相关跳频转移函数的双随机矩阵模型及其应用

该文分别从状态空间的分解和平稳分布等角度对双随机矩阵以及双随机马氏(Markov)链的性质进行了研究,并将这些性质应用到相关跳频转移函数的分析和建模。文中证明了转移函数的双随机矩阵数学模型就状态转移过程的均匀性来说是完备的。基于对该模型的分析,提出了一种转移函数构造方法周期分组法,通过将频率转移过程构造成一个周期性双随机马氏链,可以获得纠错性能和频率间隔性能俱佳的转移函数。     

一种状态事件故障树的定量分析方法

状态事件故障树是一种适合于描述复杂系统中失效因果链的建模技术,对系统失效结果的概率特性进行定量分析是获得系统安全性参数的一种重要途径.由于状态事件故障树是半形式化模型,需先精确描述其语义才能进行定量分析.为此,本文提出一种基于交互马尔可夫链的状态事件故障树定量分析方法.首先,通过将交互马尔可夫链的交互动作精化为输入和输出动作,提出接口交互马尔可夫链模型用于状态事件故障树的形式语义描述.然后,在此形式语义的基础上设计了一种状态事件故障树定量分析方法.最后给出了一个飞机起落架收放系统的状态事件故障树建模及概率特性定量分析的实例研究.     

一种基于马氏链的可容侵网络状态评估模型

分析了可容侵网络的运行状态转移过程,在此基础上提出了一种基于马氏链的可客侵网络状态评估模型,并给出了计算实例.该模型可用于对可容侵网络性能进行评估.     

一种基于积分微分方程的泊松噪声去除算法

该文提出一种新的基于积分微分方程的泊松噪声去除算法.首先讨论了经典的总变差(TV)最小模型,在此基础上提出一种新的变分多尺度分层图像表示方法,然后在逆尺度空间上积分“尺度”图像从而得到了新的积分微分方程.这种新的积分微分方程含有一个单调增加的尺度函数.通过选取适当的尺度函数,该方程可以有效地去除泊松型噪声.数值实验证明了该算法比经典的TV和四阶偏微分方程算法具有更好的去噪效果.     

基于轻量化区块链节点的通信数据安全技术研究

为了确保网络通信的安全可靠,针对交互过程中数据被恶意攻击、篡改与泄漏等问题,文中在轻量化区块链节点的基础上提出了一种通信数据交互处理方案。该方案设计并采用了基于“私有链-联合链-私有链”的分组-分配数据存储结构来传输及保存通信数据,同时还通过改进型的加密算法解决了交互通信过程中的数据安全问题。加解密和安全性分析实验结果表明,相较于“联合-私有”双链结构的区块链通信数据交互方案以及可撤销属性基加密算法,所提方案在相同节点情况下的数据加密复杂度下降了40%,加密时间减少约33%,且密钥敏感度可以保持在50%以上。在通信数据交互处理过程中,该方法既保障了数据传输的安全性与完整性,又降低了传输时延。     

多站比例积分式调节系统的调节过程

自动调节系统的过渡历程是评价调节品质的一个重要特性。但通信调节系统的特点是多个调节器链接,因而全系统的传递函数总是高阶多重极点。它不适宜于用常见的状态变量法来求解。 本文提出将各个极点按负幂展开,然后再按拉氏变换求解。这样避免了常微分方程数值求解中常出现的步长误差积累,积分不稳定等问题。 本文以国产比例积分式调节器作为实际举例,研究了全系统的调节过程、过调度与站数、校正网络参数的关系。理论计算结果和实测数据是一致的。     

数据链路层协议通用排队模型及性能分析

本文提出一种考虑认可帧影响的数据链路系统通用排队模型，该模型是一个多的齐次马氏过程，采用快速直接计算迭代法求出排队系统状态的稳态概率分布，从而求得其性能指标和计算机仿真验证了数值计算结果，讨论了如何选择链路参数以提高性能。     

图像分解的多尺度变分模型

该文提出了一种新的多尺度变分图像分解模型.首先在Tadmar的分层多尺度变分模型的基础上,给出了一种新的(,)BV H-分层多尺度图像分解方法,然后在逆尺度空间上积分“尺度”图像并将拉普拉斯算子作用于曲1率项就得到了新的积分微分方程.该方程包含一个单调递增的尺度函数,它的值与残差图像的星范数成反比.接着讨论了该方程的重要性质,并给出了数值离散算法.理论分析与数值实验表明新的积分微分方程是一种有效的图像分解模型.     

微分中值定理中辅助函数的类型及应用

拉格朗日中值定理是微分学中重要的基本定理。在这个定理的证明过程中,基本思路是构造一个满足罗尔定理的辅助函数,利用罗尔定理结论来证明。但如何构造辅助函数是一个值得深入讨论和研究的问题。本文从距离、面积、旋转变换、积分、待定系数法、微分方程几个不同角度探讨了如何构造辅助函数,以帮助初学者开阔视野,加深对这两个定理证明的理解。     

一种新的VBR视频业务理论分析模型

目前没有一个理论分析模型可以描述Ｇａｍｍａ分布以及负指数下降的自相关性质，而这些性质对视频业务模型是很重要的。本文在ＤＡＲ（１）模型的基础上发展出一种适合理论分析的视频业务模型Ｃ－ＤＡＲ（１）。它是一个符合视频业务Ｇａｍｍａ分布及自相关特点的分析模型。文中同时指出了一条将离散时间马氏链模型转化为连续时间马氏链的途径。     

Linear optimal filtering for discrete-time systems with random jump delays

This paper is concerned with the dynamic Markov jump filters for discrete-time system with random delays in the observations. It is assumed that the delay process is modeled as a finite state Markov chain. To overcome the difficulty of estimation caused by the random delays, the single random delayed measurement system is firstly rewritten as the multiplicative noise constant-delay system. Then, by applying the measurement reorganization approach, the system is further transformed into the delay-free one with Markov jump parameters. Finally, the estimator is derived by using the standard Markov jump filter theories. It is interesting to show that the presented filter for the system with random jump delays can be designed by performing two sets of standard Riccati equations with the same dimension as that of the original system. A simulation example is given to illustrate the effectiveness of the proposed result.     

Estimation, Hypothesis Testing and Parameter Correlation for Markov Chains

In this report we will discuss four problems in statistical inference for Markov chains. Specifically, techniques are described to do the following: 1) estimate the transition probabilities of first- and second-order stationary Markov chains; 2) test the hypothesis that a stationary Markov chain is of first order against the alternate hypothesis that the chain is of second order; and 3) test the hypothesis that a first-order Markov chain has stationary transition probabilities against the alternate hypothesis that the transition probabilities are not stationary. A technique is also developed which can be used in testing to determine whether two parameters of a single electronic component drift independently of each other. The results of these tests are used to draw some inference about continuous-time Markov processes.     

Relations entre distribution stationnaire et distribution aux instants d’arrivée pour des files d’attente usuelles

In queueing theory, three probability distributions naturally arise: arriving customer’s distribution, departing customer’s distribution and stationary queue length distribution. The aim of this paper is to generalize the PASTA property by using a martingale formulation, so to obtain easily relations between these probability distributions. This approach is applied to queues arising when modelling networks based upon the asynchronous transfer mode, namely those composed of a Markov jump process, an Erlang process or a renewal process whose interarrivai time has a Cox distribution.     

Expectation maximization algorithms for MAP estimation of jumpMarkov linear systems

In a jump Markov linear system, the state matrix, observation matrix, and the noise covariance matrices evolve according to the realization of a finite state Markov chain. Given a realization of the observation process, the aim is to estimate the state of the Markov chain assuming known model parameters. Computing conditional mean estimates is infeasible as it involves a cost that grows exponentially with the number of observations. We present three expectation maximization (EM) algorithms for state estimation to compute maximum a posteriori (MAP) state sequence estimates [which are also known as Bayesian maximum likelihood state sequence estimates (MLSEs)]. The first EM algorithm yields the MAP estimate for the entire sequence of the finite state Markov chain. The second EM algorithm yields the MAP estimate of the (continuous) state of the jump linear system. The third EM algorithm computes the joint MAP estimate of the finite and continuous states. The three EM algorithms optimally combine a hidden Markov model (HMM) estimator and a Kalman smoother (KS) in three different ways to compute the desired MAP state sequence estimates. Unlike the conditional mean state estimates, which require computational cost exponential in the data length, the proposed iterative schemes are linear in the data length     

An averaging principle for filtering a jump process with pointprocess observations

A proof of the following result is given. Le X_t and Y_t be two jump processes which modulate the intensity of a multivariate point process N _t, and suppose that the process X_t is a fast' Markov chain with a unique invariant probability distribution. Then the filtering equations for Y_t can be obtained by considering, instead of the original problem, the averaged problem where the intensity is replaced by the averaged intensity     

带丢包Markov切换线性系统的状态估计问题研究

针对一类带丢包的Markov切换系统,提出一种含有双Markov切换参数的交互式多模型算法.该算法利用一个二态的Markov链对系统是否丢包进行建模,得到双Markov链系统,通过定义乘积集将两个Markov切换参数所对应的模型集进行融合,并给出单个模型集中各模型与乘积集中各模型的对应关系.在此基础上,以交互式多模型算法为框架,采用分层的方法,并利用一种新的最优估计算法对双Markov链系统进行滤波.仿真实验证明了该算法的有效性.     

Robust Kalman Filter Design for Markovian Jump Linear Systems with Norm-Bounded Unknown Nonlinearities

This paper considers the problems of stability and filtering for a class of linear hybrid systems with nonlinear uncertainties and Markovian jump parameters. The hybrid system under study involves a continuous-valued system state vector and a discretevalued system mode. The unknown nonlinearities in the system are time varying and norm bounded. The Markovian jump parameters are modeled by a Markov process with a finite number of states. First, we show the equivalence of the sets of norm-bounded linear and nonlinear uncertainties. Then, instead of the original hybrid linear system with nonlinear uncertainties, we consider the same system with linear uncertainties. By using a Riccati equation approach for this new system, a robust filter is designed using two sets of coupled Riccati-like equations such that the estimation error is guaranteed to have an upper bound.     

The reflection method with a change of sign in problems of the quality analysis of signal detection

The reflection method with a change of sign, initially used as a technique for solving the first boundary value problem of the heat conduction equation, has been extended for allowing us to elucidate the solution of earlier known problems of the quality analysis of signal detection algorithms using the tool of Markov processes and also to derive an expression for the probability of finding the absolute maximum of the normal stationary Markov process in the negative half-plane of values. A comparative analysis with a similar probability was performed for the root-mean-square differentiable process.     

Distribution of absolute maximum of Gaussian Markov’s stationery process

The absolute maximum of Gaussian Markov’s stationary process is obtained by means of solution of the Fokker-Planck-Kolmogorov equation with method of variables division. It is shown, known results are special cases of obtained solution. The probability of process location in one of half-plane of its values is specified.