Autoregressive forecast of monthly total ozone concentration: A neurocomputing approach

The present study endeavors to generate autoregressive neural network (AR-NN) models to forecast the monthly total ozone concentration over Kolkata (22°34′, 88°22′), India. The issues associated with the applicability of neural network to geophysical processes are discussed. The autocorrelation structure of the monthly total ozone time series is investigated, and stationarity of the time series is established through the periodogram. From various autoregressive moving average (ARMA) and autoregressive models fit to the time series, the autoregressive model of order 10 is identified as the best. Subsequently, 10 autoregressive neural network (AR-NN) models are generated; the 10th order autoregressive neural network model with extensive input variable selection performs the best among all the competitive models in forecasting the monthly total ozone concentration over the study zone.     

基于偏差消除最小二乘估计和Durbin方法的两阶段ARMAX参数辨识

针对带有外生变量的自回归移动平均模型(Autoregressive moving average with exogenous variable, ARMAX)的参数辨识问题提出一种两阶段辨识方法. 首先通过偏差消除最小二乘方法辨识带有外生变量的自回归部分(Autoregressive part with exogenous variable, ARX),然后采用Durbin方法将移动平均部分(Moving average, MA)的参数辨识问题转换成一个长自回归模型(Long autoregressive, LAR)的参数辨识问题, 并利用MA与等价LAR的参数对应关系直接得到MA参数, 最后利用辨识出的MA参数计算出噪声方差. 与扩展最小二乘法的数值仿真比较验证了这种两阶段辨识方法的有效性.     

The estimation of the order of an ARMA process using third-order statistics

The paper proposes a new approach to find an autoregressive moving average (ARMA) model order. The basic idea is to extend the previous approach proposed by Liang et al. to third order statistics (TOS). The algorithm uses data matrices rather than calculating cumulants of the observed signal. Hence, we avoid the non-stationary effects, which is due to finite-length observations. The system is driven by a zero-mean independent and identically distributed (i.i.d.) non-Gaussian process. The input signal is unobservable. The observed sequence is corrupted by a zero-mean additive Gaussian noise. Examples are given to demonstrate the performance of the proposed algorithm.     

ARMA model parameter estimation based on the equivalent MA approach

The paper investigates the relation between the parameters of an autoregressive moving average (ARMA) model and its equivalent moving average (EMA) model. On the basis of this relation, a new method is proposed for determining the ARMA model parameters from the coefficients of a finite-order EMA model. This method is a three-step approach: in the first step, a simple recursion relating the EMA model parameters and the cepstral coefficients of an ARMA process is derived to estimate the EMA model parameters; in the second step, the AR parameters are estimated by solving the linear equation set composed of EMA parameters; then, the MA parameters are obtained via simple computations using the estimated EMA and AR parameters. Simulations including both low- and high-order ARMA processes are given to demonstrate the performance of the new method. The end results are compared with the existing method in the literature over some performance criteria. It is observed from the simulations that our new algorithm produces the satisfactory and acceptable results.     

非线性时间序列建模的混合自回归滑动平均模型

提出了一类用于非线性时间序列建模的混合自回归滑动平均模型(MARMA).该模型是由K个平稳或非平稳的ARMA分量经过混合得到的.讨论了MARMA模型的平稳性条件和自相关函数.给出了MARMA模型参数估计的期望极大化(expectation maximization)算法.运用贝叶斯信息准则(Bayes information criterion)来选择该模型.MARMA模型分布形式富于变化的特征使得它能够对具有多峰分布以及条件异方差的序列进行建模.通过两个实例验证了该模型,并和其他模型进行比较,结果表明MARMA模型能够更好地描述这些数据的特征.     

Sequential estimation in two-dimensional discrete random fields

A sequential minimum variance estimation algorithm for a discrete two-dimensional random field modeled by a non-symmetric half-plane (NSHP) model is derived. A modification of the algorithm to facilitate inplace computation is presented and its implementation discussed. The application of the algorithm in image processing is illustrated by using the algorithm to restore a class of monochromatic images modeled by a symmetric (1,) NSHP model.     

估计MA参数的多维强Gevers-Wouters算法及其在构造ARMA新息模型中的应用

提出了用多维Gevers-Wouters（G－W）算法得到稳定的滑动平均（MA）过程的一个频域充分条件,并给出了在构造ARMA新息模型中的应用,给出了保证ARMA新息模型的MA多项式矩阵稳定的一个时域充分条件,仿真结果表明,多维G－V算法具有快速收敛的性质。     

On the identifiability of non-Gaussian ARMA models using cumulants

A fixed set of output cumulants of order greater than two guarantees unique identification of known-order causal ARMA (autoregressive moving-average) models, which are driven by unobservable non-Gaussian i.i.d. noise. The models are allowed to be non-minimum-phase, and their outputs may be corrupted by additive colored Gaussian noise of unknown covariance. The ARMA parameters can be estimated either by means of linear equations and closed-form expressions or by minimizing quadratic cumulant matching criteria. The latter approach requires computation of cumulants in terms of the ARMA parameters, which is carried out in the state space using Kronecker products     

Identifiability of the AR parameters of an ARMA process usingcumulants

The problem of estimating the autoregressive (AR)-order and the AR parameters of a causal, stable, single input single output (SISO) autoregressive moving average (ARMA) (p,q) model, excited by an unobservable i.i.d. process, is addressed. The observed output is corrupted by additive colored Gaussian noise, whose power spectral density is unknown. The ARMA model may be mixed-phase, and have inherent all-pass factors and repeated poles. It is shown that consistent AR parameter estimates can be obtained via the normal equations based on (p+1) 1-D slices of the mth-order ( m>2) cumulant. It is shown via a counterexample that consistent AR estimates cannot, in general, be obtained from a subset of these p+1 slices. Necessary and sufficient conditions for the existence of a full-rank slice are also derived     

一种基于PCI技术的谱估计方法

Burg方法是自回归模型谱估计方法中一个最受欢迎的方法。但Burg方法对含有噪声的正弦信号进行谱估计时存在两个方面的问题,为此该文提出了一种基于主成份求逆技术的谱估计方法。推导了利用主成份求逆技术计算自回归模型系数的解析表达式,利用该方法计算自回归模型系数只涉及到相关矩阵的主成分,不需要进行Burg方法中的Levinson递推,从而避免了出现Burg算法所出现的问题。最后通过计算机仿真验证了对该方法相对于Burg方法的优越性。     

基于ARMA的混合卷烟销售预测模型

为了提高卷烟销售预测准确性,平衡生产与需求,协同工商业,建立切实合理的月供应计划,提出了一个基于ARMA(autoregressive moving average model,自回归滑动平均模型)的混合卷烟销售预测模型,实现卷烟月总量的预测。该模型首先基于ARMA建立月预测模型;再用计划评审技术PERT得到月预测经验期望值;最后通过设定加权系数,综合两个预测值得到月预测销售总量。实验结果证明该模型能够较好地预测出规格卷烟月销售总量值变化。     

非线性时间序列预报的隐多分辨ARMA模型

研究一类用于非线性时间序列预报的隐多分辨自回归滑动平均(ARMA)模型,该模型以ARMA模型为初始细水平模型(即隐多分辨模型的基本块)．证明了模型的建模精度由水平问的方差决定．研究了新模型的自相关函数结构,给出了参数估计的Bayes方法和Metropolis-Hasting算法．进一步提出了一种可以直接用于不同基本块的隐多分辨模型的非线性时间序列预报方法,证明了其比其他的线性预报方法和隐多分辨模型预报方法降低了预报误差．最后通过数值模拟和实例验证了模型和预报方法,并和其他模型进行比较,结果表明新提出模型和预报方法能够更好地描述数据的特征,提高预报的精度．     

生成粉红噪声的ARMA模型

针对现有粉红噪声的生成方法所存在的计算过程复杂,与理想粉红噪声相比偏差较大等问题,本文提出了一种利用自回归滑动平均(Auto-regressive moving average,ARMA)模型法生成粉红噪声的新方法。首先,构造一个待定系数的ARMA模型,并通过Z变换和功率谱估计的公式进行推导;其次,利用已知的粉红噪声模拟滤波器的传递函数H(s)和双线性Z变换法推导出IIR数字滤波器的传递函数H(z),进而得到粉红噪声的ARMA模型;最后,利用MATLAB对生成的粉红噪声进行功率谱估计并与理想的粉红噪声进行对比。由MATLAB仿真结果可知,利用该方法生成的粉红噪声与理想的粉红噪声拟合度更高,完全符合粉红噪声的各项性能要求。     

On the estimation of two-dimensional moving average parameters

The authors address the estimation problem of moving average (MA) parameters of a 2D autoregressive moving average (ARMA) model. The problem is equivalent to solving a set of overdetermined 2D transcendental equations. Based on some extensions of the Newton-Raphson method, an iterative algorithm is proposed for estimating 2D MA parameters. The performance of the algorithm is demonstrated by a numerical example. For 2D sinusoids in white noise spatial series, some interesting features of 2D ARMA modeling are observed     

Automatic identification of cardiac health using modeling techniques: A comparative study

Heart rate variability (HRV), a widely adopted quantitative marker of the autonomic nervous system can be used as a predictor of risk of cardiovascular diseases. Moreover, decreased heart rate variability (HRV) has been associated with an increased risk of cardiovascular diseases. Hence in this work HRV signal is used as the base signal for predicting the risk of cardiovascular diseases. The present study concerns nine cardiac classes that include normal sinus rhythm (NSR), congestive heart failure (CHF), atrial fibrillation (AF), ventricular fibrillation (VF), preventricular contraction (PVC), left bundle branch block (LBBB), complete heart block (CHB), ischemic/dilated cardiomyopathy (ISCH) and sick sinus syndrome (SSS). A total of 352 cardiac subjects belonging to the nine classes were analyzed in the frequency domain. The fast Fourier transforms (FFT) and three other modeling techniques namely, autoregressive (AR) model, moving average (MA) model and the autoregressive moving average (ARMA) model are used to estimate the power spectral densities of the RR interval variability. The spectral parameters obtained from the spectral analysis of the HRV signals are used as the input parameters to the artificial neural network (ANN) for classification of the different cardiac classes. Our findings reveal that the ARMA modeling technique seems to give better resolution and would be more promising for clinical diagnosis.     

融合HOG与ARMA模型的粒子滤波跟踪

传统的粒子滤波算法在跟踪目标受到相似背景干扰和遮挡或跟踪目标高速运动时,容易造成跟踪误差增大或跟踪失效的影响。针对室外运动目标跟踪的复杂性,提出一种对于干扰适应性较强的融合梯度方向直方图与自回归移动平均(ARMA)模型的粒子滤波跟踪方法。建立ARMA运动模型,用前两帧目标的位姿状态预测目标下一帧的状态,解决目标跟踪的角度变化与部分遮挡问题。实验结果表明,该模型能克服光照突变引发目标色彩突变的问题。     

基于OIVPM的特征值确定ARMA模型的结构

基于最小描述长度(MDL)准则,提出了一种新的自回归滑动平均(ARMA)模型结构 辨识方法.该方法将ARMA模型的结构辨识分两步进行:首先利用超定辅助变量乘积矩 (0IVPM)的最小特征值确定自回归(AR)部分的阶,然后利用协方差矩阵的特征值估计滑 动平均(MA)部分的阶.方法的可行性与有效性通过大量的数值仿真得到验证.     

On the use of calibration sensors in source localization using TDOA and FDOA measurements

The accuracy of a source location estimate is very sensitive to the presence of the random noise in the known sensor positions. This paper investigates the use of calibration sensors, each of which is capable of broadcasting calibration signals to other sensors as well as receiving the signals from the source and other calibration sensors, to reduce the loss in the source localization accuracy due to uncertainties in sensor positions. We begin the study with deriving the Cramer–Rao lower bound (CRLB) for source localization using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements when a single calibration sensor is available. The obtained CRLB result is then extended to the more general case with multiple calibration sensors. The performance improvement due to the use of calibration sensors is established analytically. We then propose a closed-form algorithm that can explore efficiently the calibration sensors to improve the source localization accuracy when the sensor positions are subject to random errors. We prove analytically that the newly developed localization method attains the CRLB accuracy under some mild approximations. Simulations verify the theoretical developments.     

一类非线性周期时间序列模型

为了描述周期时间序列中的偏倚和多峰等非线性特征,结合有限混合模型方法,提出混合周期自回归滑动平均时间序列模型（MPARMA）,给出了MPARMA模型的平稳性条件,讨论了期望最大化（EM）算法的应用,通过PM10浓度序列分析,评估了MPARMA模型的表现。     

Pole-assignment fixed-interval Kalman smoother with an exponential stability

Using the innovation analysis method in the time domain, based on the autoregressive moving average (ARMA) innovation model and white noise estimators, a pole-assignment fixed-interval steady-state Kalman smoother is presented for discrete-time linear stochastic systems. It avoids the computation of the optimal initial smoothing estimate, and can rapidly eliminate the effect of arbitrary initial smoothing estimate by assigning the poles of the smoother, with an exponentially decaying rate. Several simulation examples show its effectiveness.