Results 1 
4 of
4
Parameter Estimation of TwoDimensional Moving Average Random Fields
"... This paper considers the problem of estimating the parameters of twodimensional moving average random fields. We first address the problem of expressing the co variance matrix of nonsymmetrical halfplane, noncausal, and quarterplane moving average random fields, in terms of the model parameters ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
This paper considers the problem of estimating the parameters of twodimensional moving average random fields. We first address the problem of expressing the co variance matrix of nonsymmetrical halfplane, noncausal, and quarterplane moving average random fields, in terms of the model parameters. Assuming the random field is Gaussian, we derive a closed form expression for the CramerRao lower bound on the error variance in jointly estimating the model parameters. A computationally efficient algorithm for estimating the parameters of the moving average model is de veloped. The algorithm initially fits a twodimensional autoregressive model to the observed field, then uses the estimated parameters to compute the moving average model. A maximumlikelihood algorithm for estimating the MA model parameters is also presented. The performance of the proposed algorithms is illustrated by MonteCarlo simulations, and is compared with the CramerRao bound.
Strong Consistency of the Over and Underdetermined LSE of 2D Exponentials in White Noise
"... Abstract—We consider the problem of least squares estimation of the parameters of two–dimensional (2D) exponential signals observed in the presence of an additive noise field, when the assumed number of exponentials is incorrect. We consider both the case where the number of exponential signals is ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Abstract—We consider the problem of least squares estimation of the parameters of two–dimensional (2D) exponential signals observed in the presence of an additive noise field, when the assumed number of exponentials is incorrect. We consider both the case where the number of exponential signals is underestimated, and the case where the number of exponential signals is overestimated. In the case where the number of exponential signals is underestimated, we prove the almost sure convergence of the least squares estimates (LSE) to the parameters of the dominant exponentials. In the case where the number of exponential signals is overestimated, the estimated parameter vector obtained by the least squares estimator contains a subvector that converges almost surely to the correct parameters of the exponentials. Index Terms—Least squares estimation, modelorder selection, random fields, strong consistency, two–dimensional (2D) exponentials, 2D parameter estimation. I.
Least Squares Estimation of 2D Sinusoids in Colored Noise: Asymptotic Analysis
"... Abstract—This paper considers the problem of estimating the parameters of realvalued twodimensional (2D) sinusoidal signals observed in colored noise. This problem is a special case of the general problem of estimating the parameters of a realvalued homogeneous random field with mixed spectral d ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract—This paper considers the problem of estimating the parameters of realvalued twodimensional (2D) sinusoidal signals observed in colored noise. This problem is a special case of the general problem of estimating the parameters of a realvalued homogeneous random field with mixed spectral distribution from a single observed realization of it. The large sample properties of the least squares (LS) estimator of the parameters of the sinusoidal components are derived, making no assumptions on the type of the probability distribution of the observed field. It is shown that if the disturbance field satisfies a combination of conditions comprised of a strong mixing condition and a condition on the order of its uniformly bounded moments, the normalized estimation error of the LS estimator is consistent asymptotically normal with zero mean and a normalized asymptotic covariance matrix for which a simple expression is derived. It is further shown that the LS estimator is asymptotically unbiased. The normalized asymptotic covariance matrix is block diagonal where each block corresponds to the parameters of a different sinusoidal component. Assuming further that the colored noise field is Gaussian, the LS estimator of the sinusoidal components is shown to be asymptotically efficient. Index Terms—Cramer–Rao bound (CRB), least squares (LS) estimation, regression spectrum, strong mixing property, twodimensional
Strongly Consistent Model Order Selection for Estimating 2D Sinusoids in Colored Noise
, 801
"... We consider the problem of jointly estimating the number as well as the parameters of twodimensional sinusoidal signals, observed in the presence of an additive colored noise field. We begin by elaborating on the least squares estimation of 2D sinusoidal signals, when the assumed number of sinusoi ..."
Abstract
 Add to MetaCart
(Show Context)
We consider the problem of jointly estimating the number as well as the parameters of twodimensional sinusoidal signals, observed in the presence of an additive colored noise field. We begin by elaborating on the least squares estimation of 2D sinusoidal signals, when the assumed number of sinusoids is incorrect. In the case where the number of sinusoidal signals is underestimated we show the almost sure convergence of the least squares estimates to the parameters of the dominant sinusoids. In the case where this number is overestimated, the estimated parameter vector obtained by the least squares estimator contains a subvector that converges almost surely to the correct parameters of the sinusoids. Based on these results, we prove the strong consistency of a new model order selection rule. Keywords: Twodimensional random fields; model order selection; least squares estimation; strong consistency.