We analyze the large-sample mean square error (MSE) of MUSIC and Min-Norm direction-of-arrival (DOA) estimators under fairly general conditions, including mismodelling of the array response and the noise covariance. W...
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We analyze the large-sample mean square error (MSE) of MUSIC and Min-Norm direction-of-arrival (DOA) estimators under fairly general conditions, including mismodelling of the array response and the noise covariance. We separate the contributions to the MSE into a bias part caused by modelling errors and a variance part caused by finite (yet large) sample effects. The bias is simply evaluated by comparing the limiting estimate (corresponding to an infinite number of snapshots) with the true DOA’s (which are known to the analyzer). To simplify the variance derivation we assume that the snapshots are complex i.i.d. Gaussian vectors and that the largest eigenvalues of their covariance matrix are distinct; but, otherwise, make none of the assumptions commonly used in previous analyses; in particular we do not constrain the snapshots to satisfy any model equation. The theoretical results obtained are illustrated by means of numerical examples using various modelling errors.
Signal parameter estimation from measurements on a sensorarray is an important problem in many engineering applications. Recently, there has been a large interest in parametric methods in the literature. An important...
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Signal parameter estimation from measurements on a sensorarray is an important problem in many engineering applications. Recently, there has been a large interest in parametric methods in the literature. An important assumption in essentially all of these methods is that the spatial correlation structure of the background noise (i.e., the correlation from sensor to sensor) is known to within a multiplicative scalar. In practice, this is often achieved by measuring the array соvariance when no signals are present. This results unavoidably in errors in the noise model. In this paper, the effect of such model errors on parametric methods are examined. The methods in question are the deterministic and stochastic maximum likelihood methods, and the so-called weighted subspace fitting technique. First-order expressions for the mean square etror (MSE) of the parameter estimates are derived. The spatial noise correlation structures that lead to maximum performance loss are identified under different assumptions. In case of high signal to noise ratio (SNR), it is found that the MSE can be increased by a factor m , where m is the number of sensors in the array, as compared to spatially white noise. Simple expressions comparing the asymptotic (for large amounts of data) bias, resulting from a small noise covariance perturbation, with the asymptotic standard deviation are derived. Numerical examples are included to illustrate the obtained results.
ESPRIT (estimation of signal parameters via rotational invariance techniques) is a recently introduced algorithm for narrowband direction-of-arrival (DOA) estimation. Its principal advantage is that the DOA parameter ...
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ESPRIT (estimation of signal parameters via rotational invariance techniques) is a recently introduced algorithm for narrowband direction-of-arrival (DOA) estimation. Its principal advantage is that the DOA parameter estimates are obtained directly, without knowledge (and hence storage) of the array manifold and without computation or search of some spectral measure. This advantage is achieved by constraining the sensorarray to be composed of two identical, translationally invariant subarrays. In this paper, we analyse the sensitivity of ESPRIT to the assumption that the subarrays are identical. The analysis is applicable to a wide variety of array errors, including non-identical angle-dependent and angle-independent gain and phase perturbations, errors in the locations of the subarray elements, and mutual coupling effects. A representative simulation example will be presented to validate the analysis and compare the performance degradation of ESPRIT with that of the MUSIC algorithm.
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