Luke Rosenberg

(DSTO, Australia)

https://s3-seminar.github.io/seminars/luke-rosenberg

Title — The NRL multi-aperture SAR: system description and recent results

Abstract — The NRL multi-aperture SAR: system description and recent results The Naval Research Laboratory (NRL) multi-aperture synthetic aperture radar (MSAR) is an airborne test bed designed to investigate remote sensing and surveillance applications that exploit multiple along-track phase centers, in particular, applications that require measurement of scene motion. The system operates at X-band and supports 32 along-track phase centers through the use of two transmit horns and 16 receive antennas. As illustrated in this presentation, SAR images generated with these phase centers can be coherently combined to directly measure scene motion using the Velocity SAR (VSAR) algorithm. In September 2014, this unique radar was deployed for the first time on an airborne platform, a Saab 340 aircraft. This presentation presents a description of the system, initial images from the September 2014 tests, and the results of initial coherent analyses to produce estimates of scene and target motion. These images were collected over an ocean inlet and contain a variety of moving backscatter sources, including automobiles, ships, shoaling ocean waves, and tidal currents.

Biography — Luke Rosenberg received his Bachelor of Electrical and Electronic Engineering in 1999, Masters in Signal and Information Processing in 2001 and PhD in 2006 all from the University of Adelaide in Australia. In 2000 he joined the Defence Science and Technology Organisation as an RF engineer, then worked as a research scientist in the imaging radar systems group and recently in the maritime radar group. He is also an adjunct senior lecturer at the University of Adelaide and is currently on attachment at the US Naval Research Laboratory working on algorithms for focussing moving scatterers in synthetic aperture radar imagery. His interests are in the areas of radar signal processing and the modelling and simulation of radar backscatter. In particular, his work has covered radar image formation, adaptive filtering, detection theory, and radar and clutter modelling. He is an active member of the SET-185 NATO panel on high grazing angle sea-clutter and has published over 50 conference, journal and technical reports.

Transcript

1. UNCLASSIFIED 1 CLASSIFICATION The Application of Medium Grazing Angle Sea-clutter Models Luke Rosenberg Defence Science and Technology Organization, Australia Acknowledgement - Simon Watts, Stephen Bocquet and Matt Ritchie Work is part of the NATO SET-185 group
2. UNCLASSIFIED 2  Modelling and simulation of the sea-clutter characteristics allows analysis of a wider set of possible geometries and sea-conditions.  Large body of literature on sea-clutter analysis and modelling.  Mostly from coarse resolution radars at low grazing angles.  Use of higher resolution radars results in spikier sea-clutter which requires new models to accurately distinguish targets.  Future UAV platforms will operate at higher grazing angles > 10o.  Formation of the NATO SET-185 group on high grazing angle sea-clutter.  DSTO has been working in this area since 2004.  Release to NATO of the Ingara X-band High Grazing Angle (HGA) dataset.  Presentation will focus on: • Characterisation of the data set and parameter modelling. • Simulation of an evolving bi-modal Doppler spectrum. • Accurate performance prediction modelling. Why bother with sea-clutter modelling?
3. UNCLASSIFIED 3 Ingara Radar  X-band fully polarimetric radar.  Patch antenna transmits either horizontal or vertical polarisation, then receives both.  Antenna is mounted underneath a Beech 1900C aircraft and can rotate 360.  Radar has a maximum bandwidth of 600 MHz, 1kW transmit power.  Azimuth two-way 3 dB beamwidth is ~1.  Sea-clutter data has: • 200 MHz bandwidth / 0.75 m range resolution. • PRF is ~ 600 Hz. • Full-pol mode alternates horizontal and vertical transmit – halves the effective PRF to ~300Hz.
4. UNCLASSIFIED 4 Sea-clutter trials  First trial - SCT04 Southern ocean, 2004. • 8 days of data - 100 km south of Port Lincoln.  Second trial - MAST06 North of Australia 2006. • 2 days in littoral water, 25 km from Darwin. • 2 days in open ocean, 200 km west of Darwin.  Data collected in circular spotlight mode with ~0.75m range res. / ~64 m az. res.  Data set covers a number of runs, spanning 15o to 45o grazing, 360o azimuth.
5. UNCLASSIFIED 5 Sea-clutter trials – wind / wave ground truth  Wave buoy deployed to measure ground truth.  Wind speed supplied by local BOM weather station.  Wind and wave directions are “from”. Trial Flight Date Wind Wave Speed (m/s) Direction (deg) Height (m) Direction (deg) Period (s) SCT04 F33 9/8/04 10.2 248 4.9 220 12.3 SCT04 F34 10/8/04 7.9 248 3.5 205 11.8 SCT04 F35 11/8/04 10.3 315 2.6 210 10.4 SCT04 F36 12/8/04 13.6 0 3.2 293 8.8 SCT04 F37 16/8/04 9.3 68 2.5 169 9.7 SCT04 F39 20/8/04 9.5 315 3.0 234 11.4 SCT04 F40 24/8/04 13.2 22 3.8 254 12.2 SCT04 F42 27/8/04 8.5 0 4.3 243 12.5 MAST06 F2 17/5/06 8.5 115 0.62 112 3.1 MAST06 F4 19/5/06 3.6 66 0.25 35 2.6 MAST06 F8 23/5/06 3.5 83 0.41 46 4.0 MAST06 F9 24/5/06 10.2 124 1.21 128 4.6
6. UNCLASSIFIED 6 Sea-clutter example  Example data – F35 run, intensity in dB: • Size – 58743 pulses x 1006 fast-time samples. • Observation time: 208 s, PRF: 282 Hz. • Wave structure changes with azimuth angle – due to collection geometry. • Rotated so upwind is at 0 deg. Pol: HH grazing (deg) azimuth (deg) -200 -150 -100 -50 0 50 100 150 38 40 42 44 46
7. UNCLASSIFIED 7 • Range processing occurs in hardware. • Hardware corrections. • Motion compensation. • Geometric corrections: – Radiometric correction, – Elevation beampattern compensation. • Data sets are polarimetrically calibrated. Data processing
8. UNCLASSIFIED 8  Goal is to simulate a noise only signal to match the clutter plus noise.  Each day measurement was made with transmitter turned off.  Processed with all non-geometric terms and averaged.  Noise signal is then simulated for each clutter plus noise sample.  Apply same geometric compensations. Noise power
9. UNCLASSIFIED 9 Parameters of interest  Polarisation: • Ingara HGA dataset contains all horizontal (H) and vertical (V) polarisations. • Typically process each polarisation independently.  PDF: • Require model for the intensity distribution - important to capture high magnitude components due to sea-spikes! • Compound distributions considered: K, K+noise, K+Rayleigh, KK, Pareto+noise.  Correlation: • Pulse to pulse (speckle) correlation, spatial correlation, long-time correlation (secs). • No easy way to model correlation due to non-stationarity!  Doppler spectrum: • Mean and variance of distribution. • How many components should be represented and how should they be modelled? • How does it behave over time / range? • Relationship between intensity and Doppler spectrum.
10. UNCLASSIFIED 10 Intensity PDF  Spiky clutter is difficult to model.  Example below shows 50 range bins, 64 pulses of data.  Simple model such as a K+noise will not fit the data!  Require alternate models such as KK, Pareto+noise or K+Rayleigh. Example with spike: Example without spike:
11. UNCLASSIFIED 11 K+noise distribution  K+noise distribution extends the K model with an extra term which accounts for thermal noise.  Consider compound distribution:  Speckle mean described by x and offset by thermal noise :  Underlying RCS / texture - gamma distributed with shape and scale, b = :   0 , exp ) ( ) ( 1      x bx x b x P x    dx x P x z P z P x x z ) ( ) | ( ) ( 0 |    0 , exp 1 ) | ( |            z p x z p x x z P n n x z  Must be evaluated by numerical integration.
12. UNCLASSIFIED 12 KK and Pareto+noise distributions  KK and Pareto+noise distributions shown to be a good model for spiky sea-clutter [1].  KK distribution has a texture which is the weighted sum of 2 gamma distributions:  Results in 2 independent K components – no physical justification. • Ratio of mean, kk = 2 /1 determines the degree of separation in the tail. • determines the level at which they start to diverge.  Pareto plus noise distribution is much simpler than KK.  It uses an inverse gamma texture model with scale, = − 1 and shape, a:   1 , , 0 , / exp ) ( ) , | ( 1        d a x x d x a d a x P a a x   Both distributions must be evaluated by numerical integration. ) , | ( ) , | ( ) 1 ( ) | ( 2 2 1 1     x P k x P k x P x r x r x    
13. UNCLASSIFIED 13 PDF model comparison Fit comparison for HH polarisation, (--) data, (--) K+noise, (--) KK, (--) Pareto+noise K+noise KK Pareto+noise  Comparison of data fits: K+noise, KK and Pareto+noise.  Example data is from HH polarisation, upwind, 30o grazing.  K+N under-estimates tail of distribution.  Good fit for both KK+N and P+N.
14. UNCLASSIFIED 14 Spatial and Temporal Correlation  Modelling the correlation is essential for simulating realistic looking spectra. However its extremely difficult to model!  Requires a degree of averaging to remove effect of speckle correlation.  Long-time temporal correlation can only be measured at the mid-swath point due to circular spotlight collection and requires measurement over seconds.  Spatial correlation is averaged over time (due to small number of range samples).  Example shows correlation – strong initial decay and then complicated fluctuation.
15. UNCLASSIFIED 15 Original Doppler spectrum model  Original spectrum model is a single Gaussian, where bold implies random variable (R.V).  All data is normalised by its mean, = / . , , = 2 exp − ( − )2 22  Where the mean Doppler freq. is related to the normalised intensity:  No model for the remaining fluctuation around the mean Doppler.  The spectral width, s is modelled as a RV with mean, and standard deviation, . . n n f x B A ) (x m  
16. UNCLASSIFIED 16 Doppler bi-modal spectrum model  Bi-modal spectrum model [2]: , , 1 , 2 = 21 exp − ( − 1 )2 21 2 + 22 exp − ( − 2 )2 22 2  Where + = 1 and mean Doppler of the two components: . x B A ) (x m t x , t B A t x , x B A ) (x m n n f n n n n f r r r            2 1  Overall mean / variance:  . ) ( ) ( 2 ) ( ) ( ) ( ), ( ) ( ) ( 2 1 2 2 2 1 2 2 2 1 2 2 1 n f n f n f n f n f n f n f n f x m x m x m x m s s x x m x m x m             
17. UNCLASSIFIED 17 Measuring Doppler characteristics  Mean Doppler shift and variance determined by moments:                               12 ) , ( ) ( 2 1 ) ( ~ ) , ( 2 1 ) ( 3 1 2 2 1 r noise N n f r r f N n r r f f S k n S k m f N nf h k k n S f N nf h k m  where           r noise N n f S k n S h 1 ) , ( • N is the FFT length / CPI • n is the FFT bin number, k is the range bin • is the power spectral density of the clutter. • is the power spectral density of the noise • fr is the PRF.  Assuming Gaussian models for azimuth beamwidth and spectrum, underlying clutter spectral width is: 2 2 2 ) ( ~ ) ( antenna f f k k      2 log 2 cos 3 2 e dB antenna v      where •  is the elevation angle – equivalent to grazing angle for flat earth, no refraction, • v is platform velocity,  is the radar wavelength, •  3dB is the two-way 3dB azimuth beamwidth.
18. UNCLASSIFIED 18 Mean Doppler  Example fit of bi-modal mean Doppler and standard deviation models to Ingara HGA data.  Clear bi-modal trend observed for HH and HV.  Linear fit only for standard deviation.  Data fit results with r = 0: Direction Pol. mf (xn ) A (Hz) B (Hz) t β Upwind HH -59.54 58.06 2.21 0 HV -42.22 115.24 1.22 0 VV 0.95 2.90 - 1
19. UNCLASSIFIED 19 Doppler Width  Doppler standard deviation can be modelled as a Gaussian or gamma R.V.  Fit example: shape, = 8.01 and scale, = 6.92.  Variation around the mean Doppler, r is modelled as a Gaussian RV with zero mean.  Fit example: standard deviation: = 30.47 Hz.
20. UNCLASSIFIED 20 Parameter Modelling  Goal is to characterise and model the ‘important’ model parameters over sea-state, grazing angle, azimuth angle and polarisation.  Mean clutter and noise powers • Radar range equation modelled with ISRG mean backscatter model [3].  PDF analysis • Read in all samples in a ‘data’ block of 1o grazing, 5o azimuth. • Use the <zlogz> estimator for the shape estimate – P+N, K+N [4]. • Weighted average of shape estimates over all data blocks based on number of samples.  Spatial correlation analysis • Single run averaged over 8 x 64 pulses and 2o grazing. Repeated each 5o azimuth. • Characterise only the de-correlation length – when correlation function decays to 1/e.  Doppler model parameters • Single run with CPI of 64 pulses and 2o grazing. Repeated each 5o azimuth. • Fit bi-modal mean Doppler parameters – A, B, t, β. • Standard deviation of fluctuation around mean Doppler, . • Spectral width mean and standard deviation, ms and – used to relate gamma shape and scale. • Measurements need to account for platform!
21. UNCLASSIFIED 21  Based on relationships by Ulaby for wind speed and azimuth.  Valid over 20o to 45o grazing.  For azimuth angle , ) 2 cos( cos ' 2 ' 1 ' 0 0    a a a          . 4 / 2 , 2 / , 4 / 2 0 0 0 ' 2 0 0 ' 1 0 0 0 ' 0 d c u d u d c u a a a                 where  For grazing angle, and windspeed ,   U b b b U dB 10 ' 2 ' 1 ' 0 0 log ,        Results in 9 coefficients per polarisation.  To implement: • Use (0 ′ , 1 ′ , 2 ′ ) values to generate mean backscatter for upwind, downwind and crosswind. • Determine (0 ′ , 1 ′ , 2 ′ ) and hence mean backscatter 0. IRSG Mean Backscatter Model
22. UNCLASSIFIED 22 Clutter to Noise Ratio  All results rotated so 0o is upwind. Shaded areas contain invalid data.  CNR determined through radar range equation and model for mean noise power.  Left result shows CNR data / model.  Trends captured – sinusoidal variation in azimuth, increasing CNR with grazing.
23. UNCLASSIFIED 23 Parameter model  New parameter model provides a basis for modelling many of these parameters [5].  Extended recent K-distribution shape model [6] to better capture swell dependence.  Used for each polarisation channel independently and contains distinct models for geometry and sea-state.  Geometry variation modelled with Fourier series: • , = 0 1 + 1 cos + 2 cos 2 + 3 cos − + 4 cos 2( − ) (1) • is the grazing angle, is the azimuth angle, • is the wind swell direction, • , 0 ,…, 4 are the model coefficients.  Sea-state variation modelled with: • = 0 +1 log10 + 2 1/3 (2) • U is the wind speed, 1/3 is the significant wave height, • 0 , 1 , 2 are the model coefficients.
24. UNCLASSIFIED 24 Parameter model  To relate these two models, coefficients in (1) are altered to be independent of grazing angle by introducing a normalisation factor, 0 and then redefining (1) as , = 0 [0 + 1 cos + 2 cos(2) + 3 cos( − ) + 4 cos(2( − )] where the new coefficients are related by 0 = 0 0 , 1 = 0 1 0 , … , 4 = 0 4 0 .  The model is then implemented by equating each coefficient , 0 , . . . , 4 to the model Y in (2).  Results in 18 coefficients per polarisation.  Fixed the normalisation factor to 30o.
25. UNCLASSIFIED 25 Parameter model examples:  Results show Pareto shape / model.  Spiky result with same trends as the CNR.  Some regions where shape is less than 1 – model is not valid.
26. UNCLASSIFIED 26 Parameter model examples:  Left result shows A / B parameters from mean Doppler fit. Right result shows model.  Trends are more complicated – HH / VV similar.  VV shows components in the swell direction ~ 100o. A / B data A / B model
27. UNCLASSIFIED 27 Parameter model examples:  Left result shows threshold and β parameters from mean Doppler fit.  Threshold not defined when β =1. Model captures trends reasonably well.  β parameter often saturates. Model altered so any values above 0.8 are set to 1. Threshold, t Ratio β
28. UNCLASSIFIED 28 Parameter model examples:  Left: width of the fluctuation about the mean Dopper and right: spatial de-correlation.  Correlation especially spiky – main trends captured. Fluctuation around mean Doppler, Spatial de-correlation, R (m)
29. UNCLASSIFIED 29 Parameter model examples:  Left result shows distribution parameters from Doppler width Gaussian model. Right result shows parameter model.  Trends show swell is dominant – both mean / std. are similar. Gaussian mean / std. - data Gaussian mean / std. - model
30. UNCLASSIFIED 30 Simulation results – Comparison with Ingara HGA data:  First comparison uses measured parameters from example data set HH - upwind.  Using Ingara measured two-way azimuth beampattern.  Results show a good match visually and by comparing the mean Doppler spectrum.  a /b = mean from data / model, c/d = spiky regions from data / model.  Spiky regions determined by values which exceed bi-modal threshold.
31. UNCLASSIFIED 31 Simulation results using modelled data:  Assuming sea-state, S = 3 where wind speed, significant wave height are related by: Direction Pol. mf (x) (Hz) ms (Hz) s (Hz) CNR (dB)  R (m) A Hz B Hz t β Upwind HH -25.63 41.44 1.84 0.12 25.30 53.60 14.80 22.58 2.62 3.16 HV -24.40 56.29 - 1.0 22.19 55.40 11.44 11.30 7.18 1.98 VV -6.18 10.54 - 1.0 17.87 50.93 12.55 28.90 31.78 3.48 Crosswind HH -0.49 14.36 1.28 0.48 26.58 52.67 13.01 17.21 1.51 2.47 HV -6.09 14.43 1.09 0.66 24.08 50.77 10.12 8.61 1.36 3.91 VV 3.56 -0.07 - 1.0 14.51 47.79 9.26 23.71 16.52 6.57 Downwind HH 91.80 -58.23 1.14 0.38 19.07 43.59 13.04 18.65 3.28 2.90 HV 33.36 -76.24 1.22 0.52 19.79 43.23 9.23 10.66 5.62 2.03 VV -0.32 2.00 - 1.0 12.29 40.99 8.35 27.77 36.07 5.83 , 2 . 3 8 . 0 S U  2 3 1 024 0 U H . /    = 30o grazing, wind swell angle, =0o, PRF = 700 Hz, bandwidth = 200 MHz.  Platform velocity = 100 m/s, two way 3dB az. beamwidth = 1o -> = 49.64 Hz.  Spatial correlation using Gaussian model : = exp − 2 2
32. UNCLASSIFIED 32  Simulation results for all polarisations / major look directions.  Greater ‘spikiness’ captured for the HH polarisation. Less spiky for VV.  Smaller CNR for the cross-pol channel. Simulation results using modelled data:
33. UNCLASSIFIED 33  Target detection involves specifying a probability of false alarm, fa and calculating the probability of detection, d for different clutter & target scenarios.  Desire to know average detection performance using accurate models with realistic parameters which relate to sea conditions and geometry.  Need to account for pulse to pulse (speckle) correlation. Performance prediction modelling
34. UNCLASSIFIED 34 Parametric detection techniques  Literature has a number of methods which account for correlation: • Farina et al. uses an improvement factor – easy to use, assumes Gaussian Doppler spectrum. • Hou and Morinaga – only valid for Rayleigh fluctuating targets, numerical problems. • Ward, Tough and Watts (WTW) – Suitable for most cases – computationally expensive for large CNR, fails when noise is not present.  Developed modification to Shnidman’s calculation method to account for correlation. • Technique correlates noise with speckle. • Use a joint method which uses WTW for CNR < 0 dB and modified Shnidman method for CNR ≥ 0 dB.  Both techniques require an ‘effective’ number of looks 1 ≤ ≤ to account for the temporal correlation. • Related to auto-correlation function, 0 ≤ () ≤ 1:       1 1 2 2 | ) ( | ) ( 2 M n n n M M M L 
35. UNCLASSIFIED 35  Related to correlation by:  Pulse repetition freq. is Temporal correlation model  As sea state increases, wind speed, wave height and length increase.  Doppler spectrum model has been fitted over 15o-45o grazing and all azimuth [7].  The auto-correlation is then formed and measured at the 1/e point.  Correlation is formed by averaging over all angles – no strong trends.  Model is a function of wind speed, U and significant wave height, 1/3 . 3 / 1 2 1 0 H g U g g T    2 ~ exp ) ( 2 2 2 n PRF f T n n            Example for HH channel with 12 days of data: PRF f
36. UNCLASSIFIED 36 Target fluctuation model  Stationary target in Rayleigh distributed clutter and noise – Rice distribution:   zs I e s z L s z P L s z L 2 ) , | ( 1 ) ( 2 / ) 1 (             Fluctuating targets – use chi-squared distribution – fluctuation parameter , n K K s p x S Ks S K K s K S s P                   2 1 A M S , exp ) ( ) , | ( dz ds K S s P L s z P L S P K d     0 , ) , | ( ) , | ( ) , | (    Probability of detection is then: . 1 ; 1 1 1         M k k n M k k n A p x s y p x z where is the mean target power  Probability of false alarm is found when = ,0 (, 0, ) .
37. UNCLASSIFIED 37  Need to define global SIR and threshold: n n p p A M S         0 2 0 ;  and for compound distributions found by integrating over respective underlying RCS distribution (using numerical integration): dx x P M p x p S p x p P S P dx x P M p x p P P x n n n n x n n ) ( , ) ( ) ( | ) ( ) ( ) | ( ~ , ) ( | ) ( ) ( ) ( ~ 0 0 0 K d, 0 K d, 0 0 fa fa                                    Compound distributions
38. UNCLASSIFIED 38  CNR determined with radar range equation and IRSG RCS model.  Geometry: grazing = 30o, azimuth = 0o / upwind, swell angle, =0o .  Shape parameters: • K+N: HH = 2.62, HV = 7.18, VV = 31.77. • P+N: HH = 4.08, HV = 8.35, VV = 34.97.  Sea-state = 3: U= 7.7 m/s and 1/3 = 1.4 m.  Desired fa = 10−5.  Number of looks / non-coherent integration, M = 10.  Target model = Swerling 2 – Rayleigh fluctuation with K=M.  All curves (except for target correlation) show K-distribution in blue, Pareto in red. Default parameters used in modelling
39. UNCLASSIFIED 39  All results show K-distribution in blue, Pareto in red.  fa shows large mismatch in the HH polarisation, smaller in HV, nearly 0 in VV.  As the number of looks increases, curve shifts to the left. False alarm results
40. UNCLASSIFIED 40  Marcum = constant target - no change with non-coherent integration.  Target correlation introduced by introducing effective target fluctuation parameter, 1 ≤ ≤ determined by target correlation .  Rayleigh results less steep than chi-squared / correlation reduces slope.  Key: magenta - : (magenta, red, black, blue) = (0, 0.5, 0.9, 1). Variation in target model
41. UNCLASSIFIED 41  Results show K-distribution in blue, Pareto in red, fa = 10−5.  Big difference between expected performance in the HH / cross-wind directions.  Little change in the VV polarisation. Variation in azimuth
42. UNCLASSIFIED 42  Results show K-distribution in blue, Pareto in red, fa = 10−5.  Large difference in the HH 20o grazing result – due to low Pareto shape parameter.  Smaller difference as grazing increases.  Also difference is less for HV and almost 0 for VV. Variation in grazing
43. UNCLASSIFIED 43  Results show K-distribution in blue, Pareto in red, fa = 10−5.  Increasing sea-state reduces difference in models – reduction in correlation.  Similar trends observed for HH / VV polarisations . Variation in sea-state
44. UNCLASSIFIED 44  Demonstrated how modelling of sea-clutter can be effectively used for both realistic sea-clutter simulation and performance prediction modelling.  Modelling • Presented new parametric model for capturing trends in polarisation, geometry and sea-state. • Applied successfully to model K and Pareto distribution shape, spatial correlation and Doppler spectra parameters.  Simulation • Presented an extension of the original Doppler evolution algorithm. • Now a bi-modal simulation with accurate parameters which produces realistic sea-clutter.  Performance prediction modelling • Using the correct distribution model is vital. • Also important to include correlation in model. Summary
45. UNCLASSIFIED 45 [1] Rosenberg L. and Bocquet S., Application of the Pareto plus noise distribution to medium grazing angle sea-clutter, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2015, 8(1), pp. 255-261. [2] Watts S., Rosenberg L. and Ritchie M. Characterising the Doppler spectra of high grazing angle sea clutter, IEEE International Radar Conference, Lille, France, 2014. [3] Crisp D. J., Kyprianou R., Rosenberg L. and Stacy N. J., Modelling X-band sea clutter at moderate grazing angles, IEEE International Radar Conference, Adelaide, Australia, 2008, pp. 596-601. [4] Bocquet, S., Parameter estimation for Pareto and K distributed clutter with noise, IET Radar Sonar and Navigation, Vol. 9, pp. 104-113, 2014. [5] Rosenberg L., Watts S., Bocquet S. and Ritchie, M., Data characterisation of the Ingara HGA dataset, IEEE International Radar Conference, Washington DC, USA, 2015. [6] D. J. Crisp, L. Rosenberg, and N. J. S. Stacy, Modelling ocean backscatter in the plateau region at X-band with the K-distribution, DSTO, Research report, 2015. [7] Rosenberg L., Characterisation of high grazing angle X-band sea-clutter Doppler spectra, IEEE Transactions on Aerospace and Electronic Systems, 2014, 50(1), pp. 406-417. Doppler spectrum model