一种改进的分段平稳随机过程的参数估计方法

将非平稳随机信号划分为分段平稳随机信号进行处理,为非平稳随机信号的研究提供的一种新的分析方法。为最优地将非平稳随机信号划分为分段平稳随机信号,Djuric等人用 Bayes方法,通过递推多维条件分布概率来估计最优划分参数值,但计算相当复杂。本文在研究 AR模型本身的一些特性的基础上,通过直接递推多维联合分布概率来估计最优划分参数,大大地减少了计算量。     

分段平稳随机过程的参数估计方法

Ｐ．Ｍ．Ｄｊｕｒｉｃ等人用贝叶斯法对非平稳随机信号化为分段平稳随机信号的问题作了。导出了一个关于分段数，各段自回归模型阶数和各段之间分界点的优化方程，但未给出具体的解法。由于经方程非常繁琐，故本文对其解法进行了研究，推导出其中一些递归关系，使求解问题变得简化，大大减少了计算量，同时对非平稳随机信号的分段问题作了进一步讨论。     

分段平稳随机过程的参数估计方法

P.M.Djuric等人(1992)用贝叶斯法对非平稳随机信号化为分段平稳随机信号的问题作了研究,导出了一个关于分段数、各段自回归(AR)模型阶数和各段之间分界点的优化方程,但未给出具体的解法.由于此方程非常繁琐,故本文对其解法进行了研究,推导出其中一些递归关系,使求解问题变得简化,大大减少了计算量,同时对非平稳随机信号的分段问题作了进一步讨论。     

非平稳信号的一种ARMA模型参数估计法

本文采用一种经过特殊处理的时变自回归滑动平均（ARMA）模型对非平稳随机信号进行分析．将这种模型左边的时变参数假设为一组基时间函数的线性组合，右边时变参数简化为常数，并用反馈线性估计法进行参数估计。该方法的主要特点是简单，计算量小，占用存储空间少．并用仿真的方法对算法予以验证，可用于一些常用的非平稳随机信号的分析．     

方差平稳随机信号的一种处理方法

该文提出了一种方差平稳随机信号的处理方法－－信号分解法。通过信号分解法对待处理信号进行分解,可得到方差平稳随机信号的趋向性序列，其余部分便是方差平稳随机信号中剔除趋向性后的零均值的平稳随机信号，它可用平衡随机信号模型来研究。该方法简单、通用，是处理方差平稳随机信号的一般方法。该方法得到的趋向性序列能更准确地逼近非平稳随机信号的趋向性曲线。     

平稳信号的非均匀采样与仿真

文中引入平稳随机过程点的知识,建立了广义平稳随机信号的非均匀采样序列模型,推导了其数字频谱的一般公式,揭示出了传统的谱分析没有考虑采样时间间隔的非均匀性对信号的统计特性的影响,误把采样所得随机强度序列的功率谱当作平稳随机过程非均匀采样信号的功率谱。丈中分析了几种具有典型分布函数的随机采样情况,证明了均匀采样信号的数字频谱只是非均匀采样数字频谱的一种特例。     

调频与调相连续波雷达信号的识别

针对复杂雷达信号的识别,提出了调频连续波(FMCW)和调相连续波(PMCW)雷达信号的识别算法。首先理论分析了周期性连续波(CW)信号自相关函数的特点,利用自相关函数来提取信号的调制周期。根据调制周期将信号进行分段,对分段后的信号采用时频域的非相干积累得到信号的时频分布。通过时频分布进行了时频脊线的提取和时频图像的处理,最终识别出调制类型。仿真结果表明,该算法在低信噪比(SNR)下具有很好的识别效果。     

平稳随机过程非均匀采样信号的数字谱研究

目前的随机信号分析多是基于作等时间间隔采样以描述信号特征,而实际应用中往往不能避免采样的非均匀性;传统的谱分析方法必然产生原理误差。本文引入平稳随机点过程的知识,建立了广义平稳随机信号的非均匀采样序列模型,推导了其数字频谱的一般公式,分析了具有典型分布函数的随机采样情况。     

电离层非相干散射谱和自相关函数估计算法

非相干散射谱对电离层各物理参数的研究具有至关重要的作用。现有非相干散射谱模型推导和计算较为复杂,且无法给出相应的自相关函数模型。该文重新推导了电离层非相干谱的简化模型,并提出相应的自相关函数模型。在此基础上,针对非相干散射信号处理中零时延处距离模糊大、分辨率较低,导致自相关函数在不同时延处均衡性较差,影响电离层散射谱估计性能的问题,提出使用自相关函数模型估计零时延自相关值的数据拟合方法。考虑到计算复杂度,提出利用多项式函数逼近自相关函数模型的快速实现方法。最后,通过对实测回波数据处理结果的对比分析,证明了该方法的可行性,对提高电离层探测精度具有重要意义。

     

一种有效的分段光滑信号逼近方法

传统的Fourier变换,连续小波变换等方法在逼近具有分段光滑特性的非连续信号时,因 Gibbs现象的干扰会产生比较大的误差。本文提出了一种有效的分段光滑信号逼近方法。首先根据给定信号的分段点位置,构造一组标准正交分段多项式系,该函数系具有正交性,收敛性及再生性。然后将信号在该函数系下进行正交分解及重构,即可得到该信号的最佳平方逼近结果。数值实验表明,本文方法比传统的正交基具有更好的逼近结果。     

在线结构断点估计的非平稳时间序列模型(英文)

Non-stationary time series could be divided into piecewise stationary stochastic signal. However, the number and locations of breakpoints, as well as the approximation function of the respective segment signal are unknown. To solve this problem, a novel on-line structural breaks estimation algorithm based on piecewise autoregressive processes is proposed. In order to find the "best" combination of the number, lengths, and orders of the piecewise autoregressive (AR) processes, the Akaikes Information Criter...     

A RESEARCH ON SEGMENTATION OF NONSTATIONARY STOCHASTIC PROCESS INTO PIECEWISE STATIONARY STOCHASTIC PROCESS

P. M. Djuric, etc.(1992) researched on the segmentation of nonstationary stochastic process into piecewise stationary stochastic process by Bayesian criterion ,and gave a dynamic equation about the number of segments, their boundaries and AR model orders for each segment, but did not give detailed solution for the equation. Because the solution for the equation is very complex, this paper investigates the solution, derives some recursive relations, simplifies the problem ,saves computation time and goes further into the segmentation of nonstationary stochastic process into piecewise stationary stochastic process.     

Aseismic designs based on artificial simulations

It is commonly believed that the time-varying frequency characteristics are important for the inelastic response of structures. Design code modification means structural cost changes; therefore any change must be based on solid evidence. Although the significance of time-varying frequency characteristics to ground motion has been recognized for a while, much more in-depth research is necessary before any meaningful engineering design conclusions can be reached. We apply joint time-frequency analysis techniques to a fully non-stationary ground motion model, with both intensity and frequency being non-stationary. The chirplet-based signal approximation is used to extract the time-varying frequencies from seismic ground-motion data samples. Based on that information, we compute the frequency-dependent modulating function in the stochastic model of the evolutionary random process. We generate and compare the artificial waves based on stochastic models of a uniform modulating random process and an evolutionary random process, separately. We also investigate the importance of the time-varying frequency characteristics of earthquake ground motion through an oscillator, with a single degree of freedom and elastic-plastic material behavior     

基于自适应分割算法的多跳频信号盲检测

传统的观点大都将跳频信号盲检测问题视为能量域的门限阈值问题,而从统计域来看,实际接收到的跳频信号是在一些未知时刻突变而在这些时刻之间保持统计平稳性的分段平稳随机信号,那么基于非平稳时间序列的各种突变检测算法就可以引入其中。分析了当前跳频突变通信信号的统计特性,给出了其高阶分段平稳的模型。将Bemaola-Galan（BG）提出的自适应分割算法推导到高阶,并将其成功应用于多个跳频突发信号盲检测和自适应提取中。仿真结果表明,该算法不需要任何先验信息,能够有效检测和提取多个突发通信信号,且性能优于传统的能量检测法。     

A Stochastic Model of the Backscattered Doppler Ultrasound from Blood

A stochastic model of the continuous wave (CW) Doppler ultrasound signal backscattered from blood is developed. The model incorporates the effects due to the flow-dependent packing and aggregation of red blood cells (RBC's) at a given hematocrit. The Doppler signal is shown to be a zero-mean, stationary, Gaussian random process which can be completely specified by its autocorrelation function. From the autocorrelation function, explicit closed-form expressions are derived for the power spectral density and the backscattering coefficient. Both expressions are found to be more general than those derived from previous blood models. Further, the values of the statistical parameters in the model are discussed in relation to recently published data on the backscattering coefficient of bovine RBC's suspended in saline and of bovine whole blood. It is shown that the change in backscatter with flow conditions can be explained by RBC orientation in saline and by RBC aggregation in whole blood.     

突发业务流的TES建模方法

高速通信网络存在大量诸如可变速率(VBR)视频这类具有突发性的业务流。突发性,在数学上主要通过业务流的到达时间间隔的边缘概率分布和自相关函数来描述。TES(Transform-Expand-Sample)是一种建模静态随机过程的非参数化技术,能准确匹配边缘概率分布并很好地近似自相关函数。本文简要介绍了TES方法的基本原理,再详细讨论突发业务流的TES建模及其软件实现。对MPEG视频业务的建模的仿真结果表明,TES模型能够很好地表征网络业务流的突发性。     

Wavelet footprints: theory, algorithms, and applications

Wavelet-based algorithms have been successful in different signal processing tasks. The wavelet transform is a powerful tool because it manages to represent both transient and stationary behaviors of a signal with few transform coefficients. Discontinuities often carry relevant signal information, and therefore, they represent a critical part to analyze. We study the dependency across scales of the wavelet coefficients generated by discontinuities. We start by showing that any piecewise smooth signal can be expressed as a sum of a piecewise polynomial signal and a uniformly smooth residual (Theorem 1). We then introduce the notion of footprints, which are scale space vectors that model discontinuities in piecewise polynomial signals exactly. We show that footprints form an overcomplete dictionary and develop efficient and robust algorithms to find the exact representation of a piecewise polynomial function in terms of footprints. This also leads to efficient approximation of piecewise smooth functions. Finally, we focus on applications and show that algorithms based on footprints outperform standard wavelet methods in different applications such as denoising, compression, and (nonblind) deconvolution. In the case of compression, we also prove that at high rates, footprint-based algorithms attain optimal performance (Theorem 3).     

四阶累积量的递推估计及其应用

本文推导一种复数或实数零均值平稳随机过程的高阶累积量估计的递推算法,随机信号的“峰度”递推估计公式,在递推估计公式中引入了随时间变化的“修正”项,使得该递推算法还可适合非平稳过程高阶累积量的估计计算。并且,本文大量计算了多类型。多航速、多舰船辐射噪声的“峰度”值,分析了舰船辐射噪声特性。     

5G网络中无人机-车辆非平稳信道模型与统计特性分析

针对无人机到车辆通信场景,提出了一种椭圆-圆柱-半球几何非平稳无人机-车辆信道模型。为了描述收发端周围散射体分布情况,一次散射径的散射体分布用同心椭圆面模拟;在二次散射径建模中,无人机侧散射体分布采用同心圆柱体模拟,并且车辆侧散射体分布使用同心半球体模拟;地面一次反射径的反射点分布则通过半球底面同心圆来模拟。为了进一步研究信道的非平稳特性,在各路径分量的二维角度服从Von Mises分布、Laplacian分布以及Von Mises Fisher分布的基础上,推导了时间自相关函数、空间互相关函数和多普勒频谱密度函数。仿真结果表明,理论值与测量值具有较好的拟合度,所提出的信道模型可以作为无人机到车辆非平稳信道建模的设计方案。