Aydin Kizilkaya

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.

Estimation of 2-D ARMA model parameters by using equivalent AR approach

Abstract In this paper, the problem of estimating the parameters of a two-dimensional autoregressive moving-average (2-D ARMA) model driven by an unobservable input noise is addressed. In order to solve this problem, the relation between the parameters of a 2-D ARMA model and their 2-D equivalent autoregressive (EAR) model parameters is investigated. Based on this relation, a new algorithm is proposed for determining the 2-D ARMA model parameters from the coefficients of the 2-D EAR model. This algorithm is a three-step approach. In the first step, the parameters of the 2-D EAR model that is approximately equivalent to the 2-D ARMA model are estimated by applying 2-D modified Yule–Walker (MYW) equation to the process under consideration. Then, the moving-average parameters of the 2-D ARMA model are obtained solving the linear equation set constituted by using the EAR coefficients acquired in the first step. Finally, the autoregressive parameters of the 2-D ARMA model are found by exploiting the values obtained in first and second steps. The performance of the proposed algorithm is compared with other 2-D ARMA parameter and spectral estimation algorithms available in the technical literature by means of three different criteria. As a result of this comparison, it is shown that the parameters and the corresponding power spectrums estimated by using the proposed algorithm are converged to the original parameters and the original power spectrums, respectively.

Two empirical methods for improving the performance of statistical multirate high-resolution signal reconstruction

The problem of reconstructing a known high-resolution signal from a set of its low-resolution parts exposed to additive white Gaussian noise is addressed in this paper from the perspective of statistical multirate signal processing. To enhance the performance of the existing high-resolution signal reconstruction procedure that is based on using a set of linear periodically time-varying (LPTV) Wiener filter structures, we propose two empirical methods combining empirical mode decomposition- and least squares support vector machine regression-based noise reduction schemes with these filter structures. The methods originate from the idea of reducing the effects of white Gaussian noise present in the low-resolution observations before applying them directly to the LPTV Wiener filters. Performances of the proposed methods are evaluated over one-dimensional simulated signals and two-dimensional images. Simulation results show that, under certain conditions, considerable improvements have been achieved by the proposed methods when compared with the previous study that only uses a set of LPTV Wiener filter structures for the signal reconstruction process.

On the Parameter Estimation of 2-D Moving Average Random Fields

The problem of estimating the parameters of 2-D homogeneous moving average (MA) random fields only from output measurements is addressed. A novel computationally efficient algorithm for the estimation of the parameters of a minimum-phase 2-D MA model with a nonsymmetric half-plane (NSHP) region of support (ROS) is proposed. Using the 2-D spectral factorization, relationship between the NSHP MA model parameters and the cepstral coefficients of a 2-D MA random field is considered. Based on this relation, recursive equations are derived so as to estimate the NSHP MA model parameters. It is noteworthy that the proposed algorithm is practical, i.e., it does not require computationally complex processes namely fitting to a high-order autoregressive model, any initial estimates, nor matrix inversion. Performance analysis of the derived algorithm together with an existing method is given for comparison purposes. Index

Optimal signal reconstruction based on time-varying weighted empirical mode decomposition

Optimal signal reconstruction via the EMD-based framework is addressed.A new algorithm, termed, time-varying weighted EMD (TVW-EMD) is proposed.A formulation of reconstructing original signal through the EMD followed by time-varying weightings of the oscillation modes is derived in the minimum mean-square error (MMSE) sense.The effectiveness of the proposed new algorithm is supported by computer simulations including real biomedical signals. Empirical mode decomposition (EMD) is a tool developed for analyzing nonlinear and non-stationary signals. It is capable of splitting any signal into a set of oscillation modes known as intrinsic mode functions and a residual function. Although the EMD satisfies the perfect signal reconstruction property by superimposing all the oscillation modes, it is not based on any optimality criterion. The lack of optimality limits the signal recovery performance of the EMD in the presence of disturbances such as noise and interference. In this paper, we propose a new algorithm, termed, time-varying weighted EMD, which gives the best estimate of a given signal in the minimum mean-square error sense. The main idea of the proposed algorithm is to reconstruct the original signal through the EMD followed by time-varying weightings of the oscillation modes. Simulations including two real-life signals are performed to show the superiority of the proposed algorithm. Display Omitted

Different Scenarios on Denoising of Signals in the Intrinsic Mode Function Selection Framework

ABSTRACT Without having any information of original signal, estimating the desired signal from noisy measurements is a challenging problem. In this paper, the denoising problem of signals corrupted by additive white Gaussian noise (AWGN) is considered in the empirical mode decomposition (EMD) framework, and five different noise suppression scenarios based on the various combinations of intrinsic mode functions (IMFs) that arise from applying the EMD to a given noisy signal are suggested. In these scenarios, the idea of discarding noise-dominant IMFs from a noisy signal is adopted. Considering the root-mean-square error and the signal-to-error ratio, the performance of each scenario is evaluated over simulated and real signals contaminated by AWGN with different signal-to-noise ratios (SNRs). It is observed from simulations that the proposed scenarios provide satisfactory denoising performance especially for positive SNRs and can be exploited as a primary stage in whole of the noise-diminishing applications.

Computation of the exact cramer-rao lower bound for 2-D ARMA parameter Estimation-I: the quarter-plane case

A closed-form expression for computing the exact Cramer-Rao lower bound (CRLB) on unbiased estimates of the parameters of a two-dimensional (2-D) autoregressive moving average (ARMA) model is developed. The formulation is based on a matrix representation of 2-D homogeneous Gaussian random process that is generated uniformly from the related 2-D ARMA model. The formulas derived for the exact Fisher information matrix (FIM) are an explicit function of the 2-D ARMA parameters and are valid for real-valued homogeneous quarter-plane (QP) 2-D ARMA random fields, where data are propagated using only the past values. It is noteworthy that our approach is practical especially for quantifying the accuracy of 2-D ARMA parameter estimates realized with short data records. Computer simulations display the behavior of the derived CRLB expression for some QP causal 2-D ARMA processes, as a function of the number of data points. The extension of this algorithm for the nonsymmetric half-plane (NSHP) case will be presented in a subsequent paper

ARMA-cepstrum Recursion Algorithm for the Estimation of the MA Parameters of 2-D ARMA Models

This paper considers the problem of estimating the moving average (MA) parameters of a two-dimensional autoregressive moving average (2-D ARMA) model. To solve this problem, a new algorithm that is based on a recursion relating the ARMA parameters and cepstral coefficients of a 2-D ARMA process is proposed. On the basis of this recursion, a recursive equation is derived to estimate the MA parameters from the cepstral coefficients and the autoregressive (AR) parameters of a 2-D ARMA process. The cepstral coefficients are computed benefiting from the 2-D FFT technique. Estimation of the AR parameters is performed by the 2-D modified Yule–Walker (MYW) equation approach. The development presented here includes the formulation for real-valued homogeneous quarter-plane (QP) 2-D ARMA random fields, where data are propagated using only the past values. The proposed algorithm is computationally efficient especially for the higher-order 2-D ARMA models, and has the advantage that it does not require any matrix inversion for the calculation of the MA parameters. The performance of the new algorithm is illustrated by some numerical examples, and is compared with another existing 2-D MA parameter estimation procedure, according to three performance criteria. As a result of these comparisons, it is observed that the MA parameters and the 2-D ARMA power spectra estimated by using the proposed algorithm are converged to the original ones

Comparing the performances of least mean squares based multirate adaptive filters

In this study, sign-error, sign-data, and sign-sign modifications of the multirate least mean squares (LMS) filter are proposed as an alternative to the existing multirate LMS and normalized LMS filters for reconstructing the high rate desired signal from its several low rate noisy observations. The performance of all the existing and the proposed methods are compared by using an adaptive noise cancellation simulation example applied to an audio signal. It is seen from the simulation results that some of the proposed methods lead to better results than the existing ones especially in the convergence speed sense.

Adaptive noise cancellation with a multirate normalized least mean squares filter

Multirate adaptive filtering is related to the problem of reconstructing a high-resolution signal from two or more observations that are sampled at different rates. A popular existing method for solving this problem uses the multirate adaptive filter structure that is based on the least mean squares (LMS) approach. However, its low convergence rate restricts the use of this method. In this study, a multirate normalized LMS (NLMS) filter is proposed as an alternative to that of LMS based filter, for the reconstruction of the high-resolution signal from several low-resolution noisy observations. In the simulation example performed on an audio signal, it is observed that the proposed method leads to the better results than the existing method especially in the convergence rate.