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**PROGRESS IN SAR SHIP DETECTION AND WAKE ANALYSIS**

J.K.E. Tunaley London Research and Development Corporation, 114 Margaret Anne Drive, Ottawa, Ontario K0A 1L0 This is describes Company activities in ship detection and ship wake analysis since autumn Because of the wide scope, the results will only be summarized. Details can be found on the website; these include further summaries and papers. The overall concept is that MDA relies on AIS as the principal ship information and confirmation of AIS data (location, size, speed, propulsion) can be provided by SAR images as well as databases of ship information. Wake information is expected to be relatively low grade but should be useful in AIS verification.

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**OUTLINE K-distribution Ship Wakes See Web site for papers**

New simple asymptotic approach for large threshold values Parameter estimation difficulties Implications for ship detection Ship Wakes Study started at RMC, Kingston using RADARSAT-2 images, AIS, plus other information. Findings and implications for MDA See Web site for papers 1.Sea clutter statistics are important for ship detection. An asymptotic calculation approach is appropriate to minimize computations and speed data delivery. Clutter statistics must be described from a limited number of pixels; this affects accuracy of parameters. Effects lead to increase in false alarms or reduction in probability of ship detection. Turbulent wake is most common wake in SAR images. Wakes have a potential for confirming (or otherwise) AIS ship identification using wake information and ship data database.

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**K-Distribution Ships are bright blobs in SAR images**

Need statistics of clutter background for CFAR K-D excellent description of radar clutter Basis is modulated complex Gaussian clutter Physical / statistical basis incomplete Modulating distribution assumed gamma Modified Bessel functions of 2nd kind. Computational complexity Approximation for tail values needed Ship detection in SAR images must be accomplished against a sea clutter background. Detection thresholds must be derived from the observed clutter, which is typically variable across the image. In an operational system, the time taken to detect ships must be low to avoid staleness. The processing time for a typical SAR image (RADARSAT, Envisat) should be a fraction of a minute, in other words a few seconds. Experimentally, K-distribution is usually an excellent fit to clutter data in SAR images. It can be explained as a modulation process but the distribution of the modulation is assumed to be gamma. (Birth, death, migration stochastic process; too vague.) Modified Bessel functions of the second kind take too long to calculate. We only need values out in the tail of the distribution because false alarm rate must be about 10-9 per resolution cell. This raises questions about the validity so far out in the tail.

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**K-D APPROXIMATION Low PFA: interested in tail of distribution**

Represent pdf as an integral Use steepest descents Accurate to better than 0.1% (PFA = 10-9) Not sensitive to statistics of modulation Implies that K-D has sound physical basis Basic code can be implemented in < 18 lines of C# or C++. Code is very small with no loops (except for gamma function, which can be found efficiently). PFA is typically very small because there are about 100,000,000 pixels in an image. Integrand replaced by a simpler one with a Gaussian shape.

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**THRESHOLD COMPARISON LOOKS L = 1 L = 4 PFA Accurate Approx. 10-9 0.5**

Smoothness Accurate Approx. 10-9 0.5 214.7 214.8 91.59 91.62 5.0 47.49 47.50 18.796 18.800 50.0 24.24 8.841 8.842 10-6 95.43 95.55 46.40 46.43 25.69 25.70 11.263 11.267 15.337 15.338 6.128 Table shows a comparison between accurate and approximate evaluations of ship detection thresholds for single look and four-look SAR images. K-distribution is characterized by a mean and a shape or order parameter, nu and the number of looks, L. It is easy to estimate the mean accurately so that we focus on nu and derive a threshold as a multiple of the mean. Nu = 0.5 represents spiky clutter, Nu = 50.0 smoother clutter. These data were calculated by integrating the pdf down from very large values until a threshold was reached where the PFA was 10-6 or 10-9.

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**PARAMETER ESTIMATION Need to estimate mean and order parameter**

Number of looks is given Can estimate optimal performance Uses Fisher information (Cramer Rao) Parameter variance depends on number of independent samples, N Need to consider bias Note: Parameters need not be integer Number of looks is given from the radar and image processing specification. It is possible to estimate optimal performance for finite number of independent samples (resolution cells or larger). Parameters need not be integers; this seems to have provided problems in the past.

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**OPTIMUM MEAN INTENSITY Cramer Rao Bound**

#Samples N = 256 L = 1 L = 4 Spiky clutter is at left and smooth, Rayleigh type clutter on the right. When these curves are compared to those for the mean as a simple average, they are indistinguishable on the plot. (Calculate standard deviation of the mean of N samples; the standard deviation is estimated from the theoretical distribution variance.) However, the standard deviation for N = 256 is rather high compared with the mean ( = 1). Therefore for spiky clutter, it is questionable whether N = 256 is sufficient. L = 10 Spiky Rayleigh

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**SDs USING MOM: N = 1000 Optimum Practical**

Comparison of optimum and the practical “Method Of Moments” (ratio of the standard deviation of the data to the mean). MOM is quite poor for estimating nu, especially in spiky clutter at right hand side of plots. Note that when nu is large, the probability distribution is reasonably smooth and does not change very much with Nu. These plots are for N = 1000. Note that the standard deviation is for 1/Nu. This is for technical reasons. L = 1 Black; L = 4 Red; L = 10 Yellow

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**PRACTICAL THRESHOLD N = 100 Ideal N = 1000 N = 10000 L = 4 Rayleigh**

This shows the effect of a finite number of resolution cells, N, when the specified PFA is 10-9 per resolution cell. N less than 1000 results in a large increase in PFA unless the threshold is increased to compensate. The plot is for 4-look imagery. The calculations use the K-distribution approximation together with normally distributed randomization with a variance based on MOM. There is serious bias compared to the ideal infinite N curve, even with smooth clutter.. L = 4 Spiky Rayleigh

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CONCLUSIONS (1) K-distribution approximation will reduce computational complexity for ship detection Methodology adds support to use of K-distribution Insensitivity to modulating distribution Mean of K-distribution can be estimated as usual Parameter variance may bias detection thresholds by large factors if N < 1000 Very important in spiky clutter Without correction, PFA may increase by orders of magnitude If corrected, probability of ship detection is reduced Adaptive pixel block size (N) is desirable in variable clutter

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**SHIP WAKES Turbulent wake study with Dan Roy at RMC**

RADARSAT-2 images AIS Other ship information about propulsion system (Ship owners, Internet, etc.) Analysis (60 ships) includes Twin screws/single screw Left/right handed screws Dan Roy was a MSc student at RMC jointly supervised by Prof. Joseph Buckley and myself. Information gathered by RADARSAT2, AIS, weather stations, Internet and ship owners. Focus on explaining turbulent wakes in SAR images in terms of ship size, propulsion system, ship/radar geometry and wind speed/direction.

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**RMC RESULTS Wakes not usually visible when wind speed U > 6 m/s**

Ship speed V is important: if U < 6 m/s && V > 5 m/s, 80% of wakes are visible Bright line on side of wake consistent with propeller flows (swirling and axial) and wind direction Wakes from shallow twin screws tend to be visible Note that velocity bunching shifts must also be taken into account.

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**RSAT-2: QUEEN OF ALBERNI**

Queen of Alberni is part of BC Ferries fleet. Double ended ferry with a screw at each end to avoid turning at points of embarkation. Note bright line on port side of wake. The purple arrow is the wind vector. Wake offset is consistent with service speed of 19 knots. Data supplied by MDA Corporation

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**Q of A Parameters Parameter Length (m) 139 Maximum Beam (m) 27.1**

Mean Draft (m) 5.5 Maximum Draft (Prop. Tip, m) 5.72 Block Coefficient (estimated) 0.6 Number of Propellers 1 Number of Blades 4 Propeller Shaft Depth (m) 3 Propeller Diameter (m) 5 Propeller Type CPP Service Speed (knots) 19 Propeller 19 knots (rpm) 170 Maximum Power (MW) 8.83 Data is from the Internet and discussions with BC Ferries.

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**COMBINED SWIRLING AND AXIAL WAKE**

Consider both linear and angular momentum in propeller wake Modify Prandtl’s approach to theory Estimate fluid linear and angular momentum using standard engineering methods Apply to Queen of Alberni (BC Ferries) Note that shaft power came out to be 7.9 MW at service speed: compare with table value of 8.8 MW. This is very encouraging.

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**Q of A Wake Diameter Combined Swirling Axial**

Axial and swirling eddy diffusion contributes to wake broadening. In the far wake, axial diffusion dominates. Net slope is reduced from 0.25 and to about 0.3.

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**Queen of Alberni Maximum Surface Flow Speed**

Axial Swirling Group velocity of Bragg waves at C-band is about 13 cm/s. When flow speeds are comparable, the hydrodynamic wake can produce a large effect on the radar wake. Effects should be visible in calm waters when flows are as low as 2 cm/s. Note Queen of Alberni service speed 19 knots. The curves are the result of the new theory of combined axial and swirling turbulent wakes. Surface flows capable of affecting SAR image out to 10 km or more from axial component and about 1 km from transverse swirling component.

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**Deep Screw Case Maximum Flow Speed**

Axial When the screws are deep, the swirling component tends to predominate at small distances astern. This is for propeller tips at a depth of a few metres. Swirling

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CONCLUSIONS (2) Surface flows in the turbulent wake can be large compared with Bragg group velocity Expect significant radar wake visibility for long distances Swirling component dominates axial flow immediately astern and especially when screws are deep Wake characteristics can be used to verify ship Note: Hydrodynamic wake width is only one factor in radar wake width. Others are flow speeds, ambient wind and waves, radar effects and geometry.

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END Thank You All!

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ADDING INTEGERS 1. POS. + POS. = POS. 2. NEG. + NEG. = NEG. 3. POS. + NEG. OR NEG. + POS. SUBTRACT TAKE SIGN OF BIGGER ABSOLUTE VALUE.

ADDING INTEGERS 1. POS. + POS. = POS. 2. NEG. + NEG. = NEG. 3. POS. + NEG. OR NEG. + POS. SUBTRACT TAKE SIGN OF BIGGER ABSOLUTE VALUE.

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