关于m序列的互相关函数

m 序列由于它的伪随机性,其中特别是它的自相关函数“接近”于 Delta 函数,使得它在跟踪、测量、数字通信等无线电技术中受到重视.根据无线电信号的检测理论,信号经过恒参、线性信道中的传播并在加性白色高斯噪声背底下的提取是提取它的自相关函数,以在接收端获取最大的信噪比,常采用匹配滤波技术来实现.为了提高信道的利用率,在同一无线电系统中可以采用一个以上的 m 序列信号,这样     

随机波动率模型下技术分析指标的一些性质(英文)

一些流行的技术指标(例如布林带,RSI,ROC等)被股市交易者广为使用.交易者将每日(小时,周,……)的实际股价作为计算某个技术指标的样本,通过观察相关频率来指导投资.技术指标的有效性已在广泛的应用中得到了验证.我们已经证明在Black-Scholes模型下,某些技术指标有许多有用的统计性质.作为更一般的情况,随机波动率模型在金融数学中得到了广泛的讨论.本文基于随机波动率模型对技术指标的统计性质进行了研究.研究结果表明,如果股票价格服从随机波动率模型,则技术指标的合理性可以得到有力的证明,从这个角度我们为技术分析奠定理论基础.     

AR模型识别及其参数的高阶Yule—Walker估计

一、引言自回归谱估计在许多领域获得了广泛的应用,随着科学技术的不断发展,对谱估计分辨力的要求越来越高.高阶 Yule-Walker 谱估计就是具有较高分辨力的一种估计(见[1]).为了进一步研究这种估计首先必须研究自回归模型阶的识别及其参数的高阶Yule-Walker 估计.通常使用的自回归定阶方法与参数的矩估计方法使用了样本自协方差函数(或样本自相关函数)在零点的值(?)(0)(或(?)(0))。而(?)(0)(或(?)(0))就是影响自回归谱估计分辨力的一个重要因素.实际上,通常的信号观测值包含两部分     

基于ARMA模型和自由振动提取技术的海洋平台结构参数识别

用随机减量方法提取海洋平台结构在随机环境荷载非白噪声输入下的自由振动信号和用ARMA(Auto Regressive Moving Average)模型对自由振动数据建模。为了消除平台输出信号中有色噪声的影响,在随机减量系统中加人了一个虚拟系统,并采用导通条件和前导点技术使自由振动提取过程仍在有色输人的状态下进行。同时为了消除参数识别的多值性,提出了采用MA系数修正技术识别海洋平台结构的频率和阻尼动力参数的方法,最后用该套技术对海洋平台结构试验模型进行了参数识别,结果表明该方法具有较好的效果和在线识别使用价值。     

不确定多通道信号鲁棒稳态估计

对于一类具有随机参数矩阵、不确定噪声方差、一步随机时滞、丢包和丢失观测的多通道自回归(Autoregressive,AR)信号系统,文章研究其鲁棒稳态Kalman滤波问题.应用状态空间方法,增广方法和虚拟噪声技术,混合不确定AR信号模型被转换为仅带不确定噪声方差和相同过程以及观测噪声的状态空间模型.根据极大极小鲁棒估计原理,基于带不确定噪声方差保守上界的最坏情形系统,提出了鲁棒稳态Kalman一步和多步信号预报器.证明了所提出的信号预报器的鲁棒性,即对于所有容许的不确定性,信号预报器的实际稳态预报误差方差被保证有相应的最小上界.仿真例子验证了所提出方法的正确性和有效性.     

一种估计Clayton模型中关联参数的方法

在右删失情形下,基于二元风险函数的核估计,我们对Clayton模型中的关联参数给出了一种新的估计方法.新的估计量具有相合性和渐近分布,随机模拟也显示这种估计方法是非常有效的.     

金融系统中的早期预警信号及其统计物理性质

金融系统与其他复杂系统一样具有临界阈值，系统状态在到达临界点之前会显示微小的变化.运用统计物理的方法研究期货价格的方差和自相关特性，引入布朗运动和Tsallis-q-Gauss分布，研究其分布函数，呈现“尖头胖尾”的特征；引入互关联函数，研究方差与自相关分别与价格时间序列的关联情况，并同时进行比较，发现其具有长程相关性.最终验证了方差和自相关作为金融系统中期货市场早期预警信号的可行性.     

随机测量矩阵齐次RIP的证明

在压缩感知理论中,若要保证重构信号的精确性,测量矩阵需要满足限制等距性质,即RIP.当测量矩阵是随机矩阵时,RIP的成立与概率相关.对高斯矩阵RIP进行了修正,其中将原高斯矩阵RIP相关的集中不等式的■范数修正为■范数,梳理了这一类RIP证明过程,并证明得到了齐次RIP.     

基于基底合并的分片稀疏恢复

如我们所知,诸如视频和图像等信号可以在某些框架下被表示为稀疏信号,因此稀疏恢复(或稀疏表示)是信号处理、图像处理、计算机视觉、机器学习等领域中被广泛研究的问题之一.通常大多数在稀疏恢复中的有效快速算法都是基于求解$l^0$或者$l^1$优化问题.但是,对于求解$l^0$或者$l^1$优化问题以及相关算法所得到的理论充分性条件对信号的稀疏性要求过严.考虑到在很多实际应用中,信号是具有一定结构的,也即,信号的非零元素具有一定的分布特点.在本文中,我们研究分片稀疏恢复的唯一性条件和可行性条件.分片稀疏性是指一个稀疏信号由多个稀疏的子信号合并所得.相应的采样矩阵是由多个基底合并组成.考虑到采样矩阵的分块结构,我们引入了子矩阵的互相干性,由此可以得到相应$l^0$或者$l^1$优化问题可精确恢复解的稀疏度的新上界.本文结果表明.通过引入采样矩阵的分块结构信息.可以改进分片稀疏恢复的充分性条件.以及相应$l^0$或者$l^1$优化问题整体稀疏解的可靠性条件.     

随机混合动态系统的状态反馈控制

针对一类以有限齐次马氏链δ(k)作为切换信号的随机混合系统,首先,通过构造随机混合Lyapunov函数,得到整个随机混合系统渐近稳定的充分条件.然后,引入可调转移概率等相关概念,通过对有限齐次马氏链δ(k)及各子系统加入控制,以实现状态反馈控制.进一步,得到随机混合闭环系统渐近稳定的充分条件.     

Chaos time-domain reflectometry for fault location on live wires

We propose a chaos time-domain reflectometry (CTDR) for locating faults on live wires. This method uses a chaotic output of an improved Colpitts oscillator as probe signal, and detects wire faults by correlating a duplicate with the echo of the probe signal. Benefiting from the anti-jamming of the correlation function of the wideband chaos, fault location on live wires can be achieved. We experimentally demonstrate the detection for live wires in a digital communication system, in which a type of digital signal named high density bipolar of order 3 (HDB3) is transmitted. The effects of the chaotic probe signal on the bit error rate (BER) of the transmitted HDB3 at different rates are analyzed. Meanwhile, the influences of the backward HDB3 reflected by wiring faults on the signal-noise-ratio (SNR) of CTDR measurement are examined experimentally. The results show that fault detection on live wires is achieved when the power of the chaotic probe signal is about from -24.8 dB to -13.5 dB lower than that of the transmitted digital signal. In this case, the BER is kept less than 3E-10, and the SNR of CTDR is higher than 3 dB. Besides, the auto-correlation properties of the improved Colpitts oscillator at different states are investigated experimentally to explore the suitable chaotic states for the CTDR.     

Fault analysis of Trivium

As a hardware-oriented stream cipher, Trivium is on the edge of low cost and compactness. In this paper we discuss how brittle Trivium is under fault attack. Our fault model is based on the following two assumptions: (1) We can make fault injection on the state at a random time and (2) after each fault injection, the fault positions are from random one of three registers, and from a random area within eight neighboring bits. Our fault model has extremely weak assumptions for effective attack , and much weaker than that of Hojsík and Rudolf, in their fault attack on Trivium. We present a checking method such that, by observing original key-stream segment and fault injected key-stream segment, the injecting time and fault positions can be determined. Then, for several distributions of the injecting time, our random simulations always show that the attacker can break Trivium by a small number of repeated fault injections. For example, suppose that the injecting time has an uniform distribution over {0, 1, . . . , 32}, then averagely no more than 16 repeated fault injection procedures will break Trivium, by averagely observing no more than 195 × 17 key-stream bits.     

Inferences in semi-parametric dynamic mixed models for longitudinal count data

This paper considers a semi-parametric mixed model for longitudinal counts under the assumption that for conditional on a common random effect over time the repeated count responses of an individual follow a Poisson AR(1) (auto-regressive order 1) non-stationary correlation structure. A step-by-step estimation approach is developed which provides consistent estimators for the non-parametric function, regression parameters, variance of the random effects, and auto-correlation structure of the model. Proofs for the consistency properties of the estimators along with their convergence rates are derived. A simulation study is conducted to examine first the estimation effects on parameters when the non-parametric function is ignored, and then an overall estimation study is carried out in the presence of the non-parametric function by including its estimation as well.     

Rolling element bearing diagnosis based on probability box theory

Feature extraction leads to the loss of statistical information of raw data and ignores the sampling uncertainty and the fluctuations in the signal over time in mechanical fault diagnosis. In this paper, novel modeling methods for mechanical signals based on probability box theory were proposed to solve the above problem. First, the type of random distribution of the bearing signals were analyzed. Then, a Dempster-Shafer structure was obtained to establish a probability box model. To address the identification difficulty of the type of random distribution for the bearing signals, a second probability box model was established based on a vector consisting of features from the bearing signals. If the data are not found to follow a random distribution, a third modeling method based on the definition of probability boxes was proposed. The effectiveness and applicability of the three proposed models were compared with experimental data from rolling element bearings. The combination of probability box theory and mechanical fault diagnosis theory can open up a new research direction for mechanical fault diagnosis.     

On wave propagation in a random conducting magneto-non-simple thermo-viscoelastic medium

The paper examines the problem of wave propagation in a random conducting magneto-non-simple thermo-viscoelastic medium. The medium has been assumed to be weakly conducting and weakly thermal. The thermomechanical coupling parameter and the conductivity are random functions, proportional to ε, with non-zero mean values, ε measuring the smallness of the scale of random fluctuation of inhomogeneities of the medium. The smooth perturbation technique enunciated by Keller (1964) has been employed to analyze the appropriate dispersion equation in non-simple thermoelastic medium. The longitudinal and transverse waves were discussed by using a particular form of thermomechanical coupling parameter representing the corresponding auto-correlation function. The effect of magnetic conductivity has been investigated. The phenomena of attenuation of waves and change of phase speed were discussed numerically in details.     

Markovian Imperfect Software Debugging Model and Its Performance Measures

Abstract

This paper considers a Markovian imperfect software debugging model incorporating two types of faults and derives several measures including the first passage time distribution. When a debugging process upon each failure is completed, the fault which causes the failure is either removed from the fault contents with probability p or is remained in the system with probability 1 ? p. By defining the transition probabilities for the debugging process, we derive the distribution of first passage time to a prespecified number of fault removals and evaluate the expected numbers of perfect debuggings and debugging completions up to a specified time. The availability function of a software system, which is the probability that the software is in working state at a given time, is also derived and thus, the availability and working probability of the software system are obtained. Throughout the paper, the length of debugging time is treated to be random and thus its distribution is assumed. Numerical examples are provided for illustrative purposes.     

The construction of markov processes in random environments and the equivalence theorems

In sec.1, we introduce several basic concepts such as random transition function, p-m process and Markov process in random environment and give some examples to construct a random transition function from a non-homogeneous density function. In sec. 2, we construct the Markov process in random enviromment and skew product Markov process by p -m process and investigate the properties of Markov process in random environment and the original process and environment process and skew product process. In sec. 3, we give several equivalence theorems on Markov process in random environment.     

在非线性回归模型中误差为AR(2)的相关性检验

本文讨论了在非线性回归模型中误差为AR(2)的相关性检验，得到了误差相关性检验的似然比检验统计量、Score检验统计量．对感兴趣参数和多余参数，利用Cox and Reid(1987)提出的正交化方法，给出了修正的似然比检验统计量和Score检验统计量．推广了胡跃清，韦博成(1994)讨论的在非线性回归模型中误差为AR(1)相关性检验的结果．     

旋转机械故障诊断中的哈尔谱研究

本文将哈尔变换应用于旋转机械故障诊断之中,并提出了用于诊断的“脉冲锐度”指标.基于付立叶分析的频谱分析是目前广泛采用的方法,与快速付立叶变换相比,哈尔变换具有实时性,逼近效果好,适用于对脉冲的提取等优点.而不足之处是受样本始点选取及样本长的影响大.对此,本文提出了控制各次样本的等效性的方法,改善了哈尔谱的稳定性与比较性.最后,通过对滚珠轴承故障模拟试验台进行试验得到的结果证实了哈尔谱及脉冲锐度指标对故障的敏感性.