Staggered PRT ground clutter filtering

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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…

✔

✔

✔

✔

✔

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