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

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?

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.

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.

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

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

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

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

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.

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:

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.

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    

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.

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.

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  

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             

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.

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

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.

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 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!

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

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.

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.

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.

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.

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

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

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)

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

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.

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

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:

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

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 

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

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, ) .

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

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

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

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

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

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

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

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

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