1. 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

2. 2 Svetlana Bachmann November 20, 2007, Norman OK Technical 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 evaluation GCF with GMAP, TABL, q3D… Finding error & bias for power, velocity, width… Examples of errors & biases… Velocity errors Mean errors… Percentage of acceptable errors… Finding a compromise… Windows… Spectral analyses Examples of mean spectra… Changes to algorithm Summary of changes… Additional possible changes…

3. 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)

4. 4 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” Spectrum Reconstructed using Motivation to change q Uniform PRT- Staggered PRT- TABLE time series spectrum Uniform PRT- Staggered PRT- GMAP Need an adaptive q for optimal filtering.

5. 5 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” How to use GMAP with SPRT q = 3

6. 6 Svetlana Bachmann November 20, 2007, Norman OK Technical 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 evaluation GCF with GMAP, TABL, q3D… Finding error & bias for power, velocity, width… Examples of errors & biases… Velocity errors Mean errors… Percentage of acceptable errors… Finding a compromise… Windows… Spectral analyses Examples of mean spectra… Changes to algorithm Summary of changes… Additional possible changes… ✔

7. 7 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” Spectra GCF with GMAP, TABL T1=1ms, 12 pairs, SNR=20 dB, CNR=50 dB, v=21 m s –1

8. 8 Svetlana Bachmann November 20, 2007, Norman OK Technical 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; %power P = mean(abs(Si).^2); Pi(i)=P; %velocity R1 = mean((abs(Si).^2).*... exp(j*2*pi*(0:M-1)')); v = va/pi * angle(R1); vi(i)=v; %width ln = 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);

9. 9 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” for PRT1=1 ms, dwell=60 ms,  v = 4 m/s Bias: Error: q from the old table TABL q from GMAP q from the new table q3D

10. 10 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” for PRT1=2 ms, dwell=60 ms,  v = 4 m/s Bias: Error:

11. 11 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” for PRT1=1 ms, dwell=60 ms,  v =½:½:8 m/s

12. 12 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” for PRT1=2 ms, dwell=60 ms,  v =½:½:8 m/s

13. 13 Svetlana Bachmann November 20, 2007, Norman OK Technical 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.

14. 14 Svetlana Bachmann November 20, 2007, Norman OK Technical 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 evaluation GCF with GMAP, TABL, q3D… Finding error & bias for power, velocity, width… Examples of errors & biases… Velocity errors Mean errors… Percentage of acceptable errors… Finding a compromise… Windows… Spectral analyses Examples of mean spectra… Changes to algorithm Summary of changes… Additional possible changes… ✔ ✔

15. 15 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” CNR, dB T 1, ms CNR, dB T 1, ms T 1 = 1 ms Velocity: mean error & bias (e&b) CNR=40 dB T 1 = 1 ms dwell = 60 ms, SNR=20 dB,  v = 4 m s –1, 100 realizations for each velocity from 0 to v a STD_v k, k=0:va = std(v i, i=1:100 ) BIAS_v k, k=0:va = mean(v i, i=1:100 ) – v o ; Mean_Error = mean(STD_v k, k=1:va ) Mean_Bias = mean(BIAS_v k, k=1:va ); Error Bias

16. 16 Svetlana Bachmann November 20, 2007, Norman OK Technical 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 v a dwell = 60 ms CNR, dB T 1, ms CNR, dB T 1, ms ✔ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✔ ✔ ✔✗✔✗ T1T1 Error Bias

17. 17 Svetlana Bachmann November 20, 2007, Norman OK Technical 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 v a dwell = 80 ms dwell = 100 ms dwell = 120 ms dwell = 80 ms dwell = 100 ms dwell = 120 ms dwell = 60 ms CNR, dB T 1, ms CNR, dB T 1, ms Error Bias

18. 18 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” 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 v a CNR, dB T 1, ms CNR, dB T 1, ms  v = 4 m s –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 Error Bias

19. 19 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” CNR, dB T 1, ms CNR, dB T 1, ms T 1 = 1 ms Velocity: % of acceptable e&b CNR=40 dB T 1 = 1 ms dwell = 60 ms, SNR=20 dB,  v = 4 m s –1, 100 realizations for each velocity from 0 to v a STD_v k, k=0:va = std(v i, i=1:100 ) BIAS_v k, k=0:va = mean(v i, i=1:100 ) – v o ; Mean_Error = mean(STD_v k, k=0:va ) Mean_Bias = mean(BIAS_v k, 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); Accept. Error Accept. Bias

20. 20 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” Velocity: % of acceptable e&b dwell = 60 ms, SNR=20 dB,  v = 4 m s –1, 100 realizations for each velocity from 0 to v a CNR, dB T 1, ms CNR, dB T 1, ms Accept. Error Accept. Bias

21. 21 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” 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 v a CNR, dB dwell = 80 ms dwell = 100 ms dwell = 120 ms dwell = 60 ms dwell = 80 ms dwell = 100 ms dwell = 120 ms dwell = 60 ms T 1, ms Accept. Error Accept. Bias

22. 22 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” 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 v a CNR, dB T 1, ms  v = 4 m s –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 Accept. Error Accept. Bias

23. 23 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” Velocity: mean e&b and % of acceptable e&b  v = 4 m s –1 80 ms 100 ms 120 ms 60 ms CNR, dB T1, ms 80 ms 100 ms 120 ms 60 ms CNR, dB T1, ms dwell = 60 ms 3 2½ 3 CNR, dB T1, ms  v = 4 3½ 2½ 3 CNR, dB 80 ms 100 ms 120 ms 60 ms T1, ms CNR, dB 80 ms 100 ms 120 ms 60 ms T1, ms CNR, dB T1, ms 4 m s –1 3½ 2½ 3 CNR, dB T1, ms 4 m s –1 3½ 2½ 3 Mean error Accept. Error Accept. bias Mean bias

24. 24 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” Velocity e&b: a compromise SNR = 20 dB,  v = 3 m/s, dwell 80 ms

25. 25 Svetlana Bachmann November 20, 2007, Norman OK Technical 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 evaluation GCF with GMAP, TABL, q3D… Finding error & bias for power, velocity, width… Examples of errors & biases… Velocity errors Mean errors… Percentage of acceptable errors… Finding a compromise… Windows… Spectral analyses Examples of mean spectra… Changes to algorithm Summary of changes… Additional possible changes… ✔ ✔ ✔ ✔

26. 26 Svetlana Bachmann November 20, 2007, Norman OK Technical Interchange Meeting “Data Quality / R-v ambiguities mitigation” Changes to algorithm Step pre-compute: Ignore the power loss correction factor, instead normalize the window Step 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, where i_CNRdB 1:2:60, i_Mp 10:59, i_va 20:5:65 x = round((CNRdb_aprox/2)); if x 30 x=30; end; y = round((Np-9)); if y 50 y=50; end; z = round(va/5-3); 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 5 th 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, If2 Step 11. Remove “1/N” from autocorrelation formula Step 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 ✔ ✔ ✔

27. 27 Svetlana Bachmann November 20, 2007, Norman OK Technical 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 evaluation GCF with GMAP, TABL, q3D… Finding error & bias for power, velocity, width… Examples of errors & biases… Velocity errors Mean errors… Percentage of acceptable errors… Finding a compromise… Windows… Spectral analyses Examples of mean spectra… Changes to algorithm Summary of changes… Additional possible changes… ✔ ✔ ✔ ✔ ✔