Suitability of Correlation Arrays and Superresolution for Minehunting ...

DSTO-TN-0443
latter approach is preferable, as it requires fewer parameters and so ‘the parameters
from the 2-D [SR] technique will be more accurate.’ Some references given by Nash
appear to be quite relevant.
Ferguson [1998] has applied the Capon beamformer (Minimum Variance
Distortionless Response beamformer) to the case where one calculates a 2-D spectrum,
which in this context refers to the spectral intensity as a function of both frequency and
wave number. He shows, for a towed, low-frequency sonar, that as well as improving
the spatial resolution of the array, the method suppresses sidelobes in a case where the
latter are very high.
8.1.3 Thoughts on Application of Capon’s Method to the Minefinder System
Early in the preparation of this report, some thought was given to how the Capon
method might be generalised to deal with the Minefinder system. While these
thoughts have been overtaken by later literature survey work (particularly methods
described by S&S), they are included as Appendix B, in case some of them may prove
of use in the Minefinder problem.
8.2 Maximum Entropy Method (MEM)
About the same time as Capon’s method was developed, Burg [1967, 1972] developed
the maximum entropy spectral estimate (or maximum entropy method—MEM). The
rationale for this method is that one chooses the spectral estimate that makes the least
number of assumptions about the data; that is, one adds in the least amount of
spurious information. The MEM method has been discussed by S&S [1991, p. 320],
Gething [1991, p. 204] and Nash [1994, pp. 4, 28].
8.3 Model-Based versus Non-Model-Based Methods
Both Haykin [1995, Chapter 1] and S&S (p. 320) emphasise this distinction. Modelbased
methods assume ‘structural and statistical models of the signals and noise’
(Haykin, p. 18). For example, the FBLP method (Section 11.3) assumes, at Equation (11-
12) of S&S, an autoregressive moving average (ARMA) process or model (in addition
to assuming other models). To motivate this model it is noted that, for a scene of T
point targets (in the far field), in the absence of noise, the signal at the nth element can
be predicted exactly as a weighted sum of the signals from the T elements lying
immediately to the left. The ARMA model assumes that this relation holds also in the
case where there is noise. This assumption makes ARMA into a model rather than
known fact.
Non-model-based methods include delay-and-sum and the Capon method. Modelbased
methods include the FBLP method and the optimal solution of the DSWN
(Deterministic Signals and White Noise) model (Haykin, pp. 25–33). Regarding
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