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Staggered PRT ground clutter filtering. Svetlana Bachmann November 20, 2007. Parameter q Recollect q… Motivation to change q… qGMAP… How to use GMAP with SPRT… New table q3D… Performance evaluation GCF with GMAP, TABL, q3D… Finding error & bias for power, velocity, width… - PowerPoint PPT Presentation
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1Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Staggered PRT ground clutter filtering
Svetlana Bachmann
November 20, 2007
2Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Parameter q Recollect q… Motivation to change q… qGMAP… How to use GMAP with SPRT… New table q3D…
Performance evaluationGCF with GMAP, TABL, q3D…Finding error & bias for power, velocity, width…
Examples of errors & biases…
Velocity errorsMean errors… Percentage of acceptable errors…Finding a compromise… Windows…
Spectral analyses Examples of mean spectra…
Changes to algorithm Summary of changes… Additional possible changes…
3Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
q is an integer.
q is the clutter width parameter used in the SPRT procedure for clutter filtering [1].
q specifies the number of spectral coefficients to be considered as the ground clutter contribution (one sided including dc).
q was tabulated [1] 3 for CNR_approx < 50 dB 4 for 50 dB < CNR_approx < 70 dB 5 for 70 dB < CNR_approx < 90 dB 6 for CNR_approx > 90 dB.
Recollect q
Reference[1] S. Torres, M. Sachidananda, D. Zrnic, “Signal design & processing techniques for WSR-88D ambiguity resolution – Part 9: Phase Coding & Staggered PRT,” NSSL Tech. report, Norman OK, 2005 (page 103, item 5)
4Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Spectrum Reconstructedusing
Motivation to change q
Uniform PRT-Staggered PRT-
TABLE
time series
spectrum Uniform PRT-Staggered PRT-
GMAP
Need an adaptive q for optimal filtering.
5Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
How to use GMAP with SPRT
q = 3
6Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Parameter q Recollect q… Motivation to change q… qGMAP… How to use GMAP with SPRT… New table q3D…
Performance evaluationGCF with GMAP, TABL, q3D…Finding error & bias for power, velocity, width…
Examples of errors & biases…
Velocity errorsMean errors… Percentage of acceptable errors…Finding a compromise… Windows…
Spectral analyses Examples of mean spectra…
Changes to algorithm Summary of changes… Additional possible changes…
✔
7Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
itera
tion
velocity
T1=1ms, Mp=12, SNR=20, CNR=50, v=21 m s-1
-50 0 50
20
40
60
80
100
-50 0 50-20
0
20
40
60
velocity
SPRT
itera
tion
velocity
GMAP
-50 0 50
20
40
60
80
100
itera
tion
velocity
TABL
-50 0 50
20
40
60
80
100
itera
tion
velocity
q3D
-50 0 50
20
40
60
80
100
-50 0 50-20
0
20
40
60
velocity
GMAP
-50 0 50-20
0
20
40
60
velocity
TABL
-50 0 50-20
0
20
40
60
velocity
q3D
Spectra GCF with GMAP, TABLT1=1ms, 12 pairs, SNR=20 dB, CNR=50 dB, v=21 m s–1
8Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Finding error & bias for P, v, w
Bias:bias(P) = mean(Pi) – Po;bias(v) = mean(vi) – vo;bias(w) = mean(wi) – wo;
%powerP = mean(abs(Si).^2);Pi(i)=P;
%velocityR1 = mean((abs(Si).^2).*... exp(j*2*pi*(0:M-1)'));v = va/pi * angle(R1);vi(i)=v;
%widthln = log(P/abs(R1))w = sqrt(2)*va/pi*... sqrt(abs(ln)).*sign(ln); wi(i)=w;
Error:SD(P) = std(Pi); 10log(1+SD(P)/Po)SD(v) = std(vi);SD(w) = std(wi);
itera
tion
velocity
T1=1ms, Mp=12, SNR=20, CNR=50, v=21 m s-1
-50 0 50
20
40
60
80
100
-50 0 50-20
0
20
40
60
velocity
SPRT
itera
tion
velocity
GMAP
-50 0 50
20
40
60
80
100
itera
tion
velocity
TABL
-50 0 50
20
40
60
80
100
itera
tion
velocity
q3D
-50 0 50
20
40
60
80
100
-50 0 50-20
0
20
40
60
velocity
GMAP
-50 0 50-20
0
20
40
60
velocity
TABL
-50 0 50-20
0
20
40
60
velocity
q3D
9Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
for PRT1=1 ms, dwell=60 ms, v= 4 m/s
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
T1=1ms, M
p=24, v
a=55, SNR=20, CNR=40, w=4
0 50
-2
0
2
velocity(m s-1)
bias
(w)
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)bi
as(S
)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
0 50
-2
0
2
velocity(m s-1)
bias
(w)
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)bi
as(v
)0 50
-2
0
2
velocity(m s-1)
bias
(w)
Bias:Error:
q from the old table TABL
q from GMAP
q from the new table q3D
10Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
for PRT1=2 ms, dwell=60 ms, v= 4 m/s
0 10 200
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 10 200
2
4
6
velocity(m s-1)
SD
(v)
0 10 200
2
4
6
velocity(m s-1)
SD
(w)
0 10 20
-2
0
2
velocity(m s-1)
bias
(S)
0 10 20
-2
0
2
velocity(m s-1)
bias
(v)
T1=2ms, M
p=12, v
a=28, SNR=20, CNR=40, w=4
0 10 20
-2
0
2
velocity(m s-1)
bias
(w)
0 10 200
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 10 200
2
4
6
velocity(m s-1)
SD
(v)
0 10 200
2
4
6
velocity(m s-1)
SD
(w)
0 10 20
-2
0
2
velocity(m s-1)bi
as(S
)
0 10 20
-2
0
2
velocity(m s-1)
bias
(v)
0 10 20
-2
0
2
velocity(m s-1)
bias
(w)
0 10 200
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 10 200
2
4
6
velocity(m s-1)
SD
(v)
0 10 200
2
4
6
velocity(m s-1)
SD
(w)
0 10 20
-2
0
2
velocity(m s-1)
bias
(S)
0 10 20
-2
0
2
velocity(m s-1)bi
as(v
)0 10 20
-2
0
2
velocity(m s-1)
bias
(w)
Bias:Error:
11Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+std(P)/P)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
SD(v)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
SD(w)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+bias(P)/P)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
bias(v)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
bias(w)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+std(P)/P)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
SD(v)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
SD(w)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+bias(P)/P)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
bias(v)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
bias(w)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+std(P)/P)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
SD(v)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
SD(w)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+bias(P)/P)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
bias(v)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
bias(w)
2 4 6 8
0
20
40
velo
city
(m s
-1)
2 4 6 8
0
20
40
0 5
velo
city
(m s
-1)
2 4 6 8
0
20
40
0 5
velo
city
(m s
-1)
2 4 6 8
0
20
40
0 5
velo
city
(m s
-1)
2 4 6 8
0
20
40
-2 0 2
velo
city
(m s
-1)
2 4 6 8
0
20
40
-2 0 2
velo
city
(m s
-1)
T1=1ms, M
p=24, v
a=55, SNR=20, CNR=40
2 4 6 8
0
20
40
-2 0 2
for PRT1=1 ms, dwell=60 ms, v=½:½:8 m/sve
loci
ty(m
s-1
)
spectrum width(m s-1)
10log(1+std(P)/P)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
SD(v)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
SD(w)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+bias(P)/P)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
bias(v)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
bias(w)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+std(P)/P)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
SD(v)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
SD(w)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+bias(P)/P)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
bias(v)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
bias(w)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+std(P)/P)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
SD(v)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
SD(w)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+bias(P)/P)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
bias(v)
2 4 6 8
0
20
40
velo
city
(m s
-1)
spectrum width(m s-1)
bias(w)
2 4 6 8
0
20
40
velo
city
(m s
-1)
2 4 6 8
0
20
40
0 5
velo
city
(m s
-1)
2 4 6 8
0
20
40
0 5
velo
city
(m s
-1)
2 4 6 8
0
20
40
0 5
velo
city
(m s
-1)
2 4 6 8
0
20
40
-2 0 2
velo
city
(m s
-1)
2 4 6 8
0
20
40
-2 0 2
velo
city
(m s
-1)
T1=1ms, M
p=24, v
a=55, SNR=20, CNR=40
2 4 6 8
0
20
40
-2 0 2
12Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+std(P)/P)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
SD(v)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
SD(w)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+bias(P)/P)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
bias(v)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
bias(w)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+std(P)/P)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
SD(v)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
SD(w)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+bias(P)/P)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
bias(v)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
bias(w)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+std(P)/P)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
SD(v)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
SD(w)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+bias(P)/P)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
bias(v)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
bias(w)
2 4 6 8
0
10
20
velo
city
(m s
-1)
2 4 6 8
0
10
20
0 5
velo
city
(m s
-1)
2 4 6 8
0
10
20
0 5
velo
city
(m s
-1)
2 4 6 8
0
10
20
0 5
velo
city
(m s
-1)
2 4 6 8
0
10
20
-2 0 2
velo
city
(m s
-1)
2 4 6 8
0
10
20
-2 0 2
velo
city
(m s
-1)
T1=2ms, M
p=12, v
a=28, SNR=20, CNR=40
2 4 6 8
0
10
20
-2 0 2
for PRT1=2 ms, dwell=60 ms, v=½:½:8 m/sve
loci
ty(m
s-1
)
spectrum width(m s-1)
10log(1+std(P)/P)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
SD(v)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
SD(w)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+bias(P)/P)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
bias(v)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
bias(w)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+std(P)/P)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
SD(v)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
SD(w)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+bias(P)/P)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
bias(v)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
bias(w)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+std(P)/P)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
SD(v)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
SD(w)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
10log(1+bias(P)/P)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
bias(v)
2 4 6 8
0
10
20
velo
city
(m s
-1)
spectrum width(m s-1)
bias(w)
2 4 6 8
0
10
20
velo
city
(m s
-1)
2 4 6 8
0
10
20
0 5
velo
city
(m s
-1)
2 4 6 8
0
10
20
0 5
velo
city
(m s
-1)
2 4 6 8
0
10
20
0 5
velo
city
(m s
-1)
2 4 6 8
0
10
20
-2 0 2
velo
city
(m s
-1)
2 4 6 8
0
10
20
-2 0 2
velo
city
(m s
-1)
T1=2ms, M
p=12, v
a=28, SNR=20, CNR=40
2 4 6 8
0
10
20
-2 0 2
13Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Error Bias
Power 〇 〇Spectral width 〇 〇Velocity 〇 〇
Performance of SPRT GCF
✔ ✔
For spectral width 4 m s–1, dwell 60 ms, PRT1 = 2 ms, q-GMAP and Blackman window
✔ ✔✘ ✘
the SPRT filter fails to meet the error requirements for velocity.
14Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Parameter q Recollect q… Motivation to change q… qGMAP… How to use GMAP with SPRT… New table q3D…
Performance evaluationGCF with GMAP, TABL, q3D…Finding error & bias for power, velocity, width…
Examples of errors & biases…
Velocity errorsMean errors… Percentage of acceptable errors…Finding a compromise… Windows…
Spectral analyses Examples of mean spectra…
Changes to algorithm Summary of changes… Additional possible changes…
✔
✔
15Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
CNR, dB
T1,
ms
CNR, dB
T1,
ms
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
T1=1ms, M
p=24, v
a=55, SNR=20, CNR=40, w=4
0 50
-2
0
2
velocity(m s-1)
bias
(w)
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
0 50
-2
0
2
velocity(m s-1)
bias
(w)
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
0 50
-2
0
2
velocity(m s-1)
bias
(w)
T1 = 1 ms
Velocity: mean error & bias (e&b)
CNR=40 dB
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
T1=1ms, M
p=24, v
a=55, SNR=20, CNR=40, w=4
0 50
-2
0
2
velocity(m s-1)
bias
(w)
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
0 50
-2
0
2
velocity(m s-1)
bias
(w)
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
0 50
-2
0
2
velocity(m s-1)
bias
(w)
T1 = 1 ms
dwell = 60 ms, SNR=20 dB, v = 4 m s–1, 100 realizations for each velocity from 0 to va
STD_vk, k=0:va = std(vi, i=1:100)BIAS_vk, k=0:va = mean(vi, i=1:100) – vo;
Mean_Error = mean(STD_vk, k=1:va)Mean_Bias = mean(BIAS_vk, k=1:va);
Err
or
Bia
s
16Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Velocity: mean e&b dwell = 60 ms, SNR=20 dB, v = 4 m s–1, 100 realizations for each velocity from 0 to va
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
dwell = 60 ms
dwell = 60 ms
CNR, dB
T1,
ms
CNR, dB
T1,
ms
✔
✘ ✘ ✘ ✘ ✘ ✘ ✘
✔✔✔✗
T1
Err
or
Bia
s
17Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Velocity: mean e&b for different dwell times
dwell = 60 ms, SNR=20 dB, v = 4 m s–1, 100 realizations for each velocity from 0 to va
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
CNR, dB
sd(v
)
SNR=20, v=4, dwell=80
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNR, dB
bias
(v)
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
CNR, dB
sd(v
)
SNR=20, v=4, dwell=80
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNR, dB
bias
(v)
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600
1
2
3
4
5
CNR, dB
sd(v
)
SNR=20, v=4, dwell=100
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNR, dB
bias
(v)
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600
1
2
3
4
5
CNR, dB
sd(v
)
SNR=20, v=4, dwell=100
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNR, dB
bias
(v)
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600.5
1
1.5
2
2.5
3
3.5
4
CNR, dB
sd(v
)
SNR=20, v=4, dwell=120
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNR, dB
bias
(v)
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600.5
1
1.5
2
2.5
3
3.5
4
CNR, dB
sd(v
)
SNR=20, v=4, dwell=120
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNR, dB
bias
(v)
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
dwell = 80 ms dwell = 100 ms dwell = 120 ms
dwell = 80 ms dwell = 100 ms dwell = 120 ms
dwell = 60 ms
dwell = 60 ms
CNR, dB
T1,
ms
CNR, dB
T1,
ms
Err
or
Bia
s
18Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600
1
2
3
4
5
6
CNR, dB
sd(v
)
SNR=20, v=2.5, dwell=60
0 20 40 60-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600
1
2
3
4
5
6
CNR, dB
sd(v
)
SNR=20, v=2.5, dwell=60
0 20 40 60-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600
1
2
3
4
5
6
CNR, dB
sd(v
)
SNR=20, v=3, dwell=60
0 20 40 60-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600
1
2
3
4
5
6
CNR, dB
sd(v
)
SNR=20, v=3, dwell=60
0 20 40 60-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
CNR, dB
sd(v
)
SNR=20, v=3.5, dwell=60
0 20 40 60-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
CNR, dB
sd(v
)
SNR=20, v=3.5, dwell=60
0 20 40 60-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
Velocity: mean e&b for different spectral widths
dwell ~ 60 ms, SNR=20 dB, v = 4 m s–1, 100 realizations for each velocity from 0 to va
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
CNR, dB
T1,
ms
CNR, dB
T1,
ms
vv = 4 m s = 4 m s–1–1 3½ m s–1 2½ m s–1 3 m s–1
v = 4 m s–1 3½ m s–1 2½ m s–1 3 m s–1
Err
or
Bia
s
19Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
CNR, dB
T1,
ms
CNR, dB
T1,
ms
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
T1=1ms, M
p=24, v
a=55, SNR=20, CNR=40, w=4
0 50
-2
0
2
velocity(m s-1)
bias
(w)
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
0 50
-2
0
2
velocity(m s-1)
bias
(w)
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
0 50
-2
0
2
velocity(m s-1)
bias
(w)
T1 = 1 ms
Velocity: % of acceptable e&b
CNR=40 dB
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
T1=1ms, M
p=24, v
a=55, SNR=20, CNR=40, w=4
0 50
-2
0
2
velocity(m s-1)
bias
(w)
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
0 50
-2
0
2
velocity(m s-1)
bias
(w)
0 500
1
2
3
4
5
velocity(m s-1)
SD
(S)
0 500
2
4
6
velocity(m s-1)
SD
(v)
0 500
2
4
6
velocity(m s-1)
SD
(w)
0 50
-2
0
2
velocity(m s-1)
bias
(S)
0 50
-2
0
2
velocity(m s-1)
bias
(v)
0 50
-2
0
2
velocity(m s-1)
bias
(w)
T1 = 1 ms
dwell = 60 ms, SNR=20 dB, v = 4 m s–1, 100 realizations for each velocity from 0 to va
STD_vk, k=0:va = std(vi, i=1:100)BIAS_vk, k=0:va = mean(vi, i=1:100) – vo;
Mean_Error = mean(STD_vk, k=0:va)Mean_Bias = mean(BIAS_vk, k=0:va);
e = STD_v(abs(STD_v) < 2); Accept_Error = length(e)/length(STD_v);
b = BIAS_v(abs(BIAS_v) < 2); Accept_Bias = length(b)/length(BIAS_v);
Acc
ept.
Err
or
Acc
ept.
Bia
s
20Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
Velocity: % of acceptable e&bdwell = 60 ms, SNR=20 dB, v = 4 m s–1, 100 realizations for each velocity from 0 to va
CNR, dB
T1,
ms
CNR, dB
T1,
ms
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
Acc
ept.
Err
or
Acc
ept.
Bia
s
21Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=120
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=100
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=80
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=120
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=100
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=80
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
Velocity: % of acceptable e&b for different dwell times
dwell ~ 60 ms, SNR=20 dB, v = 4 m s–1, 100 realizations for each velocity from 0 to va
CNR, dB
CNR, dB
dwell = 80 ms dwell = 100 ms dwell = 120 msdwell = 60 ms
dwell = 80 ms dwell = 100 ms dwell = 120 msdwell = 60 ms
T1,
ms
T1,
ms
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
Acc
ept.
Err
or
Acc
ept.
Bia
s
22Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=2.5, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=2.5, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=3, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=3, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=3.5, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=3.5, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
Velocity: % of acceptable e&b for different spectral widths
dwell ~ 60 ms, SNR=20 dB, v = 4 m s–1, 100 realizations for each velocity from 0 to va
CNR, dB
CNR, dB
T1,
ms
T1,
ms
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
vv = 4 m s = 4 m s–1–1 3½ m s–1 2½ m s–1 3 m s–1
v = 4 m s–1 3½ m s–1 2½ m s–1 3 m s–1
Acc
ept.
Err
or
Acc
ept.
Bia
s
23Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Velocity: mean e&b and % of acceptable e&bv = 4 m s–1
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
CNR, dB
sd(v
)
SNR=20, v=4, dwell=80
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNR, dB
bias
(v)
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600
1
2
3
4
5
CNR, dB
sd(v
)
SNR=20, v=4, dwell=100
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNR, dB
bias
(v)
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600.5
1
1.5
2
2.5
3
3.5
4
CNR, dB
sd(v
)
SNR=20, v=4, dwell=120
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNR, dB
bias
(v)
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
80 ms 100 ms 120 ms 60 ms
CNR, dB
T1,
ms
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
CNR, dB
sd(v
)
SNR=20, v=4, dwell=80
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNR, dB
bias
(v)
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600
1
2
3
4
5
CNR, dB
sd(v
)
SNR=20, v=4, dwell=100
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNR, dB
bias
(v)
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600.5
1
1.5
2
2.5
3
3.5
4
CNR, dB
sd(v
)
SNR=20, v=4, dwell=120
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNR, dB
bias
(v)
0 20 40 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
80 ms 100 ms 120 ms60 ms
CNR, dB
T1,
ms
dwell = 60 ms
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600
1
2
3
4
5
6
CNR, dB
sd(v
)
SNR=20, v=2.5, dwell=60
0 20 40 60-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600
1
2
3
4
5
6
CNR, dB
sd(v
)
SNR=20, v=3, dwell=60
0 20 40 60-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
CNR, dB
sd(v
)
SNR=20, v=3.5, dwell=60
0 20 40 60-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
3 2½3
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600
1
2
3
4
5
6
CNR, dB
sd(v
)
SNR=20, v=2.5, dwell=60
0 20 40 60-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 600
1
2
3
4
5
6
CNR, dB
sd(v
)
SNR=20, v=3, dwell=60
0 20 40 60-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
CNR, dB
sd(v
)
SNR=20, v=3.5, dwell=60
0 20 40 60-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 601
2
3
4
5
6
7
8
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
CNR, dB
bias
(v)
0 20 40 60-6
-5
-4
-3
-2
-1
0
1
0
1
2
3
4
5
6
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
CNR, dB
T1,
ms
v = 4 3½ 2½3
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=120
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=100
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=80
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
CNR, dB
80 ms 100 ms 120 ms60 ms
T1,
ms
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=120
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=100
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=80
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
CNR, dB
80 ms 100 ms 120 ms 60 ms
T1,
ms
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=2.5, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=3, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=3.5, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
CNR, dB
T1,
ms
4 m s4 m s–1–1 3½ 2½3
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=2.5, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)SNR=20,
v=3, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=3.5, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
CNR, dB
T1,
ms
4 m s–1 3½ 2½3
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
Mea
n er
ror
Acc
ept.
Err
or
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=4, dwell=60
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
0
20
40
60
80
100
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
Acc
ept.
bias
Mea
n bi
as
24Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Velocity e&b: a compromise
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1,
ms
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
0 20 40 6020
40
60
80
100
CNR, dB
sd(v
)
SNR=20, v=3, dwell=80
0 20 40 6020
40
60
80
100
CNR, dB
bias
(v)
0 20 40 6020
40
60
80
100
11.1
1.2
1.3
1.4
1.51.6
1.7
1.8
1.92.0
SNR = 20 dB, v = 3 m/s, dwell 80 ms
25Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Parameter q Recollect q… Motivation to change q… qGMAP… How to use GMAP with SPRT… New table q3D…
Performance evaluationGCF with GMAP, TABL, q3D…Finding error & bias for power, velocity, width…
Examples of errors & biases…
Velocity errorsMean errors… Percentage of acceptable errors…Finding a compromise… Windows…
Spectral analyses Examples of mean spectra…
Changes to algorithm Summary of changes… Additional possible changes…
✔
✔
✔
✔
26Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Changes to algorithmStep pre-compute: Ignore the power loss correction factor, instead normalize the windowStep 2. Apply normalized window – Blackman (?)Step 4. • If q3D: do not divide by N when computing CNR_approx:
CNR_aprox = sum(abs([Vr(1), Vr(2), Vr(end)].^2)).*25/4./(N*NoiseLevel);
replace “power” with “amplitude” in the comment;• If qGMAP: this step can be omitted.
Step 5. Clutter width parameter is determined either from q3D or using GMAP• If q3D: estimate CNR_approx, Np, and va and choose q from table
table q3D<30x50x10>, where i_CNRdB 1:2:60, i_Mp 10:59, i_va 20:5:65 x = round((CNRdb_aprox/2)); if x<1 x=1; end; if x>30 x=30; end; y = round((Np-9)); if y<1 y=1; end; if y>50 y=50; end; z = round(va/5-3); if z<1 z=1; end; if z>10 z=10; end; q=round(q3D(x, y, z));
• If qGMAP: modify GMAP to return number of coefficient identified as clutter; take the 5 th of the Doppler spectrum (containing the main clutter replica and whichever weather replica); initialize GMAP for spectra with va/5; pass the 5th of Doppler spectrum to GMAP; use the number of coefficients identified as clutter to estimate q.
Step 8. Add “diag” in front of the clutter filter matrices If1, If2Step 11. Remove “1/N” from autocorrelation formulaStep 12. Choose symmetric window of samples around the
rounded to the nearest sample velocity estimate k0: k1=k0 – floor(M/4)+1 ; k2=k0 + floor(M/4)
Step 16. Same as in step 12. Steps 12, 13, and 16 must be changed to accommodate odd pairs.
Step 17. Replace “6.37” with “6.27”
Acknowledgements:
David Warde, Sebastian Torres, Dusan Zrnic
✔✔✔
27Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Parameter q Recollect q… Motivation to change q… qGMAP… How to use GMAP with SPRT… New table q3D…
Performance evaluationGCF with GMAP, TABL, q3D…Finding error & bias for power, velocity, width…
Examples of errors & biases…
Velocity errorsMean errors… Percentage of acceptable errors…Finding a compromise… Windows…
Spectral analyses Examples of mean spectra…
Changes to algorithm Summary of changes… Additional possible changes…
✔
✔
✔
✔
✔
