Multichannel Autoregressive Model Research Articles

Autoregressive Model Based Polarimetric Adaptive Detection Scheme Part II: Performance Assessment Under Spectral Model Mismatch

This article addresses the problem of target detection in coherent radar systems equipped with multiple polarimetric channels. In “Part I” of this two-part study, a multichannel autoregressive model based polarimetric detection scheme has been developed and its performance has been studied against clutter with characteristics exactly matching the adopted parametric model. In the second part of this study, the performance assessment is extended, by means of theoretical and simulated analyses, to include the case of disturbance components with diverse spectral characteristics. Consequently, an appropriate modification is introduced to the detection scheme to make it robust to typical spectral mismatches occurring in practical situations. Finally, the effectiveness of the resulting detection scheme is proved against simulated and experimental data.

Adaptive Algorithm for Multichannel Autoregressive Estimation in Spatially Correlated Noise

This paper addresses the problem of multichannel autoregressive (MAR) parameter estimation in the presence of spatially correlated noise by steepest descent (SD) method which combines low-order and high-order Yule-Walker (YW) equations. In addition, to yield an unbiased estimate of the MAR model parameters, we apply inverse filtering for noise covariance matrix estimation. In a simulation study, the performance of the proposed unbiased estimation algorithm is evaluated and compared with existing parameter estimation methods.

O17: A novel method to induce human cortical plasticity using cortical disinhibition

O17: A novel method to induce human cortical plasticity using cortical disinhibition

PMU Based State Estimation by Integrating Correlation

In this paper, a novel approach for hybrid power system static state estimation (SE) in the presence of phasor measurement units (PMUs) is presented. The proposed PMU-based SE takes into account existing time correlation in the PMU measurements. The PMU time series of measurements are modeled by short memory autoregressive (AR) models over short time periods. The correlation existing between PMU measurements at different buses is included using vector or multichannel AR models. The effectiveness and improved performance of the proposed PMU-based SE is demonstrated through a comparison analysis with practical hybrid SE methods. A theoretical analysis highlights the improvement over long execution periods of SE and high PMU sampling rates. Finally, a practical comparison is carried out on results from simulated Monte Carlo runs on the IEEE 14- and 118-bus test beds.

An Effective Classification Framework for Brain–Computer Interfacing Based on a Combinatoric Setting

This paper proposes a general framework that is able to define a set of classification algorithms for brain-computer interfacing (BCI). We define a distributed representation of the EEG based on multichannel autoregressive models. In a subsequent step, we extend this multichannel modeling in a combinatoric setting, which is able to describe with a class of nonlinear combinatoric operators the embedded relationships that the EEG shows in the manifolds. The generality and the flexibility of the nonlinear combinatoric operators and their mathematical properties allow the design of an indefinite number of classification algorithms each displaying relevant properties, such as linearity with respect to the parameters, noise rejection, low computational complexity of the classification procedure. In such a way, we obtain an intuitive and rigorous way to design new BCI algorithms. As an example of this theoretical framework, we present a novel classification algorithm based on four properties of this nonlinear combinatoric operator. The method was validated on the classification of single-trial EEG signals recorded during motor imagination, and it was compared on two additional standard datasets obtained from the BCI competition, with other feature extraction and classification techniques based on common spatial pattern, common spatial subspace decomposition and Fisher discriminant analysis, linear discriminant analysis, Markov chains, and expectation maximization. In conclusion, the proposed framework is suited for a broad number of BCI applications.

Conjugate Gradient Parametric Detection of Multichannel Signals

The parametric adaptive matched filter (PAMF) detector for space-time adaptive processing (STAP) detection is reexamined in this paper. Originally, the PAMF detector was introduced by using a multichannel autoregressive (AR) parametric model for the disturbance signal in STAP detection. While the parametric approach brings in benefits such as reduced training and computational requirements as compared with fully adaptive STAP detectors, the PAMF detector as a reduced-dimensional solution remains unclear. This paper employs the conjugate-gradient (CG) algorithm to solve the linear prediction problem arising in the PAMF detector. It is shown that CG yields not only a new computationally efficient implementation of the PAMF detector, a new and efficient AR model order selection method that can naturally be integrated with CG iterations, but it also offers new perspectives of PAMF as a reduced-rank subspace detector. We first consider the integration of the CG algorithm with the matched filter (MF) and parametric matched filter (PMF) when the covariance matrix of the disturbance signal is known. It is then extended to the adaptive case where the covariance matrix is estimated from training data. Important issues such as computational complexity and convergence rate are discussed. Performance of the proposed CG-PAMF detector is examined by using the KASSPER and other computer generated data.

A new noise-compensated estimation scheme for multichannel autoregressive signals from noisy observations

In many engineering applications concerning the recovery of signals from noisy observations, a common approach consists in adopting autoregressive (AR) models. This paper is concerned with not only the estimation of multichannel autoregressive (MAR) model parameters but also the recovery of signals. A new noise compensated parameter estimation scheme is introduced in this paper. It contains an advanced least square vector (ALSV) algorithm which not only keeps the advantage of blindly estimating the MAR parameters and the variance-covariance matrix of observation noises, but also aims at ensuring the variance-covariance matrix to be symmetric in each iterative procedure. Moreover, the estimation of variance-covariance matrix of input noise is proposed, and then we form an optimal filtering to recover the signals. In the numerical simulations, the estimation performance of the ALSV estimation algorithm significantly outperforms that of other existed methods. Moreover, the optimal filtering based on the ALSV algorithm leads to more accurate recovery of the true signals.

A New Parametric GLRT for Multichannel Adaptive Signal Detection

A parametric generalized likelihood ratio test (GLRT) for multichannel signal detection in spatially and temporally colored disturbance was recently introduced by modeling the disturbance as a multichannel autoregressive (AR) process. The detector, however, involves a highly nonlinear maximum likelihood estimation procedure, which was solved via a two-dimensional iterative search method initialized by a suboptimal estimator. In this paper, we present a simplified GLRT along with a new estimator for the problem. Both the estimator and the GLRT are derived in closed form at considerably lower complexity. With adequate training data, the new GLRT achieves a similar detection performance as the original one. However, for the more interesting case of limited training, the original GLRT may become inferior due to poor initialization. Because of its simpler form, the new GLRT also offers additional insight into the parametric multichannel signal detection problem. The performance of the proposed detector is assessed using both a simulated dataset, which was generated using multichannel AR models, and the KASSPER dataset, a widely used dataset with challenging heterogeneous effects found in real-world environments.

Estimation of the parameters of multichannel autoregressive signals from noisy observations

This paper is concerned with estimation of multichannel autoregressive (MAR) model parameters using noisy observations. The NILS method proposed in W.X. Zheng [A new estimation algorithm for AR signals measured in noise, in: Proceedings of the ICSP Conference 1, 2002, pp. 186–189] for estimation of the parameters of noisy scalar autoregressive (AR) signals is generalized to the multichannel case. An improved least-squares-based parameter estimator is introduced so that the variance–covariance matrix of the multichannel noise can be estimated in an iterative manner. With this, the noise-induced estimation bias can be removed to yield the unbiased estimate of the MAR parameters. In a simulation study, the performance of the proposed unbiased estimation algorithm is evaluated and compared with that of the existing parameter estimation methods.

Phase and amplitude analysis in time–frequency space—application to voluntary finger movement

Two methods operating in time–frequency space were applied to analysis of EEG activity accompanying voluntary finger movements. The first one, based on matching pursuit approach provided high-resolution distributions of power in time–frequency space. The phenomena of event related desynchronization (ERD) and synchronization (ERS) were investigated without the need of band-pass filtering. Time evolution of μ- and β-components was observed in a detailed way. The second method was based on a multichannel autoregressive model (MVAR) adapted for investigation of short-time changes in EEG signal. The direction and spectral content of the EEG activity propagation was estimated by means of short-time directed transfer function (SDTF). The evidence of ‘cross-talk’ between different areas of motor and sensory cortex was found. The earlier known phenomena, connected with voluntary movements, were confirmed and a new evidence concerning focal ERD/surround ERS and β activity post-movement synchronization was found.

The long-term memory prediction by multiscale decomposition

This paper deals with the problem of long-term memory time-seri es prediction. Traditionally, this type of prediction is achieved using the fractionally integrated ARMA models. The method presented here, is based on the multiscale filtering which iteratively decomposes a series into a trend and a hierarchy of details that are stationary and contain only short memory. Thus, the obtained series are modeled with classical ARMA models. The advantage of this method is that it overcomes the tricky problem of the fractional integration parameter estimation. The statistical properties of the obtained series are studied and the use of multichannel autoregressive models is justified when the moving average part does not exist. Results obtained through the use of both simulated and real-life series show the efficiency of the approach.

Pilot symbol assisted modulation in frequency selective fading wireless channels

Frequency-selective fading channels are typically modeled either as a combination of Doppler components or as lowpass stochastic processes. In both cases, accurate parameter and/or Doppler frequency estimation is impeded by the fact that the Doppler frequencies are typically very low (compared with the data rate) and closely spaced. This problem is mitigated in pilot symbol assisted modulation (PSAM) systems that employ distributed training. Those systems can provide information about a time-undersampled version of the channel that may be easier to identify. We address the problem of estimating the fading channel's correlation matrices from the received data by exploiting the distributed training symbols. Multichannel autoregressive (AR) models are estimated to fit the channel's variations, and the Doppler frequencies are identified through the peaks of the AR spectrum. The performance of the proposed methods is studied through analytical and experimental results. Finally, Kalman filtering ideas are employed to track the time-varying channel taps based on the estimated AR model.

An autoregressive method for the measurement of synchronization of interictal and ictal EEG signals.

We propose a new measure of synchronization of multichannel ictal and interictal EEG signals. The measure is based on the residual covariance matrix of a multichannel autoregressive model. A major advantage of this measure is its ability to be interpreted both in the framework of stochastic and deterministic models. A preliminary analysis of EEG data from three patients using this measure documents the expected increased synchronization during ictal periods but also reveals that increased synchrony persists for prolonged periods (up to 2 h or more) in the postictal period.

EEG coherence in Alzheimer's disease

EEG coherence can be used to evaluate the functionality of cortical connections and to get information about the synchronization of the regional cortical activity. We studied EEG coherence in patients affected by clinically probable Alzheimer's disease (AD) in order to quantify the modifications in the cortico-cortical or cortico-subcortical connections. The EEGs were recorded in 10 AD patients (with mild or moderate degrees of dementia) and in 10 normal age-matched subjects, at rest and eye-closed, from 16 electrodes with linked-ears reference. Spectral parameters and coherence were calculated by a multichannel autoregressive model using 50 artifact-free epochs, 1 s duration each. Alpha coherence was significantly decreased in 6 patients, the decrease being more accentuated in the area near the electrode taken into account; a significant delta coherence increase was found in a few patients between frontal and posterior regions. The AD group showed a significant decrease of alpha band coherence, in particular in temporo-parieto-occipital areas, more evident in patients with a more severe cognitive impairment. These abnormalities could reflect two different pathophysiological changes: the alpha coherence decrease could be related to alterations in cortico-cortical connections, whereas the delta coherence increase could be related to the lack of influence of subcortical cholinergic structures on cortical electrical activity.

Information flow between hippocampus and related structures during various types of rat's behavior

The relationships among the CA1 field of hippocampus, the entorhinal-piriform area, the subiculum and the lateral septum were studied in various behavioral states in the rat. The EEG signals recorded simultaneously from chronically implanted electrodes were analyzed by means of a multichannel autoregressive (AR) model. Power spectra, ordinary, multiple and partial coherences, and directed transfer functions were calculated. The method of analysis which took into account all signals simultaneously, not pair-wise, made it possible to estimate the spectral characteristics and the directions of the EEG flow between structures. The pattern of the EEG activity propagation depended on the type of behavior, difficulty of the task performed by the animal, and the phase of the trial. Our results not only confirmed the existence of connections between analyzed structures, but also showed that these connections may have different strengths during various types of behavior.

A General Statistical Framework for Frequency-Domain Analysis of EEG Topographic Structure

A wide variety of rhythmic electrophysiological phenomena—including driven, induced, and endogenous activities of cortical neuronal masses—lend themselves naturally to analysis using frequency-domain techniques applied to multichannel recordings that discretely sample the overall spatial pattern of the rhythmic activity. For such cases, a large but so far poorly utilized body of statistical theory supports a third major approach to topographic analysis, complementing the more familiar mapping and source-recovery techniques. These methods, many of which have only recently become computationally feasible, collectively provide general solutions to the problem of detecting and characterizing systematic differences that arise—not only in the spatial distribution of the activity, but also in its frequency-dependent between-channel covariance structure—as a function of multiple experimental conditions presented in conformity with any of the conventional experimental designs. This application-oriented tutorial review provides a comprehensive outline of these resources, including: (1) real multivariate analysis of single-channel spectral measures (and measures of between-channel relationships such as coherence and phase), (2) complex multivariate analysis based on multichannel Fourier transforms, and (3) complex multivariate analysis based on multichannel parametric models. Special emphasis is placed on the potential of the multichannel autoregressive model to support EEG (and MEG) studies of perceptual and cognitive processes.

Multivariate autoregressive time semes modeling: one scalar autoregressive model at-A-time

Multivariate (or interchangeably multichannel) autoregressive (MCAR) modeling of stationary and nonstationary time series data is achieved doing things one channel at-a-time using only scalar computations on instantaneous data. The one channel at-a-time modeling is achieved as an instantaneous response multichannel autoregressive model with orthogonal innovations variance. Conventional MCAR models are expressible as linear algebraic transformations of the instantaneous response orthogonal innovations models. By modeling multichannel time series one channel at-a-time, the problems of modeling multichannel time series are reduced to problems in the modeling of scalar autoregressive time series. The three longstanding time series modeling problems of achieving a relatively parsimonious MCAR representation, of multichannel stationary time series spectral estimation and of the modeling of nonstationary covariance time series are addressed using this paradigm.

Multichannel Wiener filters in color image restoration

Deals with the design of multichannel Wiener filters both in the spatial and frequency domain. FIR and IIR Wiener filters are presented. Color image restoration based on multi-channel autoregressive (AR) image modeling is examined. Detailed discussions on the use of a multichannel Wiener filter in color image restoration incorporating the interchannel correlations and computer simulations are presented also. >

Autoregressive modeling for ocean wave — radar modulation transfer function

The standard technique for computing ocean wave — radar modulation transfer functions (MTFs) depends on nonparametric fast Fourier transform (FFT) methods. In this paper we suggest a new approach applying an autoregressive (AR) parametric spectral estimator. The analysis shows that the two‐channel autoregressive model produces smooth estimates of the MTF and permits better frequency resolution than FFT techniques. The feed‐across effect inherent in the methods developed to evaluate the multichannel AR coefficients causes a negligible effect on MTF. The AR‐based MTF depends weakly on the record length; for steady meteorological conditions the AR model of the MTF for a 2‐min data run is comparable with ones calculated using 10 min or more of data. In the same situation the FFT technique is unreliable for records of less than 10 min. The appropriate order of the multichannel AR model can vary without causing significant change in the MTF. In most cases any order between 8 and 16, depending on radar system parameters and meteorological conditions, will give acceptable results.

A Circular Lattice-Smoothness Priors Multichannel Time Varying Autoregressive Model

Abstract A method for the multichannel autoregressive modeling of nonstationary covariance time series data is shown. The multichannel modeling is achieved doing things one channel at-a-time using only scalar computations. Our method exploits the smoothness priors modeling (Gersch and Kitagawa 1988 ) of partial correlation coefficients in a time-varying linear regression model and the lattice-form structure (Sakai 1982) for multichannel stationary time series modeling. The circular lattice structure permits the multichannel AR model to be realized one-channel at-a- time. Smoothness priors is a Bayesian stochastic linear regression approach that permits the multichannel time varying AR model, a model with more parameters than data, to be fitted. Examples are shown.