Adnan Al-Smadi

Robust and accurate ARX and ARMA model order estimation of non-Gaussian processes

The field of higher order statistics is emerging rapidly for analyzing non-Gaussian processes. There are several motivations behind the use of higher order statistics. The emphasis of this paper is based on the property that higher order cumulants are blind to any kind of Gaussian process. Hence, when the processed signal is non-Gaussian stationary and the additive noise is stationary Gaussian, the noise will vanish in the cumulant domain. This paper presents an extension to the results of Liang et al. (1993). This extension is a straightforward generalization of Liangs approach to third-order cumulants (TOCs). The new cumulant-based algorithm provides a higher level of accuracy in the presence of noise than the original second-order algorithm. In addition, the original results of Liang have been extended to the case of colored Gaussian noise. Examples are given to demonstrate the performance of this algorithm even when the observed signal is heavily corrupted by Gaussian noise.

ARMA model order and parameter estimation using genetic algorithms

A new method for simultaneously determining the order and the parameters of autoregressive moving average (ARMA) models is presented in this article. Given an ARMA (p, q) model in the absence of any information for the order, the correct order of the model (p, q) as well as the correct parameters will be simultaneously determined using genetic algorithms (GAs). These algorithms simply search the order and the parameter spaces to detect their correct values using the GA operators. The proposed method works on the principle of maximizing the GA fitness value relying on the deviation between the actual plant output, with or without an additive noise, and the estimated plant output. Simulation results show in detail the efficiency of the proposed approach. In addition to that, a practical model identification and parameter estimation is conducted in this article with results obtained as desired. The new method is compared with other well-known methods for ARMA model order and parameter estimation.

Fitting ARMA Models to linear non-Gaussian processes using higher order statistics

This paper addresses the problem of estimating the parameters of a general autoregressive moving average model using higher order statistics (HOS) when only output data are available. The system is driven by an independent and identically distributed (i.i.d) non-Gaussian process. Simulation results are presented which demonstrate the performance of the new method and compare it with a well-known algorithm based on second order and HOS.

Combined coding and wavelet transform for ECG compression

This paper presents a combined wavelet and a modified runlength encoding scheme for the compression of electrocardiogram (ECG) signals. First, a discrete wavelet transform is applied to the ECG signal. The resulting coefficients are classified into significant and insignificant ones based on the required PRD (percent root mean square difference). Second, both coefficients are encoded using a modified run-length coding method. The scheme has been tested using ECG signals obtained from the MIT-BIH Compression Database. A compression of 20:1 (which is equivalent to 150 bit per second) is achieved with PRD less than 10.

Cumulant-based order selection of non-Gaussian autoregressive moving average models: the corner method

This paper presents a new corner location method to model order selection of an autoregressive moving average (ARMA) model. The criterion is determined in terms of the minimum eigenvalue of the third-order cumulant matrix derived from the observed data sequence. The observed sequence is modeled as the output of an ARMA system that is excited by an unobservable input, and is corrupted by zero-mean Gaussian additive noise. The system is driven by a zero-mean independent and identically distributed (i.i.d.) non-Gaussian sequence. The method is an extension to recent results based on third-order cumulant (TOC) by Al-Smadi and Wilkes. Simulations verify the performance of the proposed method even when the observed signal is heavily corrupted by additive noise. The proposed estimator, via computer simulation, is found to outperform the TOC estimator of Al-Smadi and Wilkes.

Study of the reliability of a binary symmetric channel under non-Gaussian disturbances

The field of digital and data communications is becoming increasingly dominant because digital transmission offers data processing options and flexibilities not available with analog transmission. The main feature of a digital communication system is that during a finite interval of time, it sends a waveform from a finite set of possible waveform. One of the most important and fundamental models of communications channels is the binary symmetric channel (BSC). An important measure of system performance in a digital communication system is the probability of error. In this paper, the probability of error, the reliability, the entropy and the channel capacity of a BSC model are studied under non-Gaussian noise disturbances. Namely, Cauchy, Laplace and logistic distributions are considered. It is found that the reliability of the signaling system is low under non-Gaussian noise distributions compared to the Gaussian noise distribution. Several methods were used to reduce the error probability. The amount of improvement in reliability using the reduction methods is higher in the case of Gaussian noise. In order to achieve high reliability under non-Gaussian noise distribution, it is required to increase signal-to-noise ratio (SNR) and increase number of repetitions when sending the same signal different times. Finally, it is observed that increasing the reliability for Cauchy distribution noise has totally failed based on sending the same signal different times and summing the received signals. Copyright

Frequency-based model order reduction via genetic algorithm approach

A frequency-based model order reduction (MOR) via genetic algorithm (GA) approach is presented in this paper. An exogenous autoregressive model with a smaller dimensionality, which can mimic the full order model, maybe obtained using the GA MOR approach. For a general MOR, the GA predicts the elements of the system state matrix [A] defined in a state space representation along with the elements of the [B] and [C] matrices of the reduced order model. As a frequency-based MOR technique, the GA predicts only the elements of the [B] and [C] matrices of the reduced order model while [A] is set in the modal form. The proposed GA model order reduction approach is compared to recently published work for method evaluation.

Genetic algorithm approach with frequency selectivity for model order reduction of MIMO systems

A novel genetic algorithm (GA) approach with frequency selectivity advantage for model order reduction (MOR) of multi-input–multi-output (MIMO) systems is presented in this article. Motivated by singular perturbation and other reduction techniques, the new MOR method is formulated using GAs, which can be applied to single-input–single-output (SISO)- or MIMO-type systems. The GA procedure is based on maximizing the fitness function corresponding to the response deviation between the full-order model and the reduced-order model with the option of substructure preservation. The proposed GA-MOR method is compared to the well-known reduction techniques, such as the Schur decomposition balanced truncation, proper orthogonal decomposition (POD) and state elimination through balancing-related frequency-weighted realization in addition to other recent methods. Simulation results validate the superiority and robustness of the new MOR technique as it can search the solution space for almost optimal solutions.

Automatic identification of ARMA systems

Autoregressive moving-average (ARMA) system identification with only output measurements is a well-known problem in various science and engineering areas such as spectral estimation and speech processing. Although this problem is an ‘old’ problem and widely considered to be solved, recent algorithms and results by Al-Smadi and Wilkes and Al-Smadi indicate that this is far from the actual case. In fact the much higher accuracy of these new algorithms calls for re-examination of this important problem. The objective of this article is to propose an automated procedure for selecting the model order and estimating the parameters of the ARMA system from third order cumulants (TOC) of the contaminated observations of the output data. The system is driven by a zero-mean independent and identically distributed (i.i.d.) sequence. The driving input is non-Gaussian and is not observed.

ARMA model parameters estimation using SVD

Autoregressive moving average (ARMA) modeling has been used in many fields. This paper presents an approach to time series analysis of a general ARMA model parameters estimation. The proposed technique is based on the singular value decomposition (SVD) of a covariance matrix of a third order cumulants from only the output sequence. The observed data sequence is corrupted by additive Gaussian noise. The system is driven by a zero-mean independent and identically distributed (i.i.d.) non-Gaussian sequence. Simulations verify the performance of the proposed method.