Chapter 6 ______________________________________________________ Processing Algorithms
VAISALA______________________________________________________________________ 243
pulse periods rather than one, and relies on the extra information thus
obtained to correct (i.e. unfold) the mean velocity measurement from each
individual period. The Dual PRF trigger pattern consists of alternating
(N+k)-pulse intervals where the period in each interval is either τ
l
(for the
low-PRF) or τ
h
(for the high-PRF). Here "N" is the sample size, and "k"
represents a delay that permits the clutter filter to equilibrate to the new
PRF after each change. The clutter filter impulse response lengths vary
according to which filter is selected.
The two trigger periods τ
l
and τ
h
must be chosen in either a 3:2, 4:3, or 5:4
ratio. These ratios give factors of two, three, and four times velocity
expansion over the τ
h
period alone. The unfolding algorithm makes use of
the following results. Suppose that the radar observes a target with mean
velocity V at each of the two trigger periods. The measured phase angles
for the R
1
autocorrelations at the two PRFs are:
where angles outside the basic [- π, π] interval are returned to that interval
by appropriate additions of ± 2π . These angles correspond to the ordinary
single-PRF Doppler velocity measurements, and the ± 2π uncertainties
reflects the fact that each measurement is folded into its own unambiguous
interval:
If we define φ to be the difference between the two measured phases then:
which can be interpreted as a phase angle within the unfolded interval:
Now if τ
l
and figure τ
h
are in a 3:2 ratio, then:
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