Identification of autoregressive signals in colored noise using damped sinusoidal model

Abstract

This brief addresses a new method for autoregressive (AR) parameter estimation from colored noise-corrupted observations using a damped sinusoidal model for autocorrelation function of the noise-free signal. The damped sinusoidal model parameters are first estimated using a least-squares based method from the given noisy observations. The AR parameters are then directly obtained from the damped sinusoidal model parameters. The performance of the proposed scheme is evaluated using numerical examples.

Frequency-Selective Noise-Compensated Autoregressive Estimation

“…As claimed in [21], and verified afterwards [23], [25], we may take the spectral sample to be an independent complex (bivariate) Gaussian variable (both real and imaginary parts are independent and identically distributed) of zero mean and variance equal to . The probability density function (PDF) of sample can be thus written as (14) According to the mentioned independence between the spectral samples, the likelihood of the -sample set can be thus simplified as follows: (15) In consequence, the maximization of the logarithm of the likelihood 6 results in the following optimization problem: (16) where . Since are parameterless, the optimization problem (16) can be recast 7 as follows: (17) Visual inspection of the ML functional (17) reveals common points and divergences with the MSE criterion (11).…”

“…In [15], an expectation-maximization (EM) method, shown to perform with stable convergence and better than the IWF, was proposed. An LS algorithm for identifying noisy AR systems, based on a damped sinusoidal model, was disclosed in [16]. The method remains questionable for moderate model orders, and its complexity is large as it involves optimization searches.…”

Wavelet-Packet Identification of Dynamic Systems with Coloured Measurement Noise

“…4 depicts the wavelet-packet decomposition trees obtained according to the GCV criterion in the three noise cases. As can be seen, the tree with fewer nodes (Fig.4c) corresponds to the situation in which the noise was spread over a wider frequency region (5)(6)(7)(8). It can be argued that the GCV algorithm automatically joined the subbands with poor signal-to-noise ratio in order to increase the amount of data employed in the identification of each subband model.…”

“…Appropriate treatment of coloured noise, which is the most common form of noise in practical situations [1,5], may be essential to obtain suitable models by system identification, as discussed elsewhere [8,16,18]. The present work investigates the effect of coloured measurement noise on the performance of the wavelet-packet identification algorithm proposed in [13].…”

Continuous-time identification using LS-method under colored noise perturbations

“…Correlation functions of the "colored noise" can be also estimated in a straightforward manner [23], [4] and, then they can be taken into account during the identification. Autoregression (AR) parameter estimation can be addressed by a damped sinusoidal model for autocorrelation function of the noise-free signal [10], where the parameters are then directly obtained from the damped sinusoidal model parameters. Often in some applications a correlation function is not well modeled, so robust techniques seems to be useful [12].…”