Suitability of Correlation Arrays and Superresolution for Minehunting ...

DSTO-TN-0443
Appendix A: Time for Averaging
Consider the situation in radio astronomy. Even when two sources are uncorrelated,
they are still correlated in the short term. Thus, when averaged over a short time, the
cross terms in (4.6) (or their analogue in RA) are nonzero. For these terms to be
negligible, the time for averaging must be great enough.
Our interest is in an echo-ranging sonar, requiring the signal to be either a short
pulse or a coded signal such as a chirp. Then, as suggested under assumption 3c of
Section 4.1, the requirement for a long averaging time may be difficult to satisfy.
The sonar situation is described, for example, by Equation (4.6). As we are
studying the problem of sufficient time, let us suppose that the ‘other’ problem is not
present, i.e. that the sonar targets are uncorrelated. This could be the case due to
random drifts over time, either in range or in target strength; for simplicity we may
assume that the drifts are in target strength. Then effectively, in (4.6), there are changes
in a
b
and a
c
over time.
Consider first the case of a short pulse. Consider a single point target. Since the
pulse interacts with the target only for a time T, where T is the duration of the pulse,
the effective time over which averaging occurs is T. Suppose the reflections from two
targets get ‘out of step’ in phase in a time τ . Then for decorrelation we require
1 f < τ < T
(A.1a)
and probably
1 f