A search game taking account of attributes of searching resources

This article deals with a two‐person zero‐sum game called a search allocation game (SAG), in which a searcher and a target participate as players. The searcher distributes his searching resources in a search space to detect the target. The effect of resources lasts a certain period of time and extends to some areas at a distance from the resources' dropped points. On the other hand, the target moves around in the search space to evade the searcher. In the history of search games, there has been little research covering the durability and reachability of searching resources. This article proposes two linear programming formulations to solve the SAG with durable and reachable resources, and at the same time provide an optimal strategy of distributing searching resources for the searcher and an optimal moving strategy for the target. Using examples, we will analyze the influences of two attributes of resources on optimal strategies. © 2007 Wiley Periodicals, Inc. Naval Research Logistics 2008     

数据光滑的一种新方法

提出了用变形的Fourier部分和来代替Fourier级数将输入数据光滑的一种新方法。该方法能稳定地解某些不适定的问题,如给定函数的近似,求函数微分的问题;Laplace方程Cauchy问题;时间逆向热传导方程的Cauchy问题等。     

保密通信中同相和正交通道失衡对干扰抑制性能的影响

针对同时存在恶意干扰与非法窃听的通信环境,提出一种协作干扰(cooperative jamming, CJ)掩护的保密通信架构,收发信机之间采用跳频技术躲避恶意干扰,并采用协作干扰技术阻塞非法窃听。但该架构的通信带宽较大,会在收发频率振荡器中引起显著的同相和正交(in-phase and quadrature, IQ)通道失衡。鉴于此,对收发IQ通道失衡引起的信号失真进行数学建模,给出接收机处信干噪比的数学表达式,并给出干扰抑制比的闭合表达式。仿真结果表明,收发IQ通道失衡引起的信号失真的功率远大于热噪声功率。随着收发IQ通道失衡加剧,所提架构的信干噪比和干扰抑制比性能均会急剧下降,当幅度和相位失衡分别达到0.95和π/50时,信干噪比和干扰抑制比均损失了47 dB。     

高轨双星辐射源跟踪的高斯和-容积Kalman滤波算法

针对辐射源运动方程和观测方程的强非线性,提出基于高斯和框架与5阶容积Kalman滤波(5CKF)的跟踪算法GS-5CKF。该方法将起始时刻的时差观测量所确定的位于地球表面的时差线按经度等间隔划分,初始化多个并行的5CKF,线性组合各滤波器的输出获得辐射源运动状态的估计。针对5CKF,提出新的非线性测度并引入滤波器分裂与合并,从而提高了跟踪精度,同时保持GS-5CKF算法复杂度基本不变。仿真表明,相对仅使用单个5CKF和基于高斯和框架但使用3阶容积Kalman滤波器的GS-3CKF等方法,提出的算法具有更高的估计精度。     

A search game on a cyclic graph

There is a finite cyclic graph. The hider chooses one of all nodes except the specified one, and he hides an (immobile) object there. At the beginning the seeker is at the specified node. After the seeker chooses an ordering of the nodes except the specified one, he examines each nodes in that order until he finds the object, traveling along edges. It costs an amount when he moves from a node to an adjacent one and also when he checks a node. While the hider wishes to maximize the sum of the traveling costs and the examination costs which are required to find the object, the seeker wishes to minimize it. The problem is modeled as a two‐person zero‐sum game. We solve the game when unit costs (traveling cost + examination cost) have geometrical relations depending on nodes. Then we give properties of optimal strategies of both players. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

“Government contracting options: A model and application“∗

This paper models and simulates a government‐contractor principal‐agent weapon system repair model. Insights are derived as to how government repair contracts should be constructed so as to induce optimal contractor behavior. The paper's general conclusion is that the best contracting approach combines a lump‐sum payment that does not vary with the number of units repaired, expensive item cost‐sharing, and a contractor‐provided availability guarantee. Provided there is intercontractor competition, this type of contract performs well even if the government is poorly informed about weapon system break patterns or repair costs.     

面向多最优解组合优化问题的决策求解算法

针对具有固定物品总和、多最优解特征的组合优化问题,以固定总和实数子集问题和购买鸡翅问题为例,给出了这类多最优解组合优化问题的形式化表示。在分析枚举等经典算法基础上,提出了基于整数状态表示和实数状态表示的0-1决策递归搜索多最优解动态规划算法。针对该算法在最优解数量较大时,时间复杂度趋向O(mⁿ)的问题,提出了基于相同决策路径合并和基于0-x决策的两种改进算法。实验中两种改进算法的计算时间基本符合与O(nb+nm)的正比关系,表明对于这类多最优解组合优化问题具有良好的求解性能。     

New results on a stochastic duel game with each force consisting of heterogeneous units

Two forces engage in a duel, with each force initially consisting of several heterogeneous units. Each unit can be assigned to fire at any opposing unit, but the kill rate depends on the assignment. As the duel proceeds, each force—knowing which units are still alive in real time—decides dynamically how to assign its fire, in order to maximize the probability of wiping out the opposing force before getting wiped out. It has been shown in the literature that an optimal pure strategy exists for this two‐person zero‐sum game, but computing the optimal strategy remained cumbersome because of the game's huge payoff matrix. This article gives an iterative algorithm to compute the optimal strategy without having to enumerate the entire payoff matrix, and offers some insights into the special case, where one force has only one unit. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 56–65, 2014     

基于高斯和-容积Kalman滤波的高轨双星辐射源跟踪

高轨双星系统可通过测量辐射源信号的到达时差、频差和到达高轨卫星的多普勒频移,跟踪沿地球表面巡航且载频固定、已知的运动辐射源。针对辐射源运动方程和观测方程的强非线性,提出了基于高斯和框架与5阶容积Kalman滤波的运动辐射源跟踪算法GS-5CKF。算法将起始时刻的时差观测量所确定的处于地球表面的时差线按辐射源经度等间隔划分,初始化多个并行的5阶容积Kalman滤波器,线性组合各滤波器每个时刻的输出以获得辐射源运动状态的估计。针对5阶容积Kalman滤波器,提出了相应的非线性测度并引入滤波器分裂与合并,以提高跟踪精度并保持GS-5CKF算法计算复杂度基本不变。仿真表明,相对仅使用单个5阶容积Kalman滤波器和基于高斯和框架但使用3阶容积Kalman滤波器的GS-3CKF等算法,提出的跟踪算法具有更高的估计精度。     

The solution to an open problem for a caching game

In a caching game introduced by Alpern et al. (Alpern et al., Lecture notes in computer science (2010) 220–233) a Hider who can dig to a total fixed depth normalized to 1 buries a fixed number of objects among n discrete locations. A Searcher who can dig to a total depth of h searches the locations with the aim of finding all of the hidden objects. If he does so, he wins, otherwise the Hider wins. This zero‐sum game is complicated to analyze even for small values of its parameters, and for the case of 2 hidden objects has been completely solved only when the game is played in up to 3 locations. For some values of h the solution of the game with 2 objects hidden in 4 locations is known, but the solution in the remaining cases was an open question recently highlighted by Fokkink et al. (Fokkink et al., Search theory: A game theoretic perspective (2014) 85–104). Here we solve the remaining cases of the game with 2 objects hidden in 4 locations. We also give some more general results for the game, in particular using a geometrical argument to show that when there are 2 objects hidden in n locations and n→∞, the value of the game is asymptotically equal to h/n for h≥n/2. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 23–31, 2016