Briefing for the Coastal Altimetry Workshop The Delay-Doppler Altimeter R. K. Raney Johns Hopkins University Applied Physics Laboratory 05-07 February 2008 1
What is a Delay-Doppler altimeter? Precision Tracking (Resource material) 2
Conventional ALT footprint scan Vs/c ) ))) ) ) RA RA pulse-limited footprint in in effect effect is is dragged dragged along along the the surface surface pulse pulse by by pulse pulse as as the the satellite satellite passes passes overhead Footprint: > 2 km; enlarges with SWH 3
Delay-Doppler (SAR mode*) Radar Altimetry DDA: near-optimum partially coherent processing N-pulse bursts N-pulse bursts * CryoSat (Alcatel) terminology for pulseto-pulse coherent altimetry = delay- Doppler Processing similar to that of Topex: INCOHERENT Range pulse compression Sum range waveforms (incoherent) ~ 2000 looks per second Range D2P data N Doppler bins M bursts per along-track resolution (Doppler) cell > 6000 looks per second Along-track FFTs... 0 Range curve correct... Range pulse compression.... Sum M powers P Dop at each Doppler.... Sum N P Dop at each x COHERENT Doppler frequency is proportional to along-track angle INCOHERENT 4
DDA: a fundamentally different method Pulse-to-pulse coherence => Doppler data decomposition in the along-track direction ) ))) ) )) V s/c DDA DDA spotlights each each along-track resolved footprint as as the the satellite satellite passes passes overhead (One (One result result of of Doppler Doppler processing) Footprint ~ 250 m; independent of SWH 5
On Precision (wrt Radar Self-Noise) Doppler spectral decomposition => more incoherent averaging Gamma Distribution as a function of N (mean and peak normalized) 1 0.9 All radars are precision-challenged Normalized PDF value 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 N = 1 (Single-look SAR) N = 4 (Typical SAR image) N = 16 (Mini-RF Lunar SAR) N = 64 (WS scatterometer) N = 200 (Radar ALT @ 10 Hz) N = 600 (DDA @ 10 Hz) N is the number of statisticallyindependent samples averaged for a given measurement Sigma-zero distribution (nominal = 1) *Delay-Doppler (DDA) = CryoSat SAR mode R. K. Raney 30 Jan 2008 6
Delay-Doppler Altimeter (DDA) vs Conventional: * Precision at 1 Hz Rate Delay/Doppler ~ x2 better than conventional 2.5 Height precision (cm) 0.03 Wind speed (Sigma-0) precision (db) 3.5 SWH precision (cm) 2.0 3.0 1.5 0.02 2.5 2.0 1.0 0.01 1.5 1.0 0.5 10 db SNR No noise 10 db SNR No noise 0.5 10 db SNR No noise 0 0 1 2 3 4 Significant wave height (m) Initatvs\NASA\precisn.wpg Courtesy: J. R. Jensen * 0 0 1 2 3 4 Significant wave height (m) Based on computer simulations 0 0 1 2 3 4 Significant wave height (m) rkraney 7
On Range-gate Tracking Telemetry Command Doppler spectral decomposition => more selectivity in tracker input Interface s/c time Waveform Tracker Q Processor I Fine height ADC ADC Synchronizer The waveform processor is essentially the only difference between a conventional radar altimeter and a delay-doppler instrument. Quadrature mixers Deramp mixer 90 o AGC CW Gain Coarse height Chirp rf clock The radar part of the altimeter LNA Xmtr 8
Smart On-Board Tracker: Doppler-Beam Processing Limited... cw / Delay... Data store X Range deramp Line number (e.g. 64 lines) Doppler (e.g. 64 bins) Delay phase coefficients Along-track position at zero Doppler Along-track FFT... Elevation estimates Doppler Delay IFFT Range Doppler/position mapping Look integration (e.g. 140 per bin) (Doppler bin => footprint size; e.g. 250 m) X Range-gate tracker Unique to delay/doppler Waveforms only from preferred Doppler bins 9
DDA Beam-Limited Tracker Algorithm Vs/c ) )))) ) Tracker Tracker reads reads waveforms only only from from the the center center (1, (1, 2, 2, or or 3) 3) Doppler Doppler bins bins Result? Result? Rejects Rejects all all reflections from from non-nadir sources sources 10
Delay-Doppler Altimeter Summary Precision: The standard deviation of the inherent radar selfnoise is better by (approximately) a factor of 2, which reduces by a factor of 4 the extent of in-scene averaging required to get the same results => major advantage in near-shore applications Tracking: Decomposition of the received data into Doppler frequencies corresponds one-to-one to along-track beam-limited selectivity => a major advantage in near-shore applications Other: the DDA altimeter is simple and low-risk, user can choose (along-track footprint) size (in multiples of 250 m); relies on extensive heritage in space and airborne prototypes; and compatible with well-established retrieval algorithms 11
Back-up/Resource Material 12
On Pseudo-conventional ALT waveforms SAR mode => both DDA and conventional waveforms Radar hardware is virtually the same as conventional Transmitter, Transmitter, receiver, receiver, range range gate gate tracker tracker and and AGC, AGC, Stretch Stretch demodulation demodulation (linear (linear FM FM deramp) deramp) Processing Full resolution individual waveforms 4 MHz Presum n returns, followed by conventional altimeter waveform summations DDA processing Averaged waveform output data rates 10 khz 28 khz R. K. Raney 30 Jan 2008 13
NASA-Funded proof-of-concept Aircraft Altimeter (D2P) Field campaigns 2000, 2001, 2002, 2003, 2005 Johns Hopkins University http://fermi.jhuapl.edu/d2p 14
Pulse length Pulse- Doppler limited footprint rise to a constant effective 0 footprint Altimeters Compared Unique Delay-Doppler Characteristics DDA: More averaging => x2 better precision, x10 better efficiency DDA paradigm retains advantages of a pulse-limited altimeter (pulselimited Conventional across-track) SSH accuracy (to first order) does NOT depend on attitude control/knowledge of the s/c Instantaneous pulse-limited Pulse footprint along-track length limited Δx is Annuli of footprint constant equal with areas increasing SWH Sample posting rate @ n /km gives along-track length 1 2 L 3 eff ( 6.7/n ) km Along-track posting rate 27 Hz for 250-m resolution Relative time delay Advantage: along-track incidence and Doppler equivalence (modulo PRF) Pulse length Along track 0 1 2 3 Delay/Doppler Doppler modulation Multi-looks at each location Δx ~250 m Processing: remove extra delay due to wavefront curvature, which converts all data along-track to height measurements On-board Doppler selection enables smart tracking to ignore nearshore clutter Two-dimensional section of the angular scattering function at each and every subsatellite point 15
Curvature Delay vs Doppler Before azimuth FFTs the curvature delays are multi-valued x Along-track (memory) x n x 2 x 1 ~ x - x n R 1 R 2 r Doppler { (slopes) within window f 1 f 2 f n Observation window for one burst R n Delay histories of scatterers Delay axis 16
Compressed pulse length After Doppler decomposition range curvature is single-valued Processing consists of an frequency/phase multiply in delay within each Doppler bin, one set of such operations per burst Doppler bin number 24 16 8 0-8 -16-24 -32 24 16 8 Doppler bin number 0-8 -16-24 -16-24 -2 0 2 4 6 8 10 24 16 8 0-8 relative range (m) (b) (a) spacecraft, Without delay/doppler before compensation compensation spacecraft, delay/doppler processed After delay/doppler compensation Power (per Doppler bin) -32 Delay -2 0 2 4 6 8 10 relative range (m) -2 0 2 4 6 8 10 Relative range delay (meters) -32 17
Conventional and Delay Doppler Altimeters (DDA) Measure the same Three Parameters Delay Doppler Altimeter: TOPEX Jason-1 1. Low risk, low cost path to altimeter data continuity 2. Smaller footprint: 250m x 2 km 3. Measurement closer to shore: ~0.5 km (vs ~40 km) 4. Less s/c Mass and Power An altimeter measures: Sea Surface Height Range measurement Significant Wave Height Slope of return signal Wind Speed Strength of return signal ABYSS-Lite ~1 m antenna 18
Accuracy (cm) 100 Height ACCURACY (orbit-dependent) is the essential attribute of SSH measurements, thence global topographic studies and climatology (e.g annual sea level rise) 10 Precision and Accuracy Trends 1 1975 1985 1995 2005 GEOS-3 Seasat Geosat Conventional altimeter lower limit Sun-synchronous orbit lower limit ERS-1 TOPEX ERS-2 GFO Delay-Doppler* break-through ENVISAT Jason-1 Precision (cm) 10 Height PRECISION (instrument dependent) is the 1 essential measurement attribute for geodesy, bathymetry, and 0.1 mesoscale oceanography, and enhances near-shore measurements Delay-Doppler *Delay-Doppler (DDA) = CryoSat SAR mode R. K. Raney 30 Jan 2008 19