Nonuniform array processing via the polynomial approach

Abstract

A polynomial approach for maximum likelihood estimation of superimposed signals in time series problems and array processing was recently proposed [1][2][3]. This technique was applied successfully to linear uniform arrays and to uniformly sampled complex exponential signals. However, uniformly spaced arrays are not optimal for minimum variance estimation of bearing, range or position; and uniform sampling of signals is not always possible in practice. In this communication we make use of the EM algorithm in order to apply the polynomial approach to sublattice arrays and to missing samples in time series problems.

EM-Esprit Algorithm for Direction Finding with Nonuniform Arrays

“…The CRB was calculated using the equations of [7], extended to the case of nonuniform arrays. For the second experiment, we use the d = [1,3,6] λ 2 geometry, since similar results are obtained for other geometries. The resolution of the method is tested.…”

“…The array used is d = [1,2,4,6] This result shows that EM-ESPRIT is not highly sensitive to the accuracy of the initialization. At low SNR, the performances are almost the same when using beamforming or the exact values, and they decrease when using arbitrary values far from the exact ones.…”

“…Sometimes, using a nonuniform array yields better performance than using a uniform one [1], or the sensors cannot be uniformly spaced due to spatial constraints. Except for spectral MUSIC, high resolution methods cannot be directly applied on NLA because they exploit the uniform geometry of the array.…”

“…Except for spectral MUSIC, high resolution methods cannot be directly applied on NLA because they exploit the uniform geometry of the array. Several approaches have been proposed, among them EM-IQML [1], the interpolated virtual array methods of Friedlander [2], the methods of Higher Order Statistics (HOS) [3] and the positive definite Toeplitz completion [4]. The originality of the proposed method in this paper is the combination of the EM algorithm, to interpolate the data on a Virtual Uniform Linear Array (VULA), with the ESPRIT method used for DOA estimation.…”

EM‐MODE in high‐resolution DOA estimation for nonuniform array

“…Weiss and colleagues have described DOA estimation by applying the EM-IQML method to a nonuniformly spaced array [8]. Here, nonuni -form spacing refers to an array with the elements placed at locations that are integer multiples of some basic spacing (such as a half-wavelength), namely, a sublattice array.…”