Order selection criteria for vector autoregressive models

The least-squares method for estimating the parameters of the vector autoregressive (VAR) model is considered and new estimates for the covariance matrix of the VAR model input noise and the prediction error covariance matrix are derived. Based on these new estimates, the criteria FPEF and AICF for VAR model order selection are proposed. FPEF can replace the final prediction error (FPE) criterion, and AICF, which is an estimate of the Kullback-Leibler index, can replace the Akaike information criterion (AIC) and its corrected version AICC. A simulation study shows that FPEF is less biased than FPE, and AICF is less biased than AIC and AICC. In addition, the performance of the proposed criteria is compared with that of other well-known criteria and the results show that AICF has the best performance and gives the smallest average prediction error.     

Order selection of autoregressive models

The problem of determining the order of autoregressive models by Bayesian predictive densities is addressed. A criterion employing noninformative prior densities of the model parameters is derived. Simulation results which demonstrate the good performance of the criterion are presented. Comparisons with four popular approaches verify its superiority in many cases     

3-D AR model order selection via rank test procedure

This paper deals with the problem of three-dimensional autoregressive (3-D AR) model order estimation. We show that the information for the 3-D AR model order is implicitly contained in an appropriate matrix rank built from the autocorrelation function (ACF) of the underlying 3-D Gaussian process. Exploiting this property, we develop an algorithm to estimate the order (p/sub 1/,p/sub 2/,p/sub 3/) corresponding to the quarter-space (QS) region of support. The proposed method is based upon a rank test procedure (RTP) using singular value decomposition (SVD) and solving nonlinear system equations. Numerical simulations are presented to illustrate the performances of the proposed algorithm.     

AR models for wideband source location

Wideband source location in array signal processing has received much attention in the literature lately. Methods such as the Coherent Signal Subspace (CSS) method proposed by Wang and Kaveh [12], and the signal subspace method used by Cadzow [3], are typical of the approaches used to tackle the multiple wideband source location problem. Most of these methods are variations of the narrowband high-resolution methods. Grenier [5], on the other hand, has applied the idea of time-dependent Auto-Regressive (AR) modeling [7] for a nonstationary process to the frequency domain AR modeling of the sensor outputs in a linear array and has been able to produce good results for a wideband signal. The AR coefficients in the model are expanded in a set of frequency-dependent basis functions. The choice of the basis functions was deemed immaterial and the method works even when only one snapshot of the array output is available. In this paper, we re-examine this method and present an extension of the frequency-dependent AR modeling approach to a planar array. It is shown that the use of a set of sinc functions for representing the frequency-dependent AR coefficients accurately tracks their evolution in the frequency domain, and gives superior performance compared to that when power or Legendre functions are used. We also propose two methods for smoothing the spatial spectra, from which the source locations are determined. Comparison with the CSS method are also presented.Research supported by NSERC and TRIO.     

Bayesian nonstationary autoregressive models for biomedical signal analysis

We describe a variational Bayesian algorithm for the estimation of a multivariate autoregressive model with time-varying coefficients that adapt according to a linear dynamical system. The algorithm allows for time and frequency domain characterization of nonstationary multivariate signals and is especially suited to the analysis of event-related data. Results are presented on synthetic data and real electroencephalogram data recorded in event-related desynchronization and photic synchronization scenarios.     

Adaptive AR modeling of nonstationary time series by means ofKalman filtering

An adaptive on-line procedure is presented for autoregressive (AR) modeling of nonstationary multivariate time series by means of Kalman filtering. The parameters of the estimated time-varying model can be used to calculate instantaneous measures of linear dependence. The usefulness of the procedures in the analysis of physiological signals is discussed in two examples: first, in the analysis of respiratory movement, heart rate fluctuation, and blood pressure, and second, in the analysis of multichannel electroencephalogram (EEG) signals. It was shown for the first time that in intact animals the transition from a normoxic to a hypoxic state requires tremendous short-term readjustment of the autonomic cardiac-respiratory control. An application with experimental EEG data supported observations that the development of coherences among cell assemblies of the brain is a basic element of associative learning or conditioning     

Parsimonious correlated nonstationary models for real baseband UWB data

Few ultrawide-band (UWB) models directly fit original baseband UWB data to simultaneously account for their correlation structure, non-Gaussianity, and nonstationarity. The difficulty arises from the fact that no relevant result is available, even in multivariate statistical analysis. It also arises from the attempt to pursue the details of the mechanism that is imagined to be responsible for the generation of UWB data. The consequence is the modeling complexity, which makes it difficult to handle the received signal correlation on the basis of a single realization. Accordingly, various partial characterization is used in the literature instead by virtue of second-order statistics (such as power delay profile), nonparametric characteristics (such as zero-crossing rate), or their combination. In this paper, we take a different philosophy, which believes that the information in the received UWB data itself, as long as fully exploited, plus some simple physical intuition should suffice for the model identification and its parameter estimation. A received UWB signal is decomposed into three factor processes and each is parsimoniously parameterized. The application of the new model to data regeneration and receiver design is illustrated by using the real UWB data acquired by Intel and the TimeDomain Corporation.     

非平稳随机场模型的遥感图像分割

提出一种双随机场模型。通过结合局部的统计量，将一种因果的自回归随机场模型应用于非平稳图像纹理的描述，同时，用马尔可夫随机场给标记场建模可以取得较好的分割效果。通过对实验的分析发现，分割结果仍存在一些错误。因此，在这种模型的基础上，引入了一种新的分类特征(熵率)来改善目标分割的效果。它反映了纹理的高阶相关性，改进了随机场低阶模型的不足。所提出的算法用于遥感图像的城区提取实验。     

A new method of nonstationary time series analysis based oninhomogeneous AR equation

We propose a new model for nonstationary time series analysis. The model is of a noise-contaminated signal of an AR system excited by a sequence of an input signal represented in terms of orthogonal functions. We also propose an algorithm that enables us to estimate parameters of the AR part and the input signal simultaneously. The models are finally evaluated by testing the recovery of an output signal. Examples of data analysis of the synthetic time series are shown for the ease in which the input signal is represented by a sequence of wavelets     

Application of statistical models to the efficient selection of endmembers by Field Radiometry

An efficient selection by means of Field Radiometry, of a targets set of homogenous spectral response, named endmembers, is going to optimize the methodology of the mixed spectral response modelling, obtained in the registration process of an image from remote sensors in satellites. Additionally, the information obtained through the analysis of its spectral profiles can contribute to facilitate the task of labelling in a thematic classification process in remote sensing. There is little bibliography about the selection process of endmembers from Field Radiometry with the application of statistical models to this process. In this work, the main objective is the establishment of an efficient selection protocol that allows a selection of the "endmember", based on the different types of land covers placed in a selected geographical area. This established methodology will be sustained by the application of statistical models basically applied to the phase of sampling. Specifically, a new statistic related to the sampling process and based on t-Student distribution will be shown. Its use will allow to determine the optimal number of samples in each case.     

Statistical AR models for the frequency selective indoor radio channel

A statistical model of the indoor radio channel is proposed that is derived from a second order autoregressive process representation of the channel frequency response. The accuracy of the statistical model is examined by comparing the cumulative distribution functions of the RMS delay spread and the 3 dB width of the frequency correlation function computed from the regenerated data with that of the measurements performed in two indoor radio propagation studies in the 0.9-1.1 GHz band.<>     

Compound statistical models for shadowed fading channels

The commonly used distribution for shadowed fading channels, the Nakagami-lognormal distribution, arises by compounding the Nakagami and log-normal distributions. This distribution, however, does not have a closed form and recently this led Shankar [Outage probabilities in shadowed fading channels using a compound statistical model. IEE Proc Commun 2005; 152:828–32; Error rates in generalized shadowed fading channels. Wireless Personal Commun 2004; 28:233–8; A compound scattering pdf for the ultrasonic echo envelope and its relationship to K and Nakagami distributions. IEEE Trans Ultrason Ferroelectr Frequency Control 2003; 50:339–43.] to propose an alternative form obtained by compounding the Nakagami and gamma distributions. In this note, we derive a comprehensive collection of models for shadowed fading channels obtained by compounding the Nakagami distribution with 16 flexible families. The calculations involve use of several special functions and their properties. We feel that this work could serve as a useful reference for statistical modeling of shadowed fading channels.     

A comparative study of AR order selection methods

Autoregressive (AR) modelling has assumed an important role in many application areas of signal processing. When fitting an AR model to an observed data sequence the selection of the model order is of great importance. Many criteria for selecting the AR model order have been proposed. However, these are scattered throughout the literature and little analysis of their relative performance is available. The principle aim of this paper is to compare the performance of some of the more recent methods of AR model order selection so that a broad perspective of the subject may be obtained. We compare the order selection methods using both narrowband and wideband data, with and without additive noise. The results of the study allow some basic recommendations to be made about the best types of method to be used in each case. It is observed that methods using the observed data perform best in the case of narrowband signal with no noise. Methods which employ the autocorrelation (second-order cumulant) sequence of the data show promise when used with wideband or noisy signals.     

AR model order selection based on bispectral cross correlation

A novel method is presented for optimal model order selection for autoregressive (AR) bispectrum estimation. The method depends solely on the data and requires no a priori information about the process. The method selects the model order that maximizes the cross correlation between the direct (fast Fourier transform-based) bispectrum estimate and the autoregressive bispectrum estimate. Simulation results are reviewed which demonstrate the method's performance for the case of quadratically coupled sinusoids embedded in white Gaussian noise     

A universal statistical test for random bit generators

A new statistical test for random bit generators is presented which, in contrast to presently used statistical tests, is universal in the sense that it can detect any significant deviation of a device's output statistics from the statistics of a truly random bit source when the device can be modeled as an ergodic stationary source with finite memory but arbitrary (unknown) state transition probabilities. The test parameter is closely related to the device's per-bit entropy which is shown to be the correct quality measure for a secret-key source in a cryptographic application. The test hence measures the cryptographic badness of a device's possible defect. The test is easy to implement and very fast and thus well suited for practical applications. A sample program listing is provided.This work was supported by Omnisec AG, Switzerland. A preliminary version of this paper was presented at Crypto '90, Aug. 11–15, 1990, Santa Barbara, CA.     

Asymptotic statistical properties of AR spectral estimators forprocesses with mixed spectra

The influence of a point spectrum on large sample statistics of the autoregressive (AR) spectral estimator is addressed. In particular, the asymptotic distributions of the AR coefficients, the innovations variance, and the spectral density estimator of a finite-order AR(p) model to a mixed spectrum process are presented. Various asymptotic results regarding AR modeling of a regular process with a continuous spectrum are arrived at as special cases of the results for the mixed spectrum setting. Finally, numerical simulations are performed to verify the analytical results     

Time-varying spectral estimation using AR models with variableforgetting factors

A method of estimating time-varying spectra of nonstationary signals using recursive least squares (RLS) with variable forgetting factors (VFFs) is described. The VFF is adapted to a nonstationary signal by an extended prediction error criterion which accounts for the nonstationarity of the signal. This method has better adaptability than the conventional algorithm with high fixed forgetting factor (FFF) in the nonstationary situation, and has lower variance than the conventional one with low FFF in the stationary situation. The extra computation time for the forgetting adaptation is almost negligible     

Joint antenna subset selection for spatial multiplexing systems based on statistical and instantaneous selection criteria

While the joint transmit/receive (Tx/Rx) AnSS with exhaustive search is the best solution for error rate minimization, its complexity makes it difficult for implementation on practical systems. To overcome this disadvantage, we propose a two-stage AnSS algorithm for the spatial multiplexing (SM) in the multiple input multiple output (MIMO) system, which employs both the statistical (i.e., average Euclidean distance, AED) and instantaneous selection criteria (i.e., modified instantaneous Euclidean distance, M-IED). The proposed algorithm reduces the computational complexity by decoupling the joint Tx/Rx selection into two separate selections of the numbers of Tx/Rx antennas and antenna subset, respectively. We show that the proposed AED criterion can be implemented through a simple look up table (LUT), thereby significantly reducing the computational complexity. Simulation results and computational complexity comparisons, prove that the proposed two-stage AnSS algorithm for the SM scheme reduces the hardware and computational complexity without any loss of the signal-to-noise ratio (SNR) and the diversity order, compared to the exhaustive search method.