User's Manual Part 2

Processing Algorithms (draft)
RVP8 User’s Manual
April 2003
5–16
where “ln” represents the natural logarithm. This can be compared to the expression in the
preceding section for SQI to illustrate that this expression for the variance is only valid when:
SNR
SNR ) 1
[ 1
which occurs when the SNR is large.
This variance estimator is normalized to the Nyquist interval in units of
[
* p, p
]
. Thus, for
example, a variance of
p
2
ń25 would be obtained from a Gaussian spectrum having a stan-
dard deviation equal to one fifth of the total width of the plotted spectral distribution. For
scientific purposes, the spectrum width (standard deviation) is more physically meaningful
than the variance, since it scales linearly with the severity of wind shear and turbulence. For
these reasons, the width W is output by the RVP8:
W +
Variance
Ǹ
p
Again, for efficient packing in 8-bits, width is normalized to the Nyquist interval [–1, 1 ].
For the example given above, the output width W would be (1/5). To obtain the width in me-
ters per second, one multiplies the output width by V
u
.
R
0
, R
1
, R
2
Width Algorithm
The width algorithm in this case is similar except that the addition of R
2
extends the validity
of the width estimates to weak signals. In this case the variance is:
Variance +
2
3
ln
ƪ
| R
1
|
| R
2
|
ƫ
The output width W is then defined as in the previous section.
5.2.8 Signal Quality Index (SQI threshold)
An important feature of the RVP8 is its ability to eliminate signals which are either too weak to
be useful, or which have widths too large to justify further analysis. This is done via the signal
quality index (SQI) which is defined as:
SQI +
| R
1
|
R
0
The SQI is the normalized magnitude of the autocorrelation at lag 1 and varies between 0 for an
uncorrelated signal (white noise) to 1 for a noise-free zero-width signal (pure tone). Mean
velocity estimates are degraded when the spectrum, width is large or when the signal-to-noise
ratio is weak. The SQI is a good measure of the uncertainty in the velocity estimates and is a
convenient screening parameter to compute. In terms of the Gaussian model, the SQI is :
SQI +
SNR
SNR ) 1
e
*p
2
W
2
2
where the SNR is the signal-to-noise ratio. For very large SNR’s the SQI is a function of the
spectrum width only. For a zero-width pure tone (W=0), the SQI is a function of the SNR only
(e.g., for W=0, an SNR of 1 corresponds to SQI=0.5). The SQI threshold is typically set to a
value of 0.4 to 0.5.