staggered prt algorithm update
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Staggered PRT Algorithm Update
Sebastian Torres and David WardeCIMMS/University of Oklahoma
and NSSL/NOAA
Data Quality MOU – Technical Interchange Meeting
Norman, OK
1 December, 2009
SPRT Algorithm Evolution
• 2003: 2/3 PRT ratio with DC filter– NSSL Report 7
• 2005: SACHI filter (standalone)– NSSL Report 9
• 2008: Any PRT ratio with DC filter– NSSL Report 12
• 2009: 2/3 PRT ratio with SACHI filter– Separate document delivered on 03/09
• 2009: 2/3 PRT ratio with SACHI filter and overlaid echo recovery
– Separate document delivered on 07/09– NSSL Report 13
2009 SPRT AEL (07/09)
• Notation standardization• Clutter filtering update– SACHI on Segments I and II
• Functionality same as in Report 11• Adapted to “fit” signal processing pipeline• Steps described in algorithmic form
– DC removal on Segment III
• Recovery of overlaid echoes– Segment III data reconstruction– Overlaid echo determination
Recap: Squeezing SACHI in
• Strong-point clutter canceling– Inputs: P, R1, and R2
– Outputs: P, R1, and R2
• SACHI needs to return P, R1, and R2
– Derived from SACHI’s outputs: S, v, and v
– In the absence of SPC, the spectral moment computations should produce S, v, and v again!SACHI
SPC Remov
al
Spectral moment
computations
VConversio
nSvv
PR1
R2
PR1
R2
Sv1, v2v
• Segments I and II– SACHI
• Output: “manufactured” P, R1, and R2
• Segment III– DC removal
• Output: a dwell of time-series data
– Power and correlation computations• Output: P1, P2, R1, and R2
– Combined power computation• Output: P
Recap: Clutter Filtering Logic
Further AEL Updates
• Handling overlaid echoes– Better performance from using short PRTs
• Algorithm modifications– Segment-III data “reconstruction”
• R1 and R2 are computed for all range gates
– Handling overlaid echoes• Detecting and flagging
– Ground clutter filtering• Rules to handle overlaid clutter
– Overlaid power correction for SACHI
ra,2
ra,1
rmax
Segment-III Data Reconstruction
T1 T2
I II I II III
I II III
Segment I Segment II Segment III
1
2
3
4
S1+S3 S2 S3
M 1
M
S1 S2
S1+S3 S2 S3
S1 S2
S1+S3 S2 S3
S1 S2 R1
R2
S1+S3
S1+S3
S1+S3Available only
within ra1
Available within ra2
ra1
ra2
I II III
Handling Overlaid Echoes
• Segments I and III may contain overlaid echoes
– Overlaid echoes appear on every other pulse• Correlations are not biased
– Overlaid echoes do not contaminate reflectivity• Combined powers use only “clean” data
– Moment-specific overlaid power thresholds are used to recover velocity and width for the strong trip
• Segment II does not contain overlaid echoes
Segment I Segment II Segment III
T1
T2 S1+S3 S2 S3
S1 S2 S1+S3
S3
S1
• Algorithm assumes no clutter beyond ra1
– No clutter in Segment III
• Segment I gates– Segment I clutter (C1): SACHI
– Overlaid power correction (S3): computed from T2 pulses
• Segment II gates– Segment II clutter (C2): SACHI
• Segment III gates– Segment I clutter (C1): DC removal on T1 pulses
S1+S3
S1+S3
Clutter Filtering LogicSegment I Segment II Segment III
T1
T2 S3
S1+C1
S1+C1+S3
S2
S2S2+C2
S2+C2 S1+C1+S3
S1+S3+C3
S1+S3+C3
S1+C1+S3
S1+C1+S3
Overlaid Correction for SACHI
• SACHI is not designed to handle overlaid echoes
– After perfect filtering, it would return S = S1+S3/2
– Need to remove S3/2
– S3 is computed from the T2 pulses
• S3/2 is subtracted from the power estimates that are used to produce the manufactured outputs
Segment I Segment II Segment III
T1
T2 S1+C1+S3 S2 S3
S1+C1 S2 S1+C1+S3
Final SPRT AEL (I)
Final SPRT AEL (II)
Computational Complexity (I)
• The most computationally intensive step in the SPRT algorithm is SACHI
• For SACHI, complexity is mainly driven by– DFT of the extended time series
• O(Mx2) = 6.25 O(M 2)
– Matrix multiplications• Two complex matrix multiplications
– 5-by-5 times 5-by-Mp : 2x5x5xM real multiplications ≈ O(M )
• One real matrix multiplication– 5-by-5 times 5-by-Mp : 5x5xM/2 real multiplications ≈ O(M )
– SACHI is not recursive and other steps involve routine computations performed in the FFT mode
• The GMAP notchwidth computation does not require an additional DFT nor the recursive part of GMAP
Computational Complexity (II)• VCP 221 vs. VCP 222
• DFT for SPRT compared to DFT for Batch
– Mx = (5/2) MSPRT = (5/2) (MSPRT /MBATCH) MBATCH
– O(Mx2) = [(5/2) (MSPRT /MBATCH)]2 O(MBATCH
2)
Elev. (deg
)
Batch Sample
s
SPRT Sample
s
Addt’l DFT
Complexity
2.4 61 46 3.56
3.35 61 56 5.27
4.3 61 62 6.46
6 59 80 11.49
RVP-8 CPU Load• Extracted from Steve Smith’s presentation to the
SREC (Jun 2008)
Computational Complexity (III)• Back of the envelope computations– Assume that CPU load in Batch mode is ~10%
• This includes GMAP for the short PRT pulses (all bins?)• Number should not depend on coverage
– Batch mode• Assume that DFT takes ~33% of total computations for
the Batch mode– DFT CPU load is ~3%
• “Other steps” CPU load is ~7%
– SPRT algorithm• Assume that DFT in the SPRT algorithm takes 10 times
longer– DFT CPU load is ~30%
• Assume “other steps” in the SPRT algorithm take 4 times longer than the “other steps” in the Batch mode
– Total CPU load of ~30% + 4x7% ≈ 60%
Conclusions
• Provided a new AEL for staggered PRT with updates in the following areas:
– Notation standardization– Incorporation of SACHI– Handling of overlaid echoes
• Computational complexity of SACHI is predicted to be within current processing capabilities
– SPRT should not require new hardware– Could it be “the straw that breaks the camel’s back”?
• Final version of the algorithm is complete!– Will support ROC’s implementation
and validation
Questions?
Batch ModeVCP 11
Staggered PRT( = 2/3, same DT)
ra = 147 km, va = 28.8 m/s ra = 184 km, va = 45.1 m/s
March 3, 20042.5 deg
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