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Staggered PRT and Phase Coding Algorithms

NEXRAD Range-Velocity Ambiguity Mitigation. Staggered PRT and Phase Coding Algorithms. Sebastian Torres. Part One. Staggered PRT Current Status. Block 1. Block 2. Block 3. Pattern. Pattern. Pattern. RRDA Capabilities Staggered PRT. Expanded VCP definitions

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Staggered PRT and Phase Coding Algorithms

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  1. NEXRAD Range-Velocity Ambiguity Mitigation Staggered PRT andPhase Coding Algorithms Sebastian Torres

  2. Part One Staggered PRT Current Status

  3. Block 1 Block 2 Block 3 Pattern Pattern Pattern RRDA CapabilitiesStaggered PRT • Expanded VCP definitions • Staggered PRT modes are specified using patterns T1T1T2T2 T2T3T1T1T2T2 T2T3T1T1T2T2 T2T3 … • Expanded set of PRTs • Exact PRT ratios • Resolution given by 9.6 MHz clock • Real-time staggered PRT algorithm • Hardware and software modifications • Level I and II recorder • Uninterrupted data collection for up to 8 hours

  4. T1 T2 T1 T2 … time The Staggered PRT Technique • Transmitter alternates two PRTs • T1 < T2 • PRT ratio: K = T1/T2 = m/n (m,n integers) • ra1 = cT1/2, ra2 = cT2/2 • va1 = l/4T1, va2 = l/4T2 • Maximum unambiguous range • ra = ra2 (one-overlay resolution) • Maximum unambiguous velocity • va = m va1 = n va2 (velocity dealiasing)

  5. 04/06/03 4:42 GMT KTLXVCP 11 – Batch Mode KOUNStaggered 184/276 EL = 2.5 deg 148 km 184 km va = 25.36 m s-1 va = 45.17 m s-1 The Staggered PRT Technique

  6. R1 R2 R1 R2 P1 P2 P1 P2 o o o o T1 T1 T2 The Staggered PRT Algorithm • Computation of autocovariances • P1, R1 for short range sweeps • P2, R2 for long range sweeps • P1, R1, and R2 computed up to ra1 • P2 computed up to ra2

  7. The Staggered PRT Algorithm • Ground clutter filtering • Magnitude squared of DC component is removedfromautocovariances • Bypass map is used • Filter is simple but suppression is limited to about 10 dB • Future work: Test other filtering schemes • Sachidananda’s GCF (Rep. 3 & 4) • Frequency domain filter • Regressive filters • Others

  8. 03/17/03 23:06 GMT KOUNStaggered PRT KOUNUniform PRT EL = 0.5 deg Clutter Filter Performance

  9. v1 - v2 True velocity v1 v2 ^ add 2va1 to v1 va2 va1 closest level ^ ^ v1 – v2 The Staggered PRT Algorithm • Velocity dealiasing algorithm • v1 and v2 are computed from R1 and R2 ^ ^ v

  10. 04/06/03 4:50 GMT KOUNStaggered 184/276 KOUNStaggered 240/360 EL = 2.5 deg 240 km 184 km va = 45.1 m s-1 va = 34.6 m s-1 Velocity Dealiasing Algorithm Performance

  11. Catastrophic error!! v1 - v2 True velocity v1 va1 v closest level Wrong velocity closest level ^ ^ v1 – v2 Velocity Dealiasing Algorithm Performance • What happens if SD(v1) and SD(v2) are large?

  12. 04/06/03 4:48 GMT VelocityStaggered 240/360 Spectrum WidthStaggered 240/360 EL = 2.5 deg Velocity Dealiasing Algorithm Performance Can be used for censoring

  13. The Staggered PRT Algorithm • Reflectivity computation • Use clean powers • Computed to ra2 • Future work: Extend Z to 2ra1 • Censoring • Overlaid echoes do not bias v, but act as noise • Future work: Test Sachidananda’s one-overlaid resolution scheme (Rpt. 4) T1 T2 I II I II III

  14. 03/18/03 3:28 GMT ReflectivityStaggered 184/276 VelocityStaggered 184/276 EL = 1.5 deg 276 km 184 km Censoring

  15. Statistical errors

  16. Summary • Range coverage • Z to ra2 and v to ra1, where ra1/ra2 = m/n = K • Natural “match” for NEXRAD requirements • Extension of maximum unambiguous velocity • va = m va1 = n va2 • Range-velocity ambiguities • Uniform PRT • rava = cl/8 → Inadequate for l = 10 cm • Staggered PRT • ra1va = m(cl/8) • ra1 vs. va trade-off controlled by PRTs

  17. K = 2/3 K = 2/3 PRT Trade-Off 336 km Long PRTs Staggered 336/466 va= 26.7 m s-1 240 km 184 km Medium PRTs Staggered 240/360 va= 34.6 m s-1 Short PRTs Staggered 184/276 va= 45.1 m s-1

  18. Conclusions • Algorithm works with any PRT ratio • No need to add new PRTs to the system (initially) • Only need exact ratios for Sachidananda’s ground clutter filter and one-overlaid recovery • Need good velocity estimates to avoid catastrophic errors • Future work: Determine maximum allowable errors for a given set of PRTs

  19. Conclusions • Recommended for intermediate elevations to replace legacy Batch Mode • Need better ground clutter filters to be useful at lower elevations • Future work: Derive optimum choice of PRTs to match current performance • Achieves “clean” separation of echoes • Results in very simple algorithm

  20. Part Two Phase Coding SZ-2 Algorithm Current Status

  21. RRDA CapabilitiesPhase Coding • Expanded VCP definitions • Can specify phase coding sequence number for each scan • Standard (or predefined) • Downloadable • Proposed new RPG-RDA Message • Real-time 1st-trip decoding of phase-coded signals • Hardware and software modifications • Use WSR-88D phase shifter (7 bits) • Level I and II recorder • Uninterrupted data collection for up to 8 hours

  22. SZ-2 Algorithm • Transmitted pulses are phase-modulated with SZ(8/64) switching code • Phase-coded scan is preceded by long-PRT surveillance scan • Surveillance scan is not phase coded • Powers from the surveillance scan are used to determine overlaid trips in the phase-coded scan • Spectrum widths from the surveillance scan can be used for censoring • Future work: Study limitations of spectrum width estimates obtained from long PRTs

  23. P1 P2 P3 P4 Pth SZ-2 Algorithm • Censoring and overlaid trip determination • Significant return? • Above noise plus sum of out-of-trip powers? • Within recovery region? • Based on plots of SD(vw) on the Ps/Pw vs. ww plane PL range 1st trip 2nd trip 3rd trip 4th trip

  24. Ground clutter 1st trip cohered v SZ-2 Algorithm • 1st trip cohering • Use measured switching code • Ground clutter filtering • Use bypass map • Frequency domain filter • Future work: Study other filtering schemes 2nd trip modulated 3rd trip modulated 4th trip modulated

  25. v vs SZ-2 Algorithm • Lag-one autocorrelation computation • From cohered data for two strongest trips • Final strong/weak trip determination • Use |R(Ts)| for the two strongest trips • Strong-trip cohering • Strong-trip velocity computation (vs) Strong trip cohered Weak trip cohered Strong trip modulated Weak trip modulated

  26. 1st trip cohered 2nd trip modulated vs/2 vs v SZ-2 Algorithm • Processing notch filter (PNF) • Location determined by vs and presence of clutter • Notch Width determined by strong and weak trip numbers • 8 replicas → NW = 3M/4 • 4 replicas → NW = M/2 PNF PNF

  27. Sidebands Strong trip residue v vw SZ-2 Algorithm • Weak-trip cohering • Weak-trip velocity computation (vw) • From lag-one autocorrelation of notched and cohered weak signal Weak trip cohered

  28. SZ-2 Censoring • Power adjustments • Windowing • PNF • Weak-trip • Assignment of correct range • Trip numbers are used to assign correct range location to strong- and weak-trip moments • Censoring and thresholding • Tag trips with significant powers that are unrecoverable

  29. 04/06/03 4:26 GMT ReflectivityLong PRT VelocitySZ-2 with short PRT EL = 0.5 deg 117 km 234 km SZ-2 Algorithm Performance

  30. 04/06/03 4:28 GMT VelocityNon PC “Split cut” VelocitySZ-2 with medium PRT EL = 0.5 deg 175 km 175 km SZ-2 Algorithm Performance va = 23.7 m s-1

  31. 04/06/03 4:30 GMT VelocityStaggered 240/360 VelocitySZ-2 with medium PRT EL = 0.5 deg 240 km 175 km SZ-2 vs. Staggered PRT va = 34.6 m s-1 va = 23.7 m s-1

  32. Conclusions • SZ-2 uses a non-phase-coded, long-PRT, surveillance scan to determine overlaid trips • Substitute for “split cuts” in the legacy WSR-88D • SZ-2 handles up to 2 trips out of 4 possible • Two strongest trips are selected • Future work: Fine-tune thresholds • Can use overlapping radials if M ≠ 64 • Future work: Test this technique with real data

  33. Conclusions • Phase coding may require ground clutter filters with zero phase response • Future work: Study alternatives to recursive filters • Future work: Study ways to compensate for phase distortions • Censoring in SZ-2 is simpler than in the stand-alone version (SZ-1) • Use P and sv from surveillance or both scans • Future work: Fine-tune/add(?) parameters

  34. Conclusions • SZ-2 is very sensitive to clutter residue • From the long-PRT surveillance scan • Recovery region test does not pass • Ring of censored data at the beginning of 2nd, 3rd, and 4th trips • From the phase-coded scan • Noisy data at the beginning of 2nd, 3rd, and 4th trips • Could add CSR as a censoring parameter • SZ-2 is very sensitive to out-of-trip leakage • Fixed by fine-tuned censoring parameters

  35. The End

  36. SZ-1 vs. SZ-2 04/06/03 4:30 GMT VelocitySZ-1 No cens., No GCF, 1st and 2nd trips only VelocitySZ-2 EL = 0.5 deg

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