The two trigger periods Ʈ
l
and Ʈ
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 Ʈ
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:
=
4
ℎ
=
4
ℎ
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:
=
4
ℎ
=
4
ℎ
If we define φ to be the dierence between the two measured phases then:
=
ℎ
=
4
ℎ
which can be interpreted as a phase angle within the unfolded interval:
=
4
ℎ
Now if Ʈ
l
and Ʈ
h
are in a 3:2 ratio, then:
ℎ
=
3
=
ℎ
2
and thus:
= 3
= 2
ℎ
The angle Ø represents a velocity phase angle in [- Π, Π] , but with respect to an enlarged
unambiguous interval. By
dierencing the folded angles from the high and low PRFs, we
obtain an angle that is unfolded to a larger velocity span. Similar reasoning shows that the
4:3 ratio gives a factor of three improvement over V
uh
, and 5:4 gives a factor of four.
Velocity Estimator
In practice, the unfolded angle Ø is not in itself a suitable velocity estimator. This is because
the variance of Ø is equal to the sum of the variances of each of its components, that is,
twice that of the individual measurements alone. If the target is at all noisy, then this
increase in variance can be severe. Rather than use Ø directly, the RVP900 uses it only as a
rough estimate in determining how to unfold the individual velocity measured from each
PRF.
Chapter 7 – Processing Algorithms
223
To Next Page
Loading...