Chapter 6 ______________________________________________________ Processing Algorithms
VAISALA______________________________________________________________________ 203
6.2.3 Autocorrelations
The final spectrum moment calculation (for total power or SNR, mean
velocity and spectrum width) in all processing modes is based on
autocorrelation moment estimation techniques. Typically the first three
lags are calculated, denoted as R
0
, R
1
and R
2
. However, there are two ways
to calculate these, that is, time domain or frequency domain calculation. In
the PPP mode for dual polarization, the autocorrelations are computed
directly in the time domain while in the DFT mode, they are computed by
taking the inverse DFT the Doppler power spectrum in the frequency
domain. Note that only the first three terms need be calculated in the
inverse DFT case. The time domain and frequency domain techniques are
nearly identical except that the method of taking the inverse DFT of the
power spectrum relies on the assumption that the time series is periodic.
Another difference is that for time domain calculation only a rectangular
weighting is used.
The time domain calculation of the autocorrelations and the corresponding
physical models are:
where M is the number of pulses in the time average. Here, s' denotes the
clutter-filtered time series, s denotes the original unfiltered time series and
the * denotes a complex conjugate. g
r
and g
t
represent the transmitter and
receiver gains, that is, their product represents the total system gain. Since
the RVP900 is a linear receiver, there is a single gain number that relates
the measured autocorrelation magnitude to the absolute received power.
However, since many of the algorithms do not require absolute calibration
of the power, the gain terms will be ignored in the discussion of these. T
o
for the unfiltered time series is proportional to the sum of the
Parameter and Definition Physical model
To Next Page
Loading...