Arma spectral estimation based on partial autocorrelations — Part II: Statistical analysis

In a previous paper [1], a new algorithm for ARMA spectral estimation of stationary time series has been presented. The algorithm is based on nonlinear least squares fit of the sample partial autocorrelations to the partial autocorrelations generated by the assumed ARMA model. This paper explores the statistical properties of the above algorithm, including some numerical examples of the asymptotic variance of the estimated parameters, as compared to the Cramer-Rao bound. The results confirm the good performance of the algorithm and suggest an improvement in its implementation.     

Generalized feature extraction for time-varying autoregressivemodels

In this paper, a feature extraction scheme for a general type of nonstationary time series is described. A non-stationary time series is one in which the statistics of the process are a function of time; this time dependency makes it impossible to utilize standard globally derived statistical attributes such as autocorrelations, partial correlations, and higher order moments as features. In order to overcome this difficulty, the time series vectors are considered within a finite-time interval and are modeled as time-varying autoregressive (AR) processes. The AR coefficients that characterize the process are functions of time that may be represented by a family of basis vectors. A novel Bayesian formulation is developed that allows the model order of a time-varying AR process as well as the form of the family of basis vectors used in the representation of each of the AR coefficients to be determined. The corresponding basis coefficients are then invariant over the time window and, since they directly relate to the time-varying AR coefficients, are suitable features for discrimination. Results illustrate the effectiveness of the method     

Second-order blind separation of sources based on canonical partialinnovations

This paper is devoted to the study of the second-order properties using partial autocorrelations of an instantaneous mixture of colored sources without additive noise. We introduce the notion of symmetric recursive canonical partial innovation. Then, their components, for the observation process, meet exactly with those of the source process from the order for which the autoregressive models underlying the sources are distinct. This property leads to a new separation method based on the sample counterpart of partial autocorrelation matrices associated with these innovations. Simulation results show a notable improvement of the achievements of such an approach with respect to those of similar methods. Two other separation methods related to partial autocorrelation are also discussed     

A cross-reference method of parameter estimation and noise reduction and its applications

This paper proposes a cross-reference method of nonlinear time series analysis, combining the tasks of dynamical system parameter estimation and noise reduction which were fulfilled separately before. With the positive interaction between the two processing modules, the method is somewhat superior. Some prior works can be viewed as special cases of this general framework and effective new algorithms may be devised according to it. Two examples of chaotic time series analysis are also given to show the applicability of the proposed method.     

非高斯有色噪声中的正弦信号频率估计

本文研究非高斯ＡＲＭＡ有色噪声中的正弦信号频率估计问题。利用自相关函数和三阶累积量相结合，提出了一种先估计噪声模型ＡＲ参数，然后对观测值进行预滤波，最后估计信号模型参数的新方法，模拟实验结果表明，新方法具有良好的频率估计性能。     

Formulas for the distribution of sums of independent exponential random variables

This paper derives a new type of formula for the probability that, among a collection of items with s-independent exponential times to failure, a certain subset of them fails in a given order before a certain time, and all the remaining items survive beyond that time. This formula is in the form of a power series that satisfies a certain constant coefficient linear differential equation with specified initial conditions. This provides an alternative to existing closed-form formulas of the "exponomial" variety, viz., a nonlinear combination of exponential terms, where the coefficients of the exponential terms are polynomials in the mission time. Some results are given which quantify the computation effort required to achieve a specified accuracy using partial sums of the infinite series; a simple example illustrates these results. This approach can be very efficient for system reliability analysis where the product of the mission time and the sum of the failure rates down any path leading to system failure is small. Further work is needed to expand the practical applicability of this approach to cases where some rates are large and/or the mission time is long.     

A partial spectrum approach to the analysis of quasi-stationary time series

The notion of a stationary random function is generalized to include random functions whose statistical properties vary slowly with time. A criterion for quasi-stationarity is proposed, and two methods for the spectral analysis of quasi-stationary time series are presented. The first of these, the method of partial series, is equivalent to treating the series as stationary in each of several subseries. The second, the method of partial spectra, involves an expansion of the time dependent local energy spectrum in orthogonal functions of the interval of analysis. An estimate of the coefficient of the nth-order function is given by the cosine transform of the timewise cross correlation of the series with the product of the series and the nth-order function, The statistical reliability of this estimate and of the reconstructed spectral estimate is investigated, and a numerical example from a field study of the wind generation of ocean waves is presented.     

二维正弦波检测的直接数据法

本文用一种新方法证明了,二维正弦波频率服从的二维特征多项式可取四种不同形式,并提出了一种直接数据法,借助它可直接利用观测数据本身高分辨检测出白噪声中的多个二维正弦波。     

Signal estimation via selective harmonic amplification: MUSIC,Redux

The technique known as multiple signal classification (MUSIC) is a semi-empirical way to obtain pseudo-spectra that highlight the spectral-energy distribution of a time series. It is based on a certain canonical decomposition of a Toeplitz matrix formed out of an estimated autocorrelation sequence. The purpose of this paper is to present an analogous canonical decomposition of the state-covariance matrix of a stable linear filter driven by a given time series. Accordingly, the paper concludes with a modification of MUSIC. The new method starts with filtering the time series and then estimating the covariance of the state of the filter. This step in essence improves the signal-to-noise ratio (SNR) by amplifying the contribution to the actual value of the state-covariance of a selected harmonic interval where spectral lines are expected to reside. Then, the method capitalizes on the canonical decomposition of the filter state-covariance to retrieve information on the location of possible spectral lines. The framework requires uniformly spaced samples of the process     

PEEC Modeling of Dispersive and Lossy Dielectrics

In this paper a general formulation is presented for the time-domain partial element equivalent circuit method in a general dispersive medium. The formulation is based on Debye and Lorentz models where the resulting model is passive. The incorporation of such models into a partial element equivalent circuit solver is described by both convolution techniques and equivalent circuits. The new circuit models can be applied in the frequency as well as the time domain. Numerical examples are given to validate the proposed formulation and to show that the proposed method is accurately capturing the physics of dispersive and lossy dielectrics.      

A novel approach to controlled programming of tunnel-basedfloating-gate MOSFETs

This paper presents a new approach to obtain automatic and accurate control of the threshold voltage of floating-gate MOSFETs programmable by means of tunneling current. The proposed method avoids using a series of partial write/erase operations followed by measurements and adjustment steps, thus achieving a significant advantage in terms of programming time for the same accuracy. The simplicity of the proposed method and its inherent speed make it ideal in a wide range of possible applications     

Periodic variation method for blind symbol rate estimation

In order to obtain unknown symbol rate of incoming signal at a receiver, in this paper, cyclostationary features of linear digitally modulated signals are exploited by proposed periodic variation method. A low complexity but highly accurate symbol rate estimation technique is obtained. The proposed method is based on a superposed epoch analysis over autocorrelations obtained blindly in different sampling frequencies. The obtained autocorrelations are analyzed in the frequency domain, and it is seen that there are large oscillations when the autocorrelation is obtained around the symbol rate. Then, a superposed epoch analysis is developed in order to estimate symbol rate based of the periodic variations on the frequency responses of autocorrelations. The proposed algorithm is quite accurate in the noisy environment because the noise is having no frequency component after taking Fourier transform of autocorrelations in all sampling rates, and this feature is also valid for the offset frequency that the purposed estimation is not affected by offset frequency. Thus, a successful blind symbol rate estimation algorithm is obtained, and it performs much better error performance than those using the well‐known cyclic correlation based symbol rate estimations, as it is proven by the obtained performances presented in the paper. Copyright © 2013 John Wiley & Sons, Ltd.     

一种新颖的混沌时间序列分析方法

本文提出了一种新颖的混沌时间序列分析方法,即从被加性高斯白噪声污染的混沌时间序列中估计其系统参数并同时进行噪声抑制的方法。假定产生混沌时间序列的模型已知,但相应的参数未知。这种新方法把对混沌时间序列的参数估计和噪声抑制看作是一种最小化过程,并利用了最速梯度下降方法解决。数值模拟实验表明新方法要优于现有的方法,是估计混沌系统系数和噪声抑制的一种有效的方法。     

On a two-dissimilar-unit system with three modes and random check

This paper considers a two-dissimilar-unit series system with three modes (normal, partial failure and total failure) of each unit under the assumption that the system is checked at a random time to make sure that it is in normal or partial failure. By using probability analysis and the supplementary variable method, some reliability indices are derived.     

Futuristic speed prediction using auto‐regression and neural networks for mobile ad hoc networks

In this paper, we propose a speed prediction model using auto‐regressive integrated moving average (ARIMA) and neural networks for estimating the futuristic speed of the nodes in mobile ad hoc networks (MANETs). The speed prediction promotes the route discovery process for the selection of moderate mobility nodes to provide reliable routing. The ARIMA is a time‐series forecasting approach, which uses autocorrelations to predict the future speed of nodes. In the paper, the ARIMA model and recurrent neural network (RNN) trains the random waypoint mobility (RWM) dataset to forecast the mobility of the nodes. The proposed ARIMA model designs the prediction models through varying the delay terms and changing the numbers of hidden neuron in RNN. The Akaike information criterion (AIC), Bayesian information criterion (BIC), auto‐correlation function (ACF), and partial auto‐correlation function (PACF) parameters evaluate the predicted mobility dataset to estimate the model quality and reliability. The different scenarios of changing node speed evaluate the performance of prediction models. Performance results indicate that the ARIMA forecasted speed values almost match with the RWM observed speed values than RNN values. The graphs exhibit that the ARIMA predicted mobility values have lower error metrics such as mean square error (MSE), root MSE (RMSE), and mean absolute error (MAE) than RNN predictions. It yields higher futuristic speed prediction precision rate of 17% to 24% throughout the time series as compared with RNN. Further, the proposed model extensively compares with the existing works.     

数据挖掘中的现代时间序列分析方法

在比较了现代时间序列分析方法与传统时间序列分析方法优缺点基础上，认为现代时间序列分析方法，是目前处理海量时间序列数据挖掘的一种新的非常适用的较好方法，具有一定的推广和应用价值。同时提出在目前时间序列数据挖掘中，采用现代时间序列分析算法，全面代替传统时间序列分析算法这一新的观点。     

短时序列预测的新方法

We propose a procedure to forecast short time series with stable seasonal pattern. This new method is motivated by the observations that short time series arise in many situations for the fierce competition. The quantity to be predicted is a yearly accumulation assuming that the partially accumulated data within the year are available. A simple model is proposed to describe the relationship between the yearly accumulation and partial accumulation and analytic results are obtained for both the point prediction and the predicative distribution. A comparison will be conducted between this model and traditional time series forecasting model with data from telecommunication industry. This method works better than the traditional models when only small amount of data are available. It can also be applied to forecast individual observations with a proper disaggregation algorithm.     

Performance of polarity correlators or limiters with pseudorandom additive input noise (Corresp.)

Uniformly distributed noise is often added to the inputs of limiters, quantizers, and polarity correlators to decrease the effects of the nonlinearities. This paper derives the error autocorrelations of the outputs of those devices when the additive noise is not purely vhite, but is of sample-and-hold form as might easily be produced by a pseudorandom noise generator and a digital to analog converter. These error autocorrelations then permit analyses of the errors in the outputs of the analog filters which follow the limiters.     

Extensions of the weighted-sample method for digitizingcontinuous-time filters

Methods continue to improve for taking the transfer function of a stable, continuous-time, single-input single-output system or filter and converting it to an “equivalent” discrete-time filter. The weighted-sample (WS) method of carrying out the digitizing process is one such method. It is a higher order method, compared with the first-order Tustin's method, so it usually achieves a smaller error for a given system, input, and sample time. Like the Tustin method, but unlike some higher order digitization methods, it allows the sample time to be selected without being constrained by stability considerations. This paper describes two extensions to the weighted-sample method. The first provides the ability to handle cases in which the continuous filter contains one or more series integrators. The second extension modifies the WS filter to a new form, termed the WS' filter, which turns out to be the same as the MSRP filter. Several examples are given, and accuracy is assessed     

基于神经网络的时间序列动态预测器的调整学习算法

时间序列预测在金融等领域有着广泛的应用,近年来,基于时间网络的时间序列预测器引起了人们极大的研究兴趣,然而,基于神经网络的时间序列预测器经常给出无效的预测值。本文首先从理论上分析了基于神经网络的时间序列预测器给出无效预测值的概率,然后给出基于神经网络的时间序列预测器的调整学习算法（ＲＬＮＮＰ）,采用ＲＬＮＮＰ算法,基于神经网络的时间序列预测器,给过充分训练能够给出时间序列的有铲预测值。