Suitability of Correlation Arrays and Superresolution for Minehunting ...

DSTO-TN-0443
6.4 Correlation Arrays
These arrays in essence involve forming the element-by-element products of the
voltages of two arrays, and integrating each product over time. They may therefore be
viewed as a form of multiplicative array. Correlation arrays have been discussed in
Sections 2 to 4, where the problems in the sonar context have been pointed out.
On a positive note, both Clarke [1970] and Shearman et al. [1973] succeeded in
forming simple images, in the areas of sonar and radar respectively, each using a
variant of the correlation array (see Section 11.1).
7. Superresolution Methods with Adaptive Weights:
A. General
In the methods described so far, no rationale is given for selecting a particular set of
weights (with the possible exception of Pritchard’s work). In the methods to be
discussed in Sections 7 to 9, a rational procedure is given by which the weights are
optimised in some sense. An essential step in the procedures to be discussed is to
make the weights depend on the signals received; thus the weights are adaptive. The
use of adaptivity appears to lead to a marked improvement in performance over fixedweight
arrays in one area (the ratio of the spacing to λ 2 ), as discussed towards the
end of Section 6.1. (Adaptivity possibly also leads to improvement in the area of
signal-to-noise ratio.) Because of this marked difference, when we speak of
‘superresolution’ (SR) in the remainder of this report, we exclude fixed-weight arrays
except where the context implies otherwise.
A consequence of the adaptive feature is as follows. Consider the narrowband, farfield
case. In fixed-weight, additive beamforming, when the ‘look’ direction is
changed, the absolute values of the (augmented) weights remain unaltered, and their
phases are altered in proportion to the changes in the path length. But with SR
beamforming, when the look direction is changed, neither of these properties holds.
Sections 7 to 9 form a group. The methods of Section 8 result in an estimate of a
continuous angular spectrum, while those in Section 9 produce a discrete angular
spectrum. But there is a further difference as follows. Each method in Section 8 simply
involves a selection of weights followed by beamforming with those weights. The
methods of Section 9 involve a further level of interpretation, in which the data are
attributed to a finite number of point sources or point targets. The problem is to
estimate the number of targets, their position and their strength.
Nash [1994, pp. 27–42] outlines the six main SR spectral estimators. These are said
to be Linear Prediction (LP), Maximum Entropy Method (MEM), Minimum Variance
(MV) (also called Capon’s method), Prony’s Method (PM), Multiple Signal
Classification (MUSIC) and Estimation of Signal Parameters via Rotational Invariance
Techniques (ESPRIT). Nash goes on to discuss three of these (LP, MV and MUSIC) in
more detail in the context of the Inverse Synthetic Aperture Radar (ISAR) problem.
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