimal traveling salesman tour overall customer locations and the central location. We provide instances showing that this analysis is tight. We also prove a 1 + 0.271Δ/δ lower‐bound on the competitive ratio of any algorithm in this setting. In the Poisson setting, we relax our assumption of deterministic travel times by assuming that travel times are distributed with a mean equal to the excursion length. We prove that optimal policies in this setting follow a threshold structure and describe this structure. For the half‐line metric space we bound the performance of the randomized algorithm in the Poisson setting, and show through numerical experiments that the performance of the algorithm is often much better than this bound.     

基于方位角和多普勒的机动目标无源定位跟踪可观测条件

可观测性分析是无源定位与跟踪系统的前提和基础,只有满足可观测条件才能对系统进行正确求解。应用线性系统理论,以目标方位角和多普勒频率为观测量,对匀加速和匀转弯这两类最常见的机动目标进行了可观测分析,为进一步研究机动目标的无源定位与跟踪提供了理论前提。最后给出了仿真实例,验证了理论分析的正确性。     

非线性系统中的机动目标跟踪算法

对于非线性系统中的机动目标跟踪问题 ,首先针对“当前”统计模型的缺陷提出了一种修正算法 ,然后应用转换测量Kalman滤波算法进行跟踪。仿真结果表明在非线性观测条件下 ,算法明显提高了对弱机动和非机动目标的跟踪性能 ,同时保持了对强机动目标的高性能跟踪     

一种新的多传感器多机动目标快速跟踪算法

基于FAFDA滤波算法,根据Houles和Shalom将PDA算法推广到解决两个传感器单目标的跟踪问题的思路中,构造一种两个同类传感器的序列观测数据的融合来跟踪多个机动目标的数据关联方法(MSFAFDA)。它主要使用的是点/航迹联合和序列估计法。算法计算量远小于原先的顺序和并行多传感器联合概率数据关联算法,蒙特卡洛仿真结果也表明它对多机动目标的跟踪具有比FAFDA更好的跟踪性能。     

卫星导航天线阵的载波联合跟踪算法

测量卫星导航信号在天线阵各阵元上的载波相位之差可用于卫星波达方向解算,但传统的各阵元独立跟踪算法在干扰条件下无法实现高精度跟踪且容易失锁。针对此问题,通过将天线阵各阵元的载波相位分解为公共的平均载波相位和低动态的残余载波相位,提出了一种联合载波跟踪算法。该算法利用平均载波相位为每个阵元共有的特点,通过对全部阵元的联合处理来提高其跟踪精度,同时通过缩小环路噪声带宽来提高残余载波相位跟踪精度。理论分析与仿真结果表明,该算法提高了波达方向解算所需的阵元间载波相位差的测量精度及跟踪灵敏度,四阵元天线阵在典型应用条件下,跟踪灵敏度提高4d B,相同载噪比下载波相位差测量精度提高3倍。     

多波束相控阵天线角跟踪性能及测试方法

针对目前对多波束相控阵天线角跟踪性能测试研究较少的问题,首先分析了多波束相控阵天线的单脉冲和差测角方法,并对波束滑动、波束穿越及信号频率变化对角跟踪性能的影响进行了仿真分析。类比传统的雷达精度校飞试验,提出了基于飞艇的角跟踪性能测试方法,对角跟踪精度及误差范围进行测试,并利用STK软件实现了可视化。仿真分析表明,该方法可以实现对多波束相控阵天线角跟踪性能的评定并具有较高的工程应用价值。     

一种结合弹道规律的模糊交互式多模型算法

针对交互式多模型算法中转移概率矩阵与实际运动不匹配而影响跟踪精度的问题,通过分析某型导弹的典型弹道,将弹道规律融合到模型概率转移矩阵中,然后将转移概率模糊化处理,提出了一种基于弹道规律的模糊交互式多模型算法,然后以导弹蛇形运动转至比例导引的机动过程为例进行了仿真验证,比较了典型交互式多模型算法和模糊交互式多模型算法的跟踪性能。仿真结果表明:该算法可显著提高导弹机动段的跟踪精度。     

Balancing stability and efficiency in team formation as a generalized roommate problem

The assignment of personnel to teams is a fundamental managerial function typically involving several objectives and a variety of idiosyncratic practical constraints. Despite the prevalence of this task in practice, the process is seldom approached as an optimization problem over the reported preferences of all agents. This is due in part to the underlying computational complexity that occurs when intra-team interpersonal interactions are taken into consideration, and also due to game-theoretic considerations, when those taking part in the process are self-interested agents. Variants of this fundamental decision problem arise in a number of settings, including, for example, human resources and project management, military platooning, ride sharing, data clustering, and in assigning students to group projects. In this article, we study an analytical approach to “team formation” focused on the interplay between two of the most common objectives considered in the related literature: economic efficiency (i.e., the maximization of social welfare) and game-theoretic stability (e.g., finding a core solution when one exists). With a weighted objective across these two goals, the problem is modeled as a bi-level binary optimization problem, and transformed into a single-level, exponentially sized binary integer program. We then devise a branch-cut-and-price algorithm and demonstrate its efficacy through an extensive set of simulations, with favorable comparisons to other algorithms from the literature.