User's Manual Part 2

Processing Algorithms (draft)
RVP8 User’s Manual
April 2003
5–15
5.2.6 Velocity
For a Doppler power spectrum that is symmetric about its mean velocity, the velocity is obtained
directly from the argument of the autocorrelation at the first lag, i.e.,
V +
l
4pt
s
q
1
where q
1
+ arg
NJ
R
1
Nj
.
l is the radar wavelength, t
s
is the sampling time (1/PRF). q
1
is constrained to be on the
interval
[
* p, p
]
. When q
1
+" p , then V +" V
u
where the unambiguous velocity is ,
V
u
+
l
4t
s
.
If the absolute value of the true velocity of the scatterers is greater than
V
u
, then the velocity
calculated by the RVP8 is folded into the interval
ƪ
* V
u
, V
u
ƫ
, which is called the Nyquist
interval. Folding is usually easily recognized on a color display by a discontinuous jump in
velocities. For example, if the true velocity is V
u
) DV, then the velocity calculated by the
RVP8 is
* V
u
) DV, which is 2V
u
away from the true mean velocity.
For 8-bit outputs, rather than calculating the absolute velocity in scientific units, the RVP8
calculates the mean velocity for the normalized Nyquist interval [–1,1], i.e., the output values
are,
VȀ+
q
1
p
.
For example, an output value of –0.5 corresponds to a mean velocity of * V
u
ń2. The
normalized velocity VȀ is more efficient use of the limited number of bits.
5.2.7 Spectrum Width Algorithms
The spectrum width is a measure of the combined effects of shear and turbulence. To a lesser
extent, the antenna rotation rate can also effect the spectrum width. At high elevation angles, the
fall speed dispersion of the scatterers also effects spectrum width.
There are two choices for the spectrum width algorithm used in the RVP8, depending on the
speed and accuracy that are required for the application:
R
0
, R
1
“fast” algorithm valid when SNR >> 10 dB
R
0
, R
1
, R
2
“accurate” algorithm for SNR >> 0 to 5 dB
The approach used is selected in the SOPRM command. The two approaches are described below:
R
0
, R
1
Width Algorithm
Given samples of the Doppler autocorrelation function, numerous estimates of spectral vari-
ance can be computed (Passarelli & Siggia, 1983). The particular estimator used by the
RVP8 employs the magnitudes of R
0
and R
1
and assumes that the Doppler spectrum is
Gaussian (usually an acceptable assumption) and that the signal-to-noise ratio is large. Spe-
cifically we have (similar to Srivastava, et al 1979):
Variance + 2ln
ƪ
R
o
| R
1
|
ƫ
+*2ln
[
SQI
]