Suitability of Correlation Arrays and Superresolution for Minehunting ...

DSTO-TN-0443
example [Giuli 1986] in which this second method was used to obtain superresolution
images. 17
A particular case of aspect-angle diversity is SAR (synthetic aperture radar), in
which the motion of an airborne radar forms a synthetic aperture. Similarly in ISAR
(inverse synthetic aperture radar), the radar is on the ground and the target is an
aircraft. It is of interest that the word ‘decorrelate’ (p. 112) appears in S&S in the
segment where they discuss the reduction of the sidelobe pattern for SAR. This
suggests again that the there is a useful connection to SR. 18
In the frequency-diversity method (S&S, Section 5-4), snapshots are obtained at a
number of frequencies and then combined.
11.3 Single Periodic Array; the FBLP Method
In their Section 11-4, Steinberg and Subbaram describe this, the fourth, decorrelation
method (of the methods listed at the start of Section 11) and apply it in the SR context.
Recall that, in Section 9.1, within an ARMA model, the solution for the angular
spectrum was found, subject to the need to first determine the data correlations. The
discussion in S&S leads to the preferred method for estimating these correlations,
namely the forward-backward linear prediction (FBLP) method.
This fourth decorrelation method may be understood physically as follows (S&S,
pp. 315–317). A periodic array may be thought of as containing subarrays, identical
with each other but shifted by a multiple of the inter-element spacing. The system
therefore satisfies the conditions for a single array moved to various locations, as in aspect-angle
diversity (i.e. the second of the listed methods). Only a single pulse from a single
transmitter is required. This use of the periodic nature of the array to synthesise
independent ‘snapshots’ of a scene of coherent targets is called spatial smoothing or
subarray smoothing.
The array considered by S&S has spacing equal to λ 2 . Recall that what remains to
be done to complete the determination of the SR image in Section 9.1 is to determine
the data correlations R ( m, n)
defined by Equation (9.1). In synthetic decorrelation, the
general method is to construct an ensemble of situations, such that the targets are
uncorrelated in the ensemble. (This is quite distinct from what happens in real time.)
∗
Then an ensemble average of e me n
yields R ( m, n)
. S&S describe four methods—to be
called submethods—for estimating the data correlations. The first three submethods
are lead-ups to the fourth, which is definitely superior. This fourth submethod is
called the modified covariance method, or alternatively the forward-backward linear
prediction (FBLP) method. The final result for R ( m, n)
is given by their Equation (11-
36). Armed with these estimates, one can immediately utilise the results of Section 9.1
to obtain the angular spectrum.
17 An interesting unanswered question is how registration of the various images onto each other
was achieved.
18 Another hint of relevance to SR is that (S&S, p. 325) experimental data that S&S use to test SR
methods is ISAR data.
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