1 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting Data Quality / R-v...
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1 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” Staggered PRT ground clutter filtering Svetlana Bachmann November 20, 2007
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3 Svetlana Bachmann November 20, 2007, Norman OK Technical 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)
Transcript of 1 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting Data Quality / R-v...
1Svetlana BachmannNovember 20, 2007, Norman OKTechnical Interchange Meeting “Data Quality / R-v ambiguities mitigation”
Staggered PRT ground clutter filtering
Svetlana BachmannNovember 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, Mp=24, va=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, Mp=12, va=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, Mp=24, va=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, Mp=24, va=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, Mp=12, va=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, Mp=12, va=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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
CNR, dB
T1, m
s
CNR, dB
T1, 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, Mp=24, va=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, Mp=24, va=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);
Erro
rB
ias
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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
dwell = 60 ms
dwell = 60 ms
CNR, dB
T1, m
s
CNR, dB
T1, m
s
✔
✘ ✘ ✘ ✘ ✘ ✘ ✘
✔✔✔✗
T1
Erro
rB
ias
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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
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, m
s
CNR, dB
T1, m
s
Erro
rB
ias
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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
CNR, dB
T1, m
s
CNR, dB
T1, m
s
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
Erro
rB
ias
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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
CNR, dB
T1, m
s
CNR, dB
T1, m
s
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
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, Mp=24, va=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&bCNR=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, Mp=24, va=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.
Erro
rA
ccep
t. B
ias
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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
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, m
s
CNR, dB
T1, m
s
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
Acc
ept.
Erro
rA
ccep
t. B
ias
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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
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, m
sT1
, ms
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
Acc
ept.
Erro
rA
ccep
t. B
ias
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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
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, m
sT1
, ms
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
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.
Erro
rA
ccep
t. B
ias
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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
80 ms 100 ms 120 ms 60 ms
CNR, dB
T1, m
s
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
1
2
3
4
5
6
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
80 ms 100 ms 120 ms60 ms
CNR, dB
T1, m
sdwell = 60 ms
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
3 2½3
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
CNR, dB
T1, m
s
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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
CNR, dB
80 ms 100 ms 120 ms60 ms
T1, m
s
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
20
20
40
60
80
100
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
CNR, dB
80 ms 100 ms 120 ms 60 ms
T1, m
s
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
CNR, dB
T1, m
s
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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
CNR, dB
T1, m
s4 m s–1 3½ 2½3
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
Mea
n er
ror
Acc
ept.
Err
or
20 40 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
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, m
s
10 20 30 40 50 60
1
1.2
1.4
1.6
1.8
2
CNR, dB
T1, m
s
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
11.11.21.31.41.51.61.71.81.92.0
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…
✔
✔
✔
✔✔
