高斯混合噪声中弱信号的Rao检测方法

期望最大化(Expectation Maximization,EM)算法是求解参数最大似然估计(MLE)的最优迭代算法,但若参数初始化不恰当,会使估计值落入"初值陷阱",导致错误的参数估计值.为此,本文提出了估计高斯混合噪声参数的矩 - EM算法,即先求参数的矩估计,并用矩估计值初始化参数,再通过EM迭代算法估计参数.在此基础上,经高斯化滤波,导出了高斯混合噪声背景下未知幅度弱信号的Rao检验统计量.仿真结果表明,矩 - EM算法可以更准确地估计噪声参数;基于矩 - EM算法的Rao检测性能优于基于EM算法的Rao检测性能.     

基于EM算法的极大似然分布式量化估计融合新方法

该文针对水下目标探测中的多传感器分布式量化估计融合问题,建立了分布式量化估计融合模型,在考虑信道噪声且其统计特性不完全已知条件下,充分利用EM算法在观测数据缺失时参数估计的优越性,提出了一种基于期望极大化(EM)算法的极大似然分布式量化估计融合新方法。该方法将未知的水声信道噪声参数以及局部量化器量化概率建模为EM算法中二元高斯混合模型参数,利用极大似然估计方法的估计不变性得到目标参数的估计融合结果。仿真实验表明:该方法在局部传感器观测样本数目大于5000和信噪比大于6 dB时与已有理想信道条件下的估计方法性能相当,该方法为水下目标探测中分布式量化估计融合系统的工程实现提供了理论依据。     

改进高斯混合粒子滤波被动目标跟踪算法

针对被动传感器跟踪系统非线性较强问题,提出了一种基于改进高斯混合粒子滤波的被动传感器目标跟踪算法。该算法基于Sigma点卡曼滤波和粒子滤波的特点,用有限的高斯混合模型来近似后验状态密度、系统噪声和观测噪声的分布。然后结合遗传算法和EM算法来实现模型的降阶,克服了EM算法假定混合成分数为已知、迭代的结果需要依赖初始值、可能收敛到局部最大点或可能收敛到参数空间的边界的缺点,从而改善粒子枯竭的问题。仿真实验结果表明在被动传感器跟踪领域,与传统粒子滤波、基于EM的高斯混合粒子滤波和基于贪心EM的高斯混合粒子滤波相比,该算法在保持高精度估计能力的同时,具有较强的鲁棒性,是解决非线性系统状态估计问题的一种有效方法。     

双基地MIMO雷达参数估计

文中探讨了双基地MIMO雷达进行参数估计的方法。针对时域噪声为高斯白噪声,存在空间高斯有色噪声的背景,引入时间延迟这个因素构造旋转因子,同时利用匹配滤波器和ESPRIT子空间算法实现目标角度以及多普勒频率的参数联合估计。仿真结果表明这种算法可以消除系统中空间高斯有色噪声的影响,得到较高的估计精度。     

基于遗传算法的K-means初始化EM算法及聚类应用

混合高斯模型能够有效地拟合概率密度函数,常用的混合高斯概率密度模型参数估计方法是EM迭代算法,这种算法的缺点是估计精度过分依赖于初始值,而且不能估计模型阶数。基于遗传算法的K-means初始化EM算法可以同时估计模型阶数和参数。试验结果表明,该算法具有更好的聚类效果。     

一种小波系数模型在图像噪声参数估计中的应用

在小波图像处理中,通常利用HH子带来估计高斯白噪声方差,目前流行的估计方法是由Donoho和Johnstone提出的(简称DJ法),但是该方法给出的估计值通常都偏大。针对这一点,该文将他们的方法结合双随机小波系数模型,提出了一种新的、递归的方差估计方法。在已由Donoho的方法获得噪声方差估计的粗略估计的情况下,新方法利用统计学理论将HH子带中的信号滤除从而得到更接近于纯噪声的HH子带,然后利用这一新的HH子带来估计噪声的方差。结合EM参数估计方法,该方法还可以实现非高斯噪声参数的估计,实验表明新方法同Donoho法相比有很大的改善。     

一种LFM信号最大似然估计模型与参数估计快速算法

从最大似然估计模型入手,提出了一种适合在一般高斯噪声环境（包括色噪声）下LFM信号目标的参数估计模型和基于此估计模型的调频斜率和初始频率估计的快速算法。此方法获得了最大似然方法估计精度高的优点,且运算量比传统的最大似然方法大大降低。另外推导出了一般高斯环境下的LFM参数估计的CRB界,为一般高斯环境下的估计的参数的方差提供实际下界。     

利用EM算法估计寿命模型中的参数

针对寿命模型中未知参数估计的复杂度较高,计算量较大这一问题提出了一种EM算法。通过引用了相关寿命模型,采用混合高斯分布的期望最大化算法(EM),对寿命中的未知参数进行了估计,并利用仿真数据对不同时间段的寿命预测结果进行对比,证明了利用EM算法估计参数可减少计算量,降低了参数估计的复杂度。     

混合高斯自回归模型参数估计方法之ML-DC

混合高斯自回归模型可以对有色非高斯数据的概率密度和功率谱密度进行有效的拟合.而ML-DC算法则可解决这一模型的参数估计问题。描述了混合高斯自回归模型及其参数估计问题之后,分别导出了功率谱密度参数的最大似然估计和概率密度参数估计的动态簇算法,并由此组成了参数耦合估计的ML-DC算法。最后结合一组仿真实例对其估计性能进行了详细探讨,指出并解释了算法的适用范围。     

高斯噪声中的参数盲估计

盲信号处理方法中常忽略噪声的影响,而实际问题中噪声的影响是存在的.本文主要讨论了在协方差矩阵未知的加性高斯噪声中混合系数的盲估计问题.本文以最大似然估计为基础,提出一种求解参数的最优化算法,给出了混合矩阵和协方差矩阵的计算式.采用高斯混合模型(GMM)来逼近源信号的概率密度函数,简化了算法中的积分,导出了一种基于EM算法的迭代式.仿真表明,算法不仅能稳定收敛,而且在低信噪比下也能获得良好性能.     

Efficient estimation of Class A noise parameters via the EMalgorithm

The Class A Middleton noise model is a commonly used statistical-physical, parametric model for non-Gaussian interference superimposed on a Gaussian background. In this study, the problem of efficient estimation of the Class A parameters for small sample sizes is considered. The proposed estimator is based on the EM algorithm, a two-step iterative estimation technique that is ideally suited for the Class A estimation problem since the observations can be readily treated as incomplete data. For the single-parameter estimation problem, a closed-form expression for the estimator is obtained. Furthermore, for the single-parameter estimation problem, it is shown that the sequence of estimates obtained via the EM algorithm converges, and a characterization of the point to which the sequence converges is given. In particular, it is shown that if the limit point of this convergent sequence is an interior point of the parameter set of interest, then it must be a stationary point of the traditional likelihood function. In addition, for both the single-parameter and two-parameter estimation problems, the small-sample-size performance of the proposed EM algorithm is examined via an extensive simulation study     

Recursive blind identification of non-Gaussian time-varying ARmodel and application to blind equalisation of time-varying channel

A novel method for the blind identification of a non-Gaussian time-varying autoregressive model is presented. By approximating the non-Gaussian probability density function of the model driving noise sequence with a Gaussian-mixture density, a pseudo maximum-likelihood estimation algorithm is proposed for model parameter estimation. The real model identification is then converted to a recursive least squares estimation of the model time-varying parameters and an inference of the Gaussian-mixture parameters, so that the entire identification algorithm can be recursively performed. As an important application, the proposed algorithm is applied to the problem of blind equalisation of a time-varying AR communication channel online. Simulation results show that the new blind equalisation algorithm can achieve accurate channel estimation and input symbol recovery     

Spectral estimation of nonstationary EEG using particle filtering with application to event-related desynchronization (ERD)

This paper proposes non-Gaussian models for parametric spectral estimation with application to event-related desynchronization (ERD) estimation of nonstationary EEG. Existing approaches for time-varying spectral estimation use time-varying autoregressive (TVAR) state-space models with Gaussian state noise. The parameter estimation is solved by a conventional Kalman filtering. This study uses non-Gaussian state noise to model autoregressive (AR) parameter variation with estimation by a Monte Carlo particle filter (PF). Use of non-Gaussian noise such as heavy-tailed distribution is motivated by its ability to track abrupt and smooth AR parameter changes, which are inadequately modeled by Gaussian models. Thus, more accurate spectral estimates and better ERD tracking can be obtained. This study further proposes a non-Gaussian state space formulation of time-varying autoregressive moving average (TVARMA) models to improve the spectral estimation. Simulation on TVAR process with abrupt parameter variation shows superior tracking performance of non-Gaussian models. Evaluation on motor-imagery EEG data shows that the non-Gaussian models provide more accurate detection of abrupt changes in alpha rhythm ERD. Among the proposed non-Gaussian models, TVARMA shows better spectral representations while maintaining reasonable good ERD tracking performance.     

EM框架下实现被动测距的状态估计和参数学习

在红外成像跟踪系统中,通常仅能测量目标的角度信息,不能直接测量目标与观测站间的距离。研究了基于红外成像系统的被动测距技术,首先利用状态空间模型的分析方法建立被动测距的状态估计和参数学习的混合估计模型,然后介绍EM的基本原理和参数的最大似然估计。EM算法的E步利用粒子滤波和粒子平滑器来完成,实现被动测距的状态估计;M步利用梯度搜索的方法来求解参数。被动测距是一个带有未知参数的非线性系统的状态估计,文中利用状态估计与参数学习的状态空间模型来描述,并利用EM法来求解,为被动测距的求解提供了一条新的途径。模拟实验表明,基于粒子滤波和梯度搜索的EM方法能同时完成被动测距的状态估计和参数学习。     

Noise Estimation in Magnitude MR Datasets

Estimating the noise parameter in magnitude magnetic resonance (MR) images is important in a wide range of applications. We propose an automatic noise estimation method that does not rely on a substantial proportion of voxels being from the background. Specifically, we model the magnitude of the observed signal as a mixture of Rice distributions with common noise parameter. The expectation-maximization (EM) algorithm is used to estimate all parameters, including the common noise parameter. The algorithm needs initializing values for which we provide some strategies that work well. The number of components in the mixture model also needs to be estimated en route to noise estimation and we provide a novel approach to doing so. Our methodology performs very well on a range of simulation experiments and physical phantom data. Finally, the methodology is demonstrated on four clinical datasets.     

非高斯有色噪声背景下二维谐波频率估计的累积量投影方法

针对非高斯有色噪声中的二维谐波频率估计问题,该文提出了复数线性非高斯过程的二维累积量投影定理。应用该定理并巧妙地构造观测信号的高阶累积量求得非高斯噪声的自相关,并通过求解一个广义特征值对噪声空间进行预白化,然后结合高分辨率的子空间方法二维MUSIC估计得到二维谐波参量。该文方法解决了非高斯有色噪声中的二维谐波频率估计问题,特别地当非高斯噪声为对称分布和谐波信号中存在二次相位耦合时该文方法同样有效。仿真实验验证了该文结论。     

复杂电磁环境无线电系统SUE评估

针对复杂电磁环境下无线电系统的频谱效率评估问题,提出了一种带环境参数的SUE评估方法,用以解决复杂电磁环境及动态频率指配策略带来的电磁空间占用表示问题。给出了移动通信系统的SUE的仿真计算示例,结果表明该方法计算结果与经验吻合,计算过程可操作性强。通过根据具体的系统用途和所处的电磁环境复杂性设定M、Tw、Tc等参数,该方法的应用具有较好的扩展性。     

基于群Monte Carlo的大气噪声二维模型参数估计

为解决多天线最佳接收下的多维非高斯噪声参数估计问题,提出了基于群蒙特卡洛的大气噪声二维模型参数估计方案,通过联合设计蒙特卡洛马尔科夫链和优化重要性重采样算法,实现噪声模型的全局最优参数估计。针对该算法高强度运算需求,在GPU平台上对核心运算作细粒度并行计算处理并优化设计,使运算速度大幅提升,以满足实时处理要求。仿真实验结果表明,该算法迭代收敛快,精度高,各参数估计相对误差普遍小于0.02,最大相对误差可控制在0.05以内,运算速度较传统计算有大幅度的提高,可充分满足低频通信系统中实时计算的要求。     

Gaussian mixture density modeling of non-Gaussian source forautoregressive process

A new approach is taken to model non-Gaussian sources of AR processes using Gaussian mixture densities that are known to be effective for approximating wide varieties of probability distributions. A maximum likelihood estimation algorithm is derived for estimating the AR parameters by solving a generalized normal equation, and a clustering algorithm is used for estimating the parameters of Gaussian mixture density of the source signals. The correlation matrix of the generalized normal equation is not Toeplitz but is symmetric and in general positive definite. Higher order statistics of skewness and kurtosis are used for identifying the source distribution as being Gaussian or non-Gaussian and, consequently, determining the parameter estimation technique between the conventional method and the proposed method. Experiments on non-Gaussian source AR processes demonstrate that under high SNR conditions (SNR⩾20 dB), the proposed algorithm outperforms the conventional AR estimation algorithm and the cumulant-based algorithm by an order-of-magnitude reduction of average estimation errors. The proposed algorithm also has very low estimation errors with short data records. Finally, a maximum likelihood prediction method is formulated for non-Gaussian source AR processes that has shown potential in achieving higher efficiency signal coding than linear predictive coding     

An adaptive spatial diversity receiver for non-Gaussianinterference and noise

Standard linear diversity combining techniques are not effective in combating fading in the presence of non-Gaussian noise. An adaptive spatial diversity receiver is developed for wireless communication channels with slow, flat fading and additive non-Gaussian noise. The noise is modeled as a mixture of Gaussian distributions and the expectation-maximization (EM) algorithm is used to derive estimates for the model parameters. The transmitted signals are detected using a likelihood ratio test based on the parameter estimates. The new adaptive receiver converges rapidly, its bit error rate performance is very close to optimum when relatively short training sequences are used, and it appears to be relatively insensitive to mismatch between the noise model and the actual noise distribution. Simulation results are included that illustrate various aspects of the adaptive receiver performance