Enhancing radar maritime surveillance incoastal areas using DTM

VINCENT MESLOT

Master’s Degree ProjectStockholm, Sweden January 2014

XR-EE-SB 2014:001

Contents

Glossary v

Notations vii

Abstract xiii

Introduction 1

1 Radar Theory 31.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 The radar equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1 Transmitting antenna . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.2 Receiving antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.3 Reflection on target . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.4 Radar equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Target information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3.1 Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3.2 Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.3 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Interferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.5 Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Land and Sea Clutter 152.1 Sea clutter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.1 Sea surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.1.2 Reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.1.3 Amplitude statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 192.1.4 Doppler spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2 Land clutter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2.1 Reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2.2 Temporal amplitude distribution . . . . . . . . . . . . . . . . . . . 262.2.3 Spatial amplitude distribution . . . . . . . . . . . . . . . . . . . . 262.2.4 Compound amplitude distribution . . . . . . . . . . . . . . . . . . 28

i

2.2.5 Doppler spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.3 Land-Sea clutter comparison . . . . . . . . . . . . . . . . . . . . . . . . . 30

3 DTM Masking Algorithm 313.1 Background to the problem . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1.2 Literature survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1.3 Algorithm description . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 DTM description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2.2 Data representation . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2.3 Comparison of DTMs . . . . . . . . . . . . . . . . . . . . . . . . . 333.2.4 Choice of the DTM . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Algorithm implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.4 Change of coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.4.1 Spherical coordinates to cartesian, body frame . . . . . . . . . . . 393.4.2 Body frame to local Earth frame . . . . . . . . . . . . . . . . . . . 393.4.3 Local Earth frame to global Earth frame . . . . . . . . . . . . . . . 423.4.4 Global Earth frame to geodetic coordinates . . . . . . . . . . . . . 43

3.5 Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4 Results 454.1 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2 Detections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.3 Tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Conclusion 51

ii

List of Figures

1.1 Diagram summarising the radar principle . . . . . . . . . . . . . . . . . . 41.2 Pulse radar recurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Geometrical configuration of the radar and a target . . . . . . . . . . . . . 51.4 Distance and direction of a target to the onboard radar . . . . . . . . . . 71.5 Amplitude of the received signal vs time, with an echo from a target . . . 81.6 Range resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.7 Echoes pointing out the range ambiguity . . . . . . . . . . . . . . . . . . . 101.8 Configuration of monopulse systems for amplitude comparison . . . . . . 111.9 Sectional view of the four resulting beams for monopulse radar . . . . . . 111.10 Probability Density Functions (PDF) under both hypotheses, with the

detection and false alarm probabilities for a threshold λ. . . . . . . . . . . 13

2.1 Amplitude of sea clutter signal varying with time, for calm and rough sea,with the same mean power . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Representation of a range cell on the sea illuminated by the radar . . . . 172.3 Variation of the normalised RCS at various angles of incidence (source [25]) 182.4 K-distribution PDFs for different parameter values . . . . . . . . . . . . . 212.5 Doppler Power Spectral Density (PSD) for sea clutter. fn is the nor-

malised Doppler frequency, the PSD is in dB. . . . . . . . . . . . . . . . . 232.6 Doppler PSD of sea clutter, with gaussian-components model . . . . . . . 242.7 Amplitude of a land clutter signal depending on the range bin . . . . . . . 252.8 Rice PDFs for different parameter values . . . . . . . . . . . . . . . . . . . 272.9 Weibull PDFs for different parameter values . . . . . . . . . . . . . . . . . 282.10 AC-component PSD with an exponential model, depending on the Doppler

velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.1 A comparison between the two different data representations for DTM . . 333.2 Comparison between raw data for the Strait of Hormuz . . . . . . . . . . 363.3 Zoom on the different data after processing for the Strait of Hormuz . . . 373.4 Land and sea coverage of the SRTM DTM. Areas in pale green and white

are not covered by the DTM. (source [20]) . . . . . . . . . . . . . . . . . . 38

iii

3.5 Spherical coordinate system in the body frame. The target T has coordi-nates (βr, εr, D). βr is the relative bearing, εr the relative elevation andD the distance to the radar. . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.6 Geodetic coordinate system. The point T located on the ellipsoidal Earthsurface has coordinates (α, φ). . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.7 Difference between geodetic latitude φ and geocentric latitude φ. . . . . . 403.8 The different reference frames and coordinate systems used . . . . . . . . 403.9 Illustration of the Tait-Bryan angles, with an intermediary figure without

roll. (M0;nl, el, zl) is the local Earth frame, and (MO,xr,yr, zr) the bodyframe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.10 Illustration of the geocentric frame (O;xe,ye, ze) and the local Earthframe (M0;nl, el, zl), with M0 located by its GPS coordinates (αp, φp)and its altitude h = LM0. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1 Illustration of the aircraft trajectory for the two flights near Lorient, inFrance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2 Comparison between the detections for one scan for the dataset TO63with and without DTM processing. The sea is in grey, and the land inblack ; the red crosses represent the detections. . . . . . . . . . . . . . . . 47

4.3 Comparison between the detections for one scan for the dataset TO26with and without DTM processing. The sea is in grey, and the land inblack ; the red crosses represent the detections. . . . . . . . . . . . . . . . 48

4.4 Comparison between the tracks for TO63 with and without DTM process-ing. The sea is in grey, and the land in black ; the red circles representthe tracks, and the green line their trajectory over all scans. . . . . . . . . 49

4.5 Comparison between the tracks for TO26 with and without DTM process-ing. The sea is in grey, and the land in black ; the red circles representthe tracks, and the green line their trajectory over all scans. . . . . . . . . 50

iv

Glossary

ASTER Advanced Spaceborne Thermal Emission and Reflection Radiome-ter

CFAR Constant False Alarm Rate

CUT Cell Under Test

DEM Digital Elevation Model

DTM Digital Terrain Model

GPS Global Positioning System

ID Identification number

KA Knowledge-Aided

MODIS Moderate Resolution Imaging Spectroradiometer

NRCS Normalised Radar Cross-Section

PDF Probability Density Function

PSD Power Spectrum Density

RCS Radar Cross-Section

SRTM Shuttle Radar Topography Mission

SWBD SRTM Water Body Data

WGS84 World Geodetic System 1984

v

Notations

Chapter 1

αFA False alarm probability threshold

βr Relative bearing angle

εr Relative elevation angle

δβ Bearing angle offset

δε Elevation angle offset

δθ Deviation angle

λ Wavelength

λT Threshold satisfying the Neyman-Pearson criterion

ϕs Phase shift

σ Target’s radar cross-section

τ Time offset of the target’s radar echo, also called propagation time

θ3dB Azimuthal beamwidth

ζ Backscattering coefficient attenuation

∆ε Difference between the signals of the top quadrant and the bottomquadrant of the receiving antenna

∆β Difference between the signals of the right quadrant and the leftquadrant of the receiving antenna

Σ Sum of all the signals from each antenna

c Speed of light

kB Boltzmann’s constant

sr(t) Received signal

st(t) Transmitted signal

ft Transmitted wave frequency

fD Doppler frequency shift

fR Pulse repetition frequency

vii

ra Range ambiguity

rr Range resolution

u(t) Transmitted information signal

vr Target’s radial velocity

~vt Target’s velocity vector

~u Radar-target unit vector

Aeff Antenna aperture

Bt Transmitted frequency bandwidth

D Radial distance between the radar and the target

Fn Amplifier noise factor

Gr Receiving antenna gain

Gt Transmitting antenna gain

K Antenna parameter for direction

L Loss coefficient in the radar equation

Nel Number of elementary reflectors in a range cell

Nr Number of range bins in one recurrence

Nrec Number of recurrences in one burst

Pr Power received by the radar

Pt Power transmitted by the radar

Ptarg Power reflected by the target

PD Detection probability

PFA False alarm probability

Ta Absolute temperature

Tpulse Time duration of a pulse

TR Pulse repetition period

W Surface power density

b Sampled noise signal (vector notation)

s Sampled target signal (vector notation)

z Sampled received signal (vector notation)

Chapter 2

δvD Spectral widening in Doppler velocity

εa Target’s absolute elevation

εp Plane’s elevation

viii

η Ratio of the dc-component power to the ac-component power forthe land clutter spectrum

γ Euler constant

λ Transmitted wavelength

µ Scale parameter of the Weibull distribution

ν Shape parameter of the K-distribution

ω Shape parameter of the Weibull distribution

Φ Grazing angle

ϕi Phase of the signal scattered by the ith reflector

ψ Digamma function

ρ Scale parameter of the Rice distribution

σ0 Normalised radar cross-section

σH0 Normalised radar cross-section for horizontal polarisation

σV0 Normalised radar cross-section for vertical polarisation

σφ Roughness parameter in the GIT model

σh Standard deviation of the surface roughness

Vw Wind velocity

θw Angle between the wind direction and the antenna direction

ξ Shape parameter of the Rice distribution

∆f Normalised half-power width of the Doppler spectrum

Γ Gamma function

a Scale parameter of the K-distribution

ai Amplitude of the signal scattered by the ith reflector

b Shape parameter for the exponential distribution

fn Normalised Doppler frequency

fn0 Mean Normalised Doppler frequency shift

h Radar altitude

mf Mean Doppler frequency of the sea clutter spectrum

s Standard deviation of the sea clutter spectrum

vD Doppler velocity

vD0 Mean Doppler velocity

vHD0 Mean Doppler velocity for horizontal polarisation

vVD0 Mean Doppler velocity for vertical polarisation

x Clutter amplitude

z Clutter power

ix

Ai Interference factor in the GIT model

Au Direction factor in the GIT model

Aw Wind velocity factor in the GIT model

(Ah, Bh, Ch, Dh) Parameters for the land clutter reflectivity model

D Radial distance between the radar and the target

G(f) Doppler power spectral density

(GB, fB, wB) Parameters corresponding to the Bragg scattering in the land clut-ter PSD model

(GW , fW , wW ) Parameters corresponding to the whitecap scattering in the landclutter PSD model

(GS , fS , wS) Parameters corresponding to the burst scattering in the land clut-ter PSD model

Hw Average wave height

I0 Modified Bessel function of the first kind of order 0

Ki Modified Bessel function of the second kind of order i

U Normalised log estimator

U Mean of the normalised log estimator

X z log z estimator

X Mean of the z log z estimator

Chapter 3

α Longitude

α0 Longitude of the first element of a raster DTM

αp Aircraft’s longitude

βr Absolute bearing angle

βr Relative bearing angle

βp Plane’s heading (yaw)

δα Longitude step for raster DTM

δφ Latitude step for raster DTM

εa Absolute elevation angle

εp Plane’s elevation (pitch)

εr Relative elevation angle

φ Latitude

φ0 Latitude of the first element of a raster DTM

φp Aircraft’s latitude

x

φ Geocentric latitude

Θ Plane’s bank (roll)

ae Major semi-axis of the WGS84 ellipsoid

be Minor semi-axis of the WGS84 ellipsoid

ee Eccentricity of the WGS84 ellipsoid

fe Flattening of the WGS84 ellipsoid

h Radar altitude

L Aircraft’s normal projection on the Earth’s surface

MO Plane center of gravity

N Length of a particular segment defined by a point on an ellipse

Re Earth radius

T Target’s position

nl First vector of the local Earth frame, directed from the plane’scenter to the North

el Second vector of the local Earth frame, directed from the plane’scenter to the East

ue Target’s coordinate in the global Earth frame (or geocentric frame)

ul Target’s coordinate in the local Earth frame

ur Target’s coordinate in the body frame

t Translation vector from the local Earth frame to the global Earthframe

xr First vector of the body frame, directed towards the plane’s nose

yr Second vector of the body frame, directed towards the plane’s rightwing

zl Third vector of the local Earth frame, directed from the plane’scenter to the Earth’s center

zr Third vector of the body frame

(M)(d,r) Spatial mask, depending on the range d and recurrence r

(M1D)(d) One-dimension mask, depending on the range d

(Mf )(d,fn) Spectral mask, depending on the range d and normalised Dopplerfrequency fn

R Rotation matrix from the local Earth frame to the global Earthframe

RY Yaw rotation matrix

RP Pitch rotation matrix

RR Roll rotation matrix

xi

Abstract

Radar maritime surveillance of coastal areas is a daunting challenge due to the presenceof both land and sea, whose behaviour in terms of radio waves scattering is completelydifferent. As of now, most of the radar detection algorithms use a local adaptive thresh-olding based on the radar data only. With this method, the radar detection performanceis significantly degraded in littorals.

This thesis offers a state-of-the-art of the land and sea clutter. This allows to clas-sify their characteristics, and to point out the issues causing the detection performancedegradation in coastal areas.

This thesis also proposes a knowledge-aided algorithm using a Digital Terrain Model(DTM) to enhance the detection performances of a coherent radar for maritime targetsin coastal areas. The DTM allows to distinguish if a range cell is located on the sea oron the land. A simple algorithm for non-coherent radars has been realised by discardingall the range bins located on the land.

The comparison of this algorithm with a common adaptive thresholding algorithm onreal data shows that all the detections located on the land are discarded.

xiii

Introduction

Radar is an electronic system using radio waves to detect and estimate the position andspeed of targets such as ships or aircraft. The term radar is an acronym for RadioDetection And Ranging. It is now widely used in both military and civilian contexts,such as air and road traffic control, air-defence systems, ocean surveillance, weatherobservation or missile guiding.

This master thesis is part of a wider project of small maritime surface targets detectionfrom a surveillance radar on-board an aircraft. This thesis focuses on coastal areas,where both land and sea are present. For a radar system, these two environments showmajor differences in behaviour. The main issue resides in the fact that both land and seasurfaces scatter radio waves which disturb the backscattered signal, hence provoking theappearance of detections which do not correspond to actual targets. Those detections arecalled false alarms. The knowledge of these parasitic echoes characteristics, commonlycalled clutter, is preponderant to be able to suppress the appearance of false alarms.Clutter is thus a major issue in radar signal processing.

Many studies have been realised aiming at filtering land and sea clutter influence on radardetections. The literature offers efficient methods to deal with this issue. However, landand sea clutter are most often studied separately, and the difficulty resides in combiningthese two different aspects, a necessity for coastal areas.

This thesis concerns maritime surveillance in coastal areas. As such, sea is the onlyconcern, and land is considered as a disruptive factor only. The objective is thus toremove the influence of the land on the maritime detections near littorals.

This thesis report is organised as follows. Chapter 1 gives an overview of the radar theory,focusing on the signal processing aspect rather than on the physical phenomena involved.Chapter 2 presents a state-of-the-art of the land and sea clutter modelling in order toprovide a detailed comparison of their characteristics. In Chapter 3, an algorithm isproposed to remove the land influence on the detection. The conclusions from Chapter2 motivates a knowledge-aided algorithm using Digital Terrain Models, since making thedistinction between the two types of clutter proves to be too arduous. The choice of theDTM is discussed before a detailed explanation of the algorithm principle. Chapter 4presents the results obtained with the DTM algorithm for both real and synthetic data.

1

A qualitative and quantitative assessment of the algorithm is performed and comparedto the original objectives. Finally, conclusions and perspectives are given.

2

Chapter 1

Radar Theory

1.1 Introduction

This first chapter is focused on the general principle of a radar and on its practical issues.The objective here is not to summarize the state-of-the-art of the most advanced radarsystems, such as those which can be found in the literature. The framework is thusrestricted to simple systems.

The study is focused on a radar whose characteristics are given below:

� airborne radar, since the radar is on board an aircraft carrier;

� monostatic radar, since the same antenna is used for both reception and emission.In the bistatic case, the emitting antenna and the receiving one are physicallyseparated;

� surveillance radar, since it continually observes a specific coverage area;

� high range resolution radar, since it can distinguish between two targets separatedof a few meters in range;

� coherent radar, since both the amplitude and phase of the signal are known. Non-coherent radars discard the phase information.

� pulse radar, since it emits short pulses periodically. Some radars, such as roadtraffic radars, emit a continuous wave.

The pulse radar can be decomposed in several phases as depicted in Figure 1.1:

� Generation of a pulse wave with a carrier frequency ft (typically in the X-band,from 8 to 12GHz). It can be modulated depending on the radar use. The trans-mitted wavelength λ verifies the following relation

λ =c

ft(1.1)

3

WaveformGenerator

Transmitter

Processing

Visualisation

Receiver

Emitted wave

Reflected wave

Figure 1.1: Diagram summarising the radar principle

where c is the speed of light.

� Emission of the electromagnetic wave through an antenna, in a precise direction,for a time duration Tpulse, with a pulse repetition frequency1 fR, as shown inFigure 1.2. The antenna has an azimuthal beamwidth of θ3dB. The transmittedwave can also be polarised. Usually, the polarisation is linear, and two directionsare possible, the horizontal and vertical polarisations.

� Each surface coming into contact with the transmitted wave scatters it in everydirection. A part of this backscattering is then received by the antenna. Thereceived signal is then filtered and sampled. The set of all the samples collectedfor a single pulse transmission is called a recurrence. Usually, the same antenna isused for both emitting and receiving, with the help of a duplexer.

� Processing of the data received to detect targets and to measure its characteristics,such as distance, velocity, or direction.

� Visualising data on a map-like display for an easy human understanding.

The algorithm proposed in this thesis is performed within the processing block of Figure1.1.

The analysis of the received signal thus gives information about the target’s distanceto the radar (denoted D), its direction and its radial velocity (denoted vr). The radialvelocity corresponds to:

vr = ~vt · ~u (1.2)

where ~vt is the velocity vector of the target, and ~u is the unit vector plane-target. Figure1.3 represents the geometrical configuration of an onboard radar and its target, with theirrespective velocities.

1or a pulse repetition period TR = 1fR

4

TimeTpulse0 TR

Recurrence 1 Recurrence N

Emission Reception

Figure 1.2: Pulse radar recurrences

~vp

vp.~u~u

~vt

vt.~u

D

Onboard radar

Target

Figure 1.3: Geometrical configuration of the radar and a target

1.2 The radar equation

The knowledge of the radar link budget is essential for the radar design, and to graspthe concept of range. The radio link is composed of three steps:

� transmission of the energy towards the target,

� backscattering of a part of the energy towards the radar,

� reception of this energy by the radar.

The radar equation will be established in free space.

1.2.1 Transmitting antenna

The antenna’s role at transmission is to focus the transmitted energy in a precise direc-tion. This capacity is described by the antenna gain Gt. For a transmitted power Pt,the surface power density W at a distance D from the antenna is shown in [11] to beequal to

W = GtPt

4πD2(1.3)

5

1.2.2 Receiving antenna

The antenna’s role at reception is to receive as much of the incoming power as possible.For an incoming surface power density W , the received power Pr depends on the antennaaperture, which is defined as the surface Aeff such as

Pr = WAeff (1.4)

It is the geometrical surface that would have a perfect antenna receiving Pr with asurface power density W .

For a transmitted wavelength λ, it can be shown [11] that the gain of an antenna isproportional to its aperture as follows

Gt =4πAeffλ2

(1.5)

1.2.3 Reflection on target

The target receives a part of the transmitted energy and scatters it in every direction,including towards the radar receiver. Since the underlying physical phenomenon is com-plex, it is usually described using a statistical model.

The target is behaving as an antenna of aperture Aeff = σ towards the radar antenna.All the received power is then isotropically scattered, without loss. σ is called the radarcross-section (RCS), it is a measure of the target’s ability to reflect the transmittedpower from the radar in the direction of the receiver.

1.2.4 Radar equation

The radar equation is established for a radar transmitting a power Pt with an antennagain Gt towards the target located at a distance D. The surface power density at thetarget is

W = GtPt

4πD2(1.6)

The power received and transmitted by the target of RCS σ is

Ptarg = W σ (1.7)

Then the power received by the antenna of aperture Aeff is

Pr =Ptarg4πD2

Aeff = PtGtAeff σ

(4π)2D4= Pt

GtGr λ2σ

(4π)3D4(1.8)

6

Since the antenna is the same for transmitting and receiving, Gr = Gt. A loss coefficientL is also introduced to take into account the losses due to the radio-frequency compo-nents, the fluctuation of RCS and the atmospheric losses. The radar equation in freespace then becomes

Pr = PtG2tλ

2σ

(4π)3D4L(1.9)

The fact that the received power decreases with the fourth power of the distance is themain limitation for the radar’s range.

1.3 Target information

The processing of the signal received by the radar yields different kinds of informationabout the observed target:

� the radial distance, which is the distance between the radar and the target. It isdenoted D in Figure 1.4.

� the direction, which consists of two angles, the relative elevation εr and the relativebearing βr. They are both represented in Figure 1.4.

� the radial velocity, in the case of coherent radars only. It is denoted vr (see (1.2)).

Towardsplane nose

Towards planeright wing

D

βr

εr

Figure 1.4: Distance and direction of a target to the onboard radar

7

Amplitude

Time

Pulse N

Tpulse0 TR

Echo

τ

Pulse N + 1

Figure 1.5: Amplitude of the received signal vs time, with an echo from a target

1.3.1 Distance

The main measure obtained with a radar is the distance between the target and theradar itself. Figure 1.5 represents the amplitude of the received signal. An echo canbe observed at time τ , this is due to an object which backscattered the transmittedwave. From the measure of τ , the radial distance between the radar and the target canbe deduced. Indeed, considering that the wave is propagating through the air with avelocity equal to the speed of light c, the distance D between the target and the radaris obtained as

D =c τ

2(1.10)

However, this measure proves to have two limitations, range resolution and range am-biguity. The range resolution is the capacity to distinguish between two targets close inrange. Indeed, if the targets are too close, the two echoes will merge as shown in Figure1.6a, and it will not be possible to distinguish between them. Thus, for two distinctechoes to appear, they must be separated in time by more than a pulse width, as shownin Figure 1.6b. This corresponds to a range resolution rr of

rr =c Tpulse

2(1.11)

The range ambiguity is an uncertainty concerning the true distance to the target. Indeed,there is no information in the receiving signal indicating which pulse engendered the echo.In the example given in Figure 1.7, it is not possible to know if the echo from the target2 was caused by the pulse N + 1 or the pulse N , or even an anterior pulse. Thus anambiguity on the actual range exists, which is expressed as

D =c (τ + k TR)

2=c τ

2+ k

c TR2

, k ∈ N (1.12)

Therefore the range ambiguity is expressed as

ra =c TR

2(1.13)

8

Amplitude

Time

Pulse N

TPulse ∆t

Echo 1Echo 2

Pulse N + 1

(a) Echoes merging due to the range resolution, ∆t < Tpulse

Amplitude

Time

Pulse N

TPulse ∆t

Echo 1Echo 2

Pulse N + 1

(b) Echoes sufficiently distant to be distinguished, ∆t > Tpulse

Figure 1.6: Range resolution

1.3.2 Direction

The target’s position depends on two parameters, the distance to the radar and thedirection, which is the angle to the radar.

For this purpose radar systems use directional antennas which concentrate the transmit-ted energy in a narrow beam. These antennas have two main advantages:

� increasing the transmitted power in the beam direction,

� allowing the target angular localisation.

Indeed, the target location is given by the beam position at the signal reception. How-ever, this measure is not precise enough, due to the beam width. To increase the pre-cision, several antenna elements are used at the reception, which allows a deviationmeasurement. The beams of each antenna element present a slight offset. This is shownin Figure 1.8 for two antenna elements. From the two signals S1 and S2 received by the

9

Amplitude

Time

Pulse N

EchoTarget 1

EchoTarget 1Echo

Target 2

Pulse N + 1 Pulse N + 2

Figure 1.7: Echoes pointing out the range ambiguity

antenna 1 and 2 respectively, a sum Σ and a difference ∆ signal are computed.

Σ = S1 + S2

∆ = S1 − S2(1.14)

Then the deviation angle δθ is obtained as shown in [22]

δθ = K∆

Σ(1.15)

where K is a parameter depending on the antenna.

Actually, the receiving antenna is composed of an array of multiple antenna elements.These elements are separated into four quadrants, resulting in four different beams, inorder to obtain both the elevation and bearing angles. The sectional view of the resultingbeams of these four quadrants is illustrated in Figure 1.9. In this case, the signals aredifferent, and expressed as follows

Σ = A+B + C +D (1.16)

∆β = (S12 + S22)− (S11 + S21) (1.17)

∆ε = (S11 + S12)− (S21 + S22) (1.18)

The elevation angle offset δε and bearing angle offset δβ are then obtained using therelations

δε = K∆ε

Σ(1.19)

δβ = K∆β

Σ(1.20)

10

Beam of antenna 2

Beamof anten

na 1

θ0

Target

δθ

Radar

Figure 1.8: Configuration of monopulse systems for amplitude comparison

S12S11

S21 S22

Figure 1.9: Sectional view of the four resulting beams for monopulse radar

1.3.3 Velocity

Another important measure is the target’s velocity. It is accessible only for coherentradars, since the knowledge of the signal phase is necessary. Each pulse can be writtenas an information signal modulated with a high frequency carrier

st(t) = u(t) ej2πftt (1.21)

where u(t) is the known envelope of the signal. The signal received after propagation ofthe transmitted signal and reflection on the target has gone through several modifica-tions:

� attenuation by a backscattering coefficient ζ,

� time shift of τ , called propagation time,

� phase shift denoted ϕs, with ϕs = 4πDλ ,

11

� frequency shift fD, called Doppler frequency, due to the radial velocity of thetarget.

The expression of the received signal is thus

sr(t) = ζ.u(t− τ)ej2πfttej2πfDtejϕs (1.22)

The radial velocity vr of the target can then be deduced from the value fD with therelation

vr = −λfD2

(1.23)

1.4 Interferences

The major issue with radar detection is the presence of parasitic signals, which arecaused by different phenomena. The main interfering signals are:

� Thermal noise: it is an internal noise caused by the electronic components ofthe radar system. This is an additive white Gaussian noise, with varianceσ2 = kBTaBtFn. kB is the Boltzmann’s constant, Ta is the absolute tempera-ture of the components, Bt is the transmitted frequency bandwidth, and Fn is thenoise factor of the amplifier.

� Clutter: this term refers to the parasitic radio frequency echoes from the targetsclose environment. These interferences come mainly from the ground, the sea, rain,and the atmosphere. The complexity of the underlying phenomena makes theirmodelling very challenging, which is the object of chapter 2. Thus, distinguishingbetween target echoes and clutter is one of the most arduous aspect of the radardetection.

� Jamming: this refers to the received radio frequency signals produced by a differentsource than the actual radar. These signals are mainly intentionally created by anenemy to disrupt the radar in order to hide potential targets. This is a commonelectronic warfare tactic.

1.5 Detection

The detection issue consists in deciding from the backscattered signal if a target is presentor not. This is a decision between two hypotheses, one corresponding to the absenceof target, while the other corresponds to the presence of a target. The most commonlyused decision criterion is the Neyman-Pearson criterion.

The backscattered signal is composed of bursts containing Nrec recurrences, and eachrecurrence is then sampled in range, say Nr range bins per recurrence. Thus, there is

12

λTz

PD

F

Pz(z|H0)

Pz(z|H1)

λTz

PD

F

PD

PFA

Figure 1.10: Probability Density Functions (PDF) under both hypotheses, with thedetection and false alarm probabilities for a threshold λ.

a total of Nr × Nrec space-time samples received for each burst. The received signal zcontains the Nrec time samples for a given range. The two different hypotheses on zare

H0 : z = b (1.24a)

H1 : z = s + b (1.24b)

H0 corresponds to the noise signal b only, while H1 corresponds to the case where thetarget signal s and the noise b are both received. Let di be the decision associated tothe hypothesis Hi. The detection probability PD and the false alarm probability PFAare then defined as

PD = P (d1|H1) (1.25a)

PFA = P (d1|H0) (1.25b)

The detection and false alarm probabilities are represented in Figure 1.10 by the greenand blue surfaces respectively. The ideal objective would be to maximise the detectionprobability while minimising the false alarm probability. However, those constraintscannot be satisfied simultaneously, thus a trade-off on the threshold is necessary. Indeed,a higher threshold will lead to a lower false alarm probability, but at the cost of a lowerdetection probability, as seen in Figure 1.10.

The Neyman-Pearson criterion aims at maximising the detection probability PD underthe constraint of a fixed false alarm probability PFA ≤ αFA, i.e.{

max(PD)

PFA ≤ αFA(1.26)

13

This leads to the following decision ruleΛ(z) =

Pz(z|H1)

Pz(z|H0)

H1

≷H0

λT

αFA =

∫ +∞

λT

PΛ(Λ|H0) dΛ

(1.27)

where Λ(z) is the likelihood ratio.

Thus, the detection depends strongly on the models used for the two probability densityfunctions Pz(z|H1) and Pz(z|H0). This is the reason for the importance of the cluttermodelling. Another daunting issue is the real-time estimation of the model parame-ters.

14

Chapter 2

Land and Sea Clutter

Enhancing the capacity of a radar to detect targets located near littorals requires theanalysis of the different physical phenomena occurring in such a situation. Indeed,the clutter modelling has a major role in target detection, as proven in the previouschapter.

The first section deals with the physical behaviour of the sea regarding radar systems.Despite the complexity of the underlying physical phenomena, the literature is abundantenough to offer a good understanding of the sea clutter properties.

In a similar fashion, the second section concerns the physical behaviour of the landregarding radar systems. The main objective here is to compare the properties of landand sea, in order to distinguish between them.

2.1 Sea clutter

The scattering of electromagnetic waves on the sea surface proves to be a very com-plex phenomenon due to the ever-changing surface, which is affected by many differentfactors such as wind or swells. Furthermore, optical phenomena such as diffraction or in-terferences between scattered signals tend to make the realisation of a theoretical modelimpossible. Thus sea clutter models are mainly empirical, and supported by observationsand measurements.

A sea clutter amplitude signal for calm sea is shown in Figure 2.1a, and for a roughersea in Figure 2.1b, for the same power. It can be observed that high amplitude pointsare present in the rough sea clutter, which could be mistakenly interpreted as targets.That is the main reason why clutter modelling is a critical aspect of the radar.

15

0

2

4

6

8

Range

Am

plitu

de

(a) Calm sea

0

2

4

6

8

Range

Am

plitu

de

(b) Rough sea

Figure 2.1: Amplitude of sea clutter signal varying with time, for calm and rough sea,with the same mean power

Douglassea state

DescriptionWaveheight, Hw(ft)

Windspeed (kn)

1 Smooth 0-1 0-62 Slight 1-3 6-123 Moderate 3-5 12-154 Rough 5-8 15-205 Very rough 8-12 20-256 High 12-20 25-307 Very high 20-40 30-50

Table 2.1: Douglas sea scale (source [17])

2.1.1 Sea surface

The different sea states are commonly classified using the Douglas sea scale shown inTable 2.1. These states describe the sea surface subject to wind influence generatingwaves and swell. The average wave height Hw is the mean crest-to-trough height of thehighest third of the waves.

Although the modelling of the waves provoking the movement of the sea surface is verycomplex, three different types of scattering mechanisms can be distinguished [30]:

� Bragg scattering: it is composed of small resonant capillary waves, which aremodulated by a large scale swell structure.

� Burst scattering: it is a scattering due to the crests of the waves just before theybreak.

16

Sea surface

Illuminatedrange cellθ3dB

cTpulse2

Aircraft directionh

εr

Φ

D

Figure 2.2: Representation of a range cell on the sea illuminated by the radar

� Whitecap scattering: scattering from the very rough surface of waves as they break.

These scattering mechanisms are the main reasons for the appearance of high amplitudeechoes, commonly referred to as spikes, in rough sea clutter.

2.1.2 Reflectivity

The sea clutter reflectivity is represented by σ0, the normalised RCS (see section 1.2.3),called NRCS. It is the average RCS of the area illuminated by the antenna beam, dividedby the surface of this area. From Figure 2.2, the surface of the illuminated range cellcan be deduced easily, yielding for σ0 the following relation

σ0 =2 cos(Φ)

Dθ3dBc Tpulseσ (2.1)

where Φ is the grazing angle. In the flat-Earth approximation, where the Earth surfaceis considered flat and not ellipsoidal, the relation Φ = εa holds, where εa is the absoluteelevation of the target (εa = εr + εp with εp the plane elevation).

Thus the power of the received signal is directly proportional to σ0. It is dependent onseveral different factors, such as transmitted frequency, polarisation, sea state, wind orgrazing angle.

A same model usually applies to either low grazing angles, typically less than 10°, ormid to high grazing angles. Figure 2.3 illustrates the different scattering mechanisms

17

Figure 2.3: Variation of the normalised RCS at various angles of incidence (source [25])

occurring depending on the incidence angle (which is the complementary angle of thegrazing angle). The scattering phenomena occurring at mid to high grazing anglesare mainly composed of specular scattering and Bragg scattering. Then, more complexphysical phenomena occur at low grazing angle, which requires a change of model. Thesephenomena include shadowing and multipath interferences.

The maritime surveillance missions require a wide coverage in distance, up to a rangeof 50 nautical miles. That means that the sea is seen at low grazing angles, typicallybetween 0.1° and 5°. Different models have been proposed for this situation, and threeare widely used:

� Nathanson model [18]: it is the first NRCS model, and gives the NRCS as afunction of the grazing angle, the polarisation and the sea state.

� Sittrop model [23]: the NRCS is given depending on the grazing angle, the polar-isation and the wind speed.

� GIT model [12]: it is the most commonly used model. The NRCS σ0 depends onthe grazing angle, the wind speed and direction, the polarisation, the wave heightand the radar wavelength. It is described in details below.

18

In the GIT model, the NRCS is described as a function of three factors: the interferencefactor Ai, the wind direction factor Au and the wind velocity factor Aw.

The interference factor Ai is obtained through the roughness parameter σΦ

σΦ = (14.4λ+ 5.5)ΦHw

λ(2.2)

From this, the interference factor is obtained as

Ai =σ4

Φ

1 + σ4Φ

(2.3)

The wind velocity factor Aw is given by

Aw =

(1.94Vw

1 + Vw15.4

) 1.1

(λ+0.02)0.4

(2.4)

where Vw is the wind velocity, which can be obtained from the average wave height asfollows

Vw = 8.67H0.4w (2.5)

The wind direction factor Au is given by

Au = exp[0.2 cos(θw)(1− 2.8Φ)(λ+ 0.02)−0.4

](2.6)

where θw is the angle between the wind direction and the antenna direction.

These three factors give the NRCS for horizontal and vertical polarisation, respectivelyσH0 and σV0

σH0 = 10log10

(λΦ0.4AiAuAw

)− 54.09 (2.7)

σV0 = σH0 − 1.05loge(Hw + 0.015) + 1.09loge(λ)

+ 1.27loge(Φ + 0.0001) + 9.7(2.8)

2.1.3 Amplitude statistics

Most of the radar systems are non-coherent, which means that they use only the am-plitude of the received signal without taking the phase into account. The fluctuation ofthis amplitude is described by specific statistical laws.

The received signal sr(D, t) from a range cell located at a distance D at at time t is thesum of the backscattering of Nel elementary reflectors, such that

sr(D, t) = exp(j2πftt)

Nel∑i=1

[ai(D, t) exp(jϕi(D, t))] (2.9)

19

where ai and ϕi are respectively the amplitude and the phase of the ith reflector.

In ideal conditions, three assumptions are verified:

� Nel can be considered as infinitely large,

� the ai are independent and identically distributed,

� the ϕi are independent and uniformly distributed over [0, 2π].

In these conditions, the central limit theorem can be applied, and the backscatteredsignal is a complex gaussian process whose amplitude is Rayleigh-distributed. However,for real conditions, two of the three conditions are not fulfilled. Indeed, due to thehigh resolution of the radar, the number Nel of reflectors is not large enough. Secondly,different kinds of reflectors can be distinguished, especially in the case of rough sea. Thatmeans that the ai are not identically distributed. Thus, the clutter statistics diverge fromthe Gaussian statistics and high amplitude echoes are more likely to appear.

Several probability distributions have been adjusted empirically to describe the sea clut-ter, among which the Lognormal distribution [24], the Weibull distribution [21], thecompound K-distribution [28] and the KA-distribution [27].

The K-distribution is a model representing the Bragg scattering mechanism, but it ig-nores whitecap and burst scattering. The KA-distribution allows to model the spikescaused by these two mechanisms [27]. However, the knowledge of these spikes char-acteristics is still too thin to allow the use of KA-distributions in radar design. TheK-distribution will thus be detailed afterwards, being currently the most commonlyused.

The K-distribution modelling is motivated by the observation that the sea clutter iscomposed of two main components, a fast fluctuation called speckle, which is modulatedby slower fluctuations. The speckle amplitude is modelled by a Rayleigh distribution,whose mean is modulated by a Gamma distribution. The resulting K-distribution has aprobability density function given by

P (x) =2

aΓ(ν)

( x2a

)νKν−1

(xa

)(2.10)

where Γ is the Gamma function1, and Kν the modified Bessel function of the secondkind2 of order ν. The scale parameter a is related to the signal mean power through the

relation a2 =E[x2]

4ν , while the shape parameter ν is related to the spikiness aspect of thesignal. The effect of these parameters can be observed in Figure 2.4.

1Γ(s) =∫∞0ts−1e−tdt

2Kν(s) =π

2

I−ν(s) − Iν(s)

sin(νπ), with Iν(s) =

∞∑m=0

1

m!Γ(m+ ν + 1)

( s2

)2m+ν

20

0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

x (Amplitude)

PD

F

a=1, ν=1a=1, ν=2a=2, ν=1a=2, ν=2a=3, ν=2

Figure 2.4: K-distribution PDFs for different parameter values

Estimating the K-distribution parameters is not a trivial task, and as such has beenwidely discussed in the literature. Indeed, optimum estimation requires numerical meth-ods, which are very time-consuming. Since a radar requires real-time processing, sub-optimal estimators with high computational efficiency have been studied widely. Lom-bardo and Oliver [16] introduced three estimators, and pointed out especially the preci-sion of the estimator U , called the normalised log, defined as

U =⟨log(x2)

⟩− log(

⟨x2⟩) (2.11)

where x is the signal amplitude, and the notation 〈·〉 is the average value: for a randomprocess W , it yields: 〈W 〉 = 1

N

∑Ni=1wi.

Indeed, for a K-distributed random process, the following relation holds

U = E[U]

= ψ(ν)− log(ν)− γ (2.12)

where E [·] is the expected value, ψ is the digamma function3 and γ is Euler con-stant.

However, the evaluation of the shape parameter ν through this method still requiresa time-consuming inversion, since equation (2.12) is a transcendental equation. Two

3it is the logarithmic derivative of the Gamma function: ψ =Γ′

Γ

21

different methods allow to deal with this issue. The first method, developed in [3], usesanother estimator, defined as

X =〈z log(z)〉〈z〉 − 〈log(z)〉 (2.13)

with z being the clutter power (often called intensity), so z = x2.

Indeed, for a K distributed random process, the following relation holds

X = E[X]

= 1 +1

ν(2.14)

The shape parameter estimation is then directly obtained as

ν =1

X − 1(2.15)

This estimator yields results similar to the estimator U in terms of precision, althoughslightly below, but improves greatly the computational efficiency.

Another method, developed in [7], consists in approximating the functionν 7−→ ψ(ν)− log(ν)− γ on the interval [0.1; 20], which contains all potential values ofthe shape parameter for sea clutter. The approximation gives

ψ(ν)− log(ν)− γ ' −0.5801

ν1.145− γ (2.16)

Thus, the shape parameter is obtained with the relation

ν =

(−0.5801

U + γ

) 11.145

(2.17)

This method yields a slightly better precision than the X estimator, for a similar com-putational efficiency.

2.1.4 Doppler spectrum

For a coherent radar, as studied here, a spectral analysis of the received signal is pos-sible. The Doppler spectrum characteristics of the sea clutter are therefore a majorconcern.

The sea surface movement relatively to the radar introduces a Doppler shift of thescatterer echoes. Thus two different aspects are to be taken into account, the effects ofthe radar movement, and the consequences of the moving sea surface. The two main

22

−0.4 −0.2 0 0.2 0.40

500

1,000

1,500

fn

Ran

ge

bin

(a) Doppler PSD, for different range bins

−0.4 −0.2 0 0.2 0.4−12

−10

−8

−6

−4

fn

Am

plitu

de

(dB

)

(b) Average Doppler PSD

Figure 2.5: Doppler Power Spectral Density (PSD) for sea clutter. fn is the normalisedDoppler frequency, the PSD is in dB.

interesting characteristics of the Doppler spectrum are its mean Doppler shift and itsspectral width. Figure 2.5a shows an example of Doppler spectra for sea clutter, fordifferent range bins. The mean Doppler shift observed in the corresponding averageDoppler spectrum in Figure 2.5b is fn0 = −0.062, with a half-power width of ∆f =0.14.

A simple model proposed in [32] gives the mean Doppler velocity4 vD0 as a linear functionof the wind speed Vw, for both vertical and horizontal polarisations, in the case of lowgrazing angles, and looking upwind, as

vVD0 = 0.25 + 0.18Vw

vHD0 = 0.25 + 0.25Vw(2.18)

Indeed, the scatterer velocity is shown to be related to the orbital velocity of the largestwaves, whose velocity is directly dependent on the wind speed. This model was proposedwhen looking upwind only, but it can be assumed [29] that it will vary as cos(θw) withθw, the angle between the wind direction and the antenna direction (which means thatθw = 0 when looking upwind).

This model also gives the relation (2.19) between the half-power width ∆f and the windspeed. This spectral width is due to the dispersion in velocity for the reflectors.

∆f = 0.24Vw (2.19)

The spectral width is also significantly influenced by the radar carrier movements. Thespectral widening δvD due to the radar carrier moving at a velocity vp can be expressed

4vD0 = −λfD02

23

−0.4 −0.2 0 0.2 0.4

fn

Dop

ple

rP

SD

Figure 2.6: Doppler PSD of sea clutter, with gaussian-components model

as shown in [6] as

δvD = vp cos(εr)

(cos

(βr +

θ3dB

2

)− cos

(βr −

θ3dB

2

))' vpθ3dB cos(εr) sin(βr)

(2.20)

with εr the relative elevation angle and βr relative bearing.

The model proposed in [26] considers the Doppler Power Spectral Density (PSD) as asum of three Gaussian-shaped components, as follows:

G(f) = GB exp

(−(f − fB)2

w2B

)+GW exp

(−(f − fW )2

w2W

)+GS exp

(−(f − fS)2

w2S

)(2.21)

Each component represents a different kind of scattering (Bragg, whitecap and burstscattering). The resulting model presents a good fit to experimental data, and as suchis the most commonly used. Two different shapes obtained with this model can beobserved in Figure 2.6. In both cases, the mean Doppler shift is clearly different thanzero, and the asymmetrical aspect of the PSD is obvious.

A recent model, developed in [31], takes into account the temporal variations of theDoppler spectrum. The clutter PSD has a Gaussian shape:

G(f, x, s) =x√2πs

exp

(−(f −mf (x))2

2s2

)(2.22)

where x is the local clutter intensity, mf (x) the mean Doppler frequency, and s thespectrum width (actually the standard deviation of the Gaussian spectrum). The local

24

clutter intensity is modelled with a Gamma distribution, and the spectrum width ismodelled with a normal distribution. The mean Doppler shift is shown to vary linearlywith the local clutter intensity.

2.2 Land clutter

The nature of the reflectors located on the ground is totally different from the sea.Indeed, land echoes are caused by vegetation, hills, buildings, or even bare ground. Anexample of the amplitude of land clutter is shown in Figure 2.7.

Two different types of land scatterers can be distinguished: those moving with the wind,such as leaves or plants, and the fixed objects, such as buildings, rocks or hills. Thus,the land clutter amplitude varies depending both on time and space.

2.2.1 Reflectivity

Several representations have been proposed to model the land reflectivity depending onthe conditions of observation. A summary is included in [17]. In the case of low-grazingangles and X-band, the following model is commonly adopted

σ0 = Ah(Φ + Ch)Bh exp

(− Dh

1 + 0.03σh

)(2.23)

where Φ is the grazing angle, σh the standard deviation of surface roughness (in cen-timetres), and Ah, Bh, Ch and Dh are parameters given in Table 2.2.

0 100 200 300 400 5000

10

20

30

40

50

Range bin

Am

pli

tud

e

Figure 2.7: Amplitude of a land clutter signal depending on the range bin

25

Terrain Type Ah Bh Ch Dh

Frequency (GHz) 9.5 5 All All All

Soil 0.025 0.0096 0.83 0.0013 2.3Grass 0.039 0.015 1.5 0.012 0Crops 0.039 0.015 1.5 0.012 0Trees 0.003 0.0012 0.7 0.002 0Sand 0.025 0.0096 0.83 0.0013 2.3Rocks 0.025 0.0096 0.83 0.0012 2.3

Table 2.2: Land clutter reflectivity model parameters, for low-grazing angles and X-band(source [17])

2.2.2 Temporal amplitude distribution

The echo amplitude for a given range cell varies depending on time. Usually, a fixedrange cell contains both moving and fixed objects. Thus, the resulting echo contains anearly constant component, and the sum of fluctuating echoes due to the moving objects.The power resulting from this sum of echoes coming from multiple scatterers shouldtheoretically approach a Rayleigh distribution. The total resulting power is modelledas a Rice distribution [14], well adapted to characterize the sum of a constant echoand a Rayleigh component. The Rice distribution probability density function is givenby

P (x) =x

ξ2exp

(−x

2 + ρ2

2ξ2

)I0

(ρx

ξ2

)(2.24)

where I0 is the modified Bessel function of the first kind of order zero, ξ the shapeparameter and ρ the scale parameter. ρ2 represents the ratio of the constant power to theaverage power of the Rayleigh component. With ρ = 0, the Rice distribution is equivalentto a Rayleigh distribution. Figure 2.8 shows Rice distributions for different values ofshape and scale parameters, which represents different conditions of observation. Indeed,a urban area, where many fixed scatterers are present, can be represented with theparameters ξ = 0.25 and ρ = 1, whereas a forest, with many moving objects, is betterrepresented with the parameters ξ = 1 and ρ = 2.

2.2.3 Spatial amplitude distribution

The spatial amplitude distribution of land clutter has been thoroughly studied by theMIT Lincoln Laboratory. Measurements have been obtained for 42 different sites overthe United States and Canada at different times of year [2]. The terrains are separated insix different types, forests, farmland, urban, mountains, deserts and marshland. For lowgrazing angles, the distribution has been shown to fit closely with a Weibull distribution

26

0 1 2 3 4 5 6 7 80

0.5

1

1.5

x (Amplitude)

PD

F

ξ = 0.25, ρ = 1

ξ = 0.25, ρ = 2

ξ = 1, ρ = 1

ξ = 1, ρ = 2

Figure 2.8: Rice PDFs for different parameter values

[2], whose probability density function is:

P (x) =ω

µ

(x

µ

)ω−1

exp

(−(x

µ

)ω)(2.25)

where µ is the scale parameter and ω the shape parameter.

The Weibull probability density function is represented in Figure 2.9 for different valuesfor both parameters. The shape parameter ω depends on the terrain type, the grazingangle and the radar range resolution. The scale parameter µ depends on the terraintype, the grazing angle and the transmitted wavelength. They can be estimated fromthe radar data using for example the method of moments [1], which exploits the followingequations

m1 = µΓ

(1 +

1

ω

),

m2

m21

=1 + Γ

(2ω

)1 + Γ

(1ω

) (2.26)

with mi the moment of order i of a Weibull-distributed random variable Z such asmi = E

[Zi].

For higher grazing angles, the Rayleigh distribution fits better to the actual land clutteramplitude. However, the Rayleigh distribution is a special case of Weibull distribution,with the shape parameter ω = 2. Thus the Weibull distribution is a good model for allgrazing angles.

27

0 1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

x (Amplitude)

PD

F

µ = 1, ω = 1µ = 1, ω = 2µ = 2, ω = 1µ = 2, ω = 2µ = 3, ω = 2

Figure 2.9: Weibull PDFs for different parameter values

2.2.4 Compound amplitude distribution

The amplitude fluctuations for land clutter depend both on space and time. Instead ofmodelling these variations separately as seen previously, a compound representation canbe adopted.

The K-distribution has been shown in [13] to fit closely to experimental radar data.The model is then exactly identical to the sea clutter, but the shape parameter canattain very low values. However, the shape parameter estimation precision drops forthose extreme cases, which provokes a significant difference between the model and thereality.

Another class of distribution, the G-distribution, is shown in [10] to be an even bet-ter match to the land clutter. The K-distribution is actually a special case of G-distribution. However, the G-distribution parameters estimation is an issue which isnot yet resolved.

2.2.5 Doppler spectrum

The Doppler spectrum of ground echoes contains two distinct components. A DC-component, caused by the fixed objects echoes, contains very low Doppler frequencies.It is usually modelled by a Dirac delta function, whose amplitude depends on the terrain

28

−2 −1.5 −1 −0.5 0 0.5 1 1.5 20

1

2

3

4

5

Doppler velocity (m/s)

PS

D

b = 1

b = 2

b = 5

b = 10

Figure 2.10: AC-component PSD with an exponential model, depending on the Dopplervelocity

type and other conditions. The AC-component represents the fluctuating echoes of mov-ing objects. Three different shapes are typically used to represent this AC-componentspectral envelop: a Gaussian function, a power-law function, and an exponential func-tion.

The general model for the power density spectrum S(f) depending on the Dopplerfrequency f is thus expressed as

S(f) =η

η + 1δ(f) +

1

η + 1SAC(f) (2.27)

where η is the ratio of the DC-component power to the AC-component power.

The modelling of the AC-component is discussed in details in [15], and the exponentialmodel is shown to fit better to measured data. This model represents the AC powerspectral density as

SAC(f) =λb

4exp

(−λb2|f |)

(2.28)

where b is the exponential shape parameter and λ the transmitted wavelength. The valueof b depends on the wind speed, in such as manner that the spectral width increaseswith higher wind speeds. The AC-component PSD is represented in Figure 2.10 with anexponential model, for different shape parameter values.

29

Sea clutter Land clutter

NRCS

GIT modelDepends on the grazingangle, the wind directionand the wind velocity

Four-parameters modelDepends on the grazingangle, the terrain type andthe surface roughness

Statisticalamplitudedistribution

K-distributionCompound distribution,represents both spatial andtemporal fluctuations

Rice distribution (temporalfluctuations)Weibull distribution(spatial fluctuations)

Dopplerspectrum

Sum of threeGaussian-shapedcomponents

Sum of a Dirac and anexponential function

Table 2.3: Comparative table of land and sea clutter models

2.3 Land-Sea clutter comparison

The main differences between land and sea clutter are summarised in Table 2.3.

It can be observed that there is no common model for representing both land andsea clutter. Thus, the detection process has to be realised in a different way for landsurveillance and for sea surveillance.

30

Chapter 3

DTM Masking Algorithm

3.1 Background to the problem

3.1.1 Introduction

Maritime radar surveillance proves quite daunting in coastal areas, due to the presenceof ground echoes. These echoes cause several issues on different scales. The main issueis due to the fact that the radar is parametrised to detect targets located within seaclutter. However, the differences in characteristics between land and sea clutter causethe radar to mistakenly interpret most of the ground echoes as targets. As shown inthe previous chapter, those differences do not allow to resolve land detections using adetection process based on a sea clutter modelling.

This effect has three main drawbacks. Firstly, the radar operator is not interested intargets located on the ground, their presence is only a disruptive factor. Secondly, thehigh amplitude ground echoes hide potential smaller targets located on the sea closeto the coastline. Thirdly, the high number of detections provokes a surge in processorload.

These issues justify the need to process the ground echoes in a specific way to removetheir influence on the maritime detections.

3.1.2 Literature survey

The land-sea interface is a well-known issue in radar signal processing, and as such it islargely discussed in the literature. The most common way to deal with this issue is usingadaptive Constant False Alarm Rate (CFAR) detection, which means that the detectionthreshold for the cell under test (CUT) is calculated depending on its surroundings [4].A block of cells around the CUT is used to estimate the clutter parameters. The size

31

of this block has to be chosen carefully. Indeed, for a large block, the clutter cannot beconsidered as homogeneous, while a small block will lead to a high estimator variancethrough lack of samples. Furthermore, near coastlines, such a block can contain bothland and sea. The corresponding estimated clutter parameters are thus meaningless,since the sample area contains two completely different types of clutter. This effectinduces a high surge in false alarm rate. This can be compensated at the price of ahigher mean false alarm rate, or a drop of the capacity to distinguish between closetargets [29] [9]. In any case, a compromise has to be done.

Another method, more recent, consists in using external data to better estimate the localclutter characteristics. This is called Knowledge-Aided algorithm (KA). The principleis quite simple, that is integrating in the radar environmental knowledge of the geo-graphical area to be surveyed. Then, the estimation of the clutter parameters takes thissupplementary information into account in order to better correspond with the reality.The most common external data used are Digital Terrain Model (DTM ), which containinformation about the altitude of the ground at a given geographic position. This kind ofsite-specific modelling claims significant improvement in detection performance [8].

However, two major points differ in the context studied here from what can be foundin the literature. Firstly, this radar uses a coherent mode, whereas all the studies con-cerning DTM in the literature are done on non-coherent processing. Secondly, one ofthe objectives is to remove all the detections on the land. That allows to focus only onthe sea detections, whereas the literature usually aims at improving the detection bothon land and sea.

3.1.3 Algorithm description

The objective is to discard all detections located on the land, while improving the detec-tion performance on the sea close to the coast. The chosen approach is a KA algorithm,based on a geographical map distinguishing the sea from the land. The main principleconsists in comparing the geographical position of each cells with the embedded DTM,and discarding the information of this cell if it is located on land.

3.2 DTM description

3.2.1 Definition

DTM stands for Digital Terrain Model. It is a generic term for information describingthe topography of a geographic area. The topographical information is usually givendepending on spatial references such as longitude and latitude.

The objective of using DTM in the algorithm is to be able to distinguish between landand sea. Thus the only information needed is the presence of land or sea at a given

32

La

titu

de

(°)

Longitude (°)

DEM representing western France

−5 −4 −3 −2 −1 045

45.5

46

46.5

47

47.5

48

48.5

49

49.5

50Altitude (m)

−20

0

20

40

60

80

100

120

(a) An image representation of a DEM(raster) showing France

−4 −3.9 −3.8 −3.7 −3.6 −3.5 −3.4 −3.3 −3.2 −3.1

47.1

47.2

47.3

47.4

47.5

47.6

47.7

47.8

47.9

48

Latitu

de (

°)

Longitude (°)

Vector map representation of a French coast

(b) An image representation of a vector mapshowing french coasts

Figure 3.1: A comparison between the two different data representations for DTM

geographic position located by longitude and latitude. This will be referred to as aland-sea mask further on.

3.2.2 Data representation

There are two main data representations for DTMs, raster and vectorial.

A raster is a data matrix representing a two-dimensional grid of regular rectangularelements. A value is associated to each element depending on the type of DTM. Thisvalue can represent for example the altitude of the corresponding geographic location (inwhich case the DTM is called a Digital Elevation Model (DEM )), the presence or absenceof water (in which case it is called a land-sea mask), or other kinds of information. Eachelement corresponds to a physical geographic location. This location is specified by thelongitude α0 and latitude φ0 of the first element of the grid, and the longitude andlatitude step (δα, δφ) of the grid. Thus, the element (i, j) corresponds to the geographicarea which stretches from (α0 + i.δα, φ0 + j.δφ) to (α0 + (i+ 1).δα, φ0 + (j + 1).δφ). Animage representation of a DEM is shown in Figure 3.1a.

A vector map is a set of subsets of points, each subset representing a polygon. Eachpoint is represented by longitude and latitude coordinates. This is a useful and preciseway of representing boundaries. An example is shown in Figure 3.1b representing thefrench oceanic coast near Lorient.

3.2.3 Comparison of DTMs

The six criteria used to choose between all the available DTMs are described below.

33

� Geographic coverage: since the radar is not aimed at a specific area, the DTM hasto cover the whole world.

� Resolution: it must be as close to the radar range resolution as possible.

� Data quality: it includes three aspects: the presence of data void (a location wherethere is an absence of information), the precision of the geographic localisation,and the precision of the information.

� Memory size: it must be low enough for the DTM to be embedded on the radar.

� Necessary post-processing: it comprehends the necessary operations to apply tothe original DTM in order to obtain the wanted land-sea mask

� Accessibility: it includes the price of the DTM and the possibility to use it formilitary purposes.

Four DTMs satisfying enough of the criteria are detailed in Table 3.1. A closer look isneeded to decide between those four DTMs.

An image representation of the four raw DTMs near the Strait of Hormuz is shown inFigure 3.2. This comparison between raw data shows the difference in the post-processingsteps needed to obtain a land-sea mask.

� ASTER DEM (Advanced Spaceborne Thermal Emission and Reflection Radiome-ter, Figure 3.2a): A distinction has to be made between land and sea, dependingon the only available information, which is the altitude. Thus, a threshold has tobe applied, and all the elements with a negative altitude are considered as sea,while all the elements of strictly positive altitude are considered as land. However,this causes a major issue for the land located below the sea level, since it will bewrongly considered as sea.

� MODIS Water Mask (Moderate Resolution Imaging Spectroradiometer, Figure3.2b): no processing needed.

� SRTM V4.1 (Shuttle Radar Topography Mission, Figure 3.2c): The sea appears inblack due to a pre-processing. Indeed, this DEM possess major advantages, sinceit has benefited from different kind of processing to enhance its overall quality,including a land-sea distinction. The elements located on the sea have an altitudeof −32768. Thus, the threshold is −32768 and the land situated at a negativealtitude will still be considered as land.

� SWBD (SRTM Water Body Data, Figure 3.2d): The large straight lines are due tothe merging of six 1°x1° tiles. The main drawback of this DTM is its representation.Since it is vector-based, knowing if a point defined by its longitude and latitudecoordinates is on the sea or on the land is arduous. This point has to be comparedto all the points of the DTM, in order to know in which polygon it is lying.Then, depending on this polygon type (land or sea), the actual type (land or sea)of the point can be deduced. This requires a very large computation time. A

34

DTM nameASTERDEM

SRTM V4.1

SWBD(SRTMWater BodyData)

MODISWater Mask

Data repre-sentation

Raster Raster Vector map Raster

Geographiccoverage

Global 56°S ; 60°N 56°S ; 60°N 64°S ; 84°N

Resolution 30m 90m 30m 250m

Data qualityAverage(voids)

Great (post-processed)

Great (post-processed)

Good (post-processed)

Memory size 25Go 15Go 1Go 3Go

Post-processingsteps

Land/seadistinctionVoid filling

Land/seadistinction

- -

AccessibilityDownloadablefreely by tiles

FreeDownloadablefreely by tiles

Downloadablefreely

Downloadablefreely

Table 3.1: Comparison of different methods for the change of coordinates

possibility is to transform this vectorial map into a raster map (this process iscalled rasterisation). This is a very slow process, but it can be done once and forall before embedding the map into the radar.

Figure 3.3 shows the four DTMs after processing and zooming. This allows a comparisonof the resolution and precision of each DTM. The scale of each figure is approximately5km x 11km.

� ASTER DEM (Figure 3.3a): The resolution is very high, close to the 30m an-nounced. However, the boundary between land and sea is quite blurry: this is aside effect of the threshold. Indeed, due to the waves, the altitude near the coastmay vary around zero, which is a cause of blur. Another cause is the imprecision ofthe altitude measure. A slight imprecision can induce an error of decision betweenland and sea if the element’s altitude is close to zero.

35

Latitu

de (

°)

Longitude (°)

ASTER raw

55 55.5 56 56.5

25.8

26

26.2

26.4

26.6

26.8

27

27.2

(a) ASTER

Latitu

de (

°)

Longitude (°)

MODIS Water Mask

55 55.5 56 56.5

25.8

26

26.2

26.4

26.6

26.8

27

27.2

(b) MODIS Water Mask

Latitu

de (

°)

Longitude (°)

SRTM, raw, zoom 1

55 55.5 56 56.5

25.8

26

26.2

26.4

26.6

26.8

27

27.2

(c) SRTM

55 55.5 56 56.5

25.8

26

26.2

26.4

26.6

26.8

27

27.2

Latitu

de (

°)

Longitude (°)

SWBD without processing

(d) SWBD

Figure 3.2: Comparison between raw data for the Strait of Hormuz

� MODIS Water Mask (Figure 3.3b): the resolution is very low, which makes thisDTM unusable.

� SRTM V4.1 (Figure 3.3c): The resolution is not perfect, the squares can be easilydistinguished. It is still totally acceptable. Here, the land-sea boundary is verysharp. This is due to the fact that this DTM has been processed using highresolution coastlines DTM such as SWBD to distinguish between land and sea.Thus, the threshold does not induce any error.

� SWBD (Figure 3.3d): This is the rasterised representation of the SWBD. Theresolution is very high, and the coastline very sharp.

3.2.4 Choice of the DTM

This comparison shows that the best choice would be to use the rasterised SWBD.However, since the rasterisation process is not the object of this study, and since ahigher resolution is not really needed, the SRTM V4.1 is chosen as a good compromise.

36

La

titu

de

(°)

Longitude (°)

ASTER, after processing, zoom 2

55.73 55.735 55.74 55.745 55.75 55.755 55.76 55.765 55.77 55.775 55.7826.77

26.78

26.79

26.8

26.81

26.82

26.83

26.84

26.85

26.86

26.87

(a) ASTER

La

titu

de

(°)

Longitude (°)

MODIS Water Mask, after processing, zoom 2

55.73 55.735 55.74 55.745 55.75 55.755 55.76 55.765 55.77 55.775 55.7826.77

26.78

26.79

26.8

26.81

26.82

26.83

26.84

26.85

26.86

26.87

(b) MODIS Water Mask

La

titu

de

(°)

Longitude (°)

SRTM, after processing, zoom 2

55.73 55.735 55.74 55.745 55.75 55.755 55.76 55.765 55.77 55.775 55.7826.77

26.78

26.79

26.8

26.81

26.82

26.83

26.84

26.85

26.86

26.87

(c) SRTM

55.73 55.735 55.74 55.745 55.75 55.755 55.76 55.765 55.77 55.775 55.7826.77

26.78

26.79

26.8

26.81

26.82

26.83

26.84

26.85

26.86

26.87

La

titu

de

(°)

Longitude (°)

SWBD, after processing, zoom 2

(d) SWBD

Figure 3.3: Zoom on the different data after processing for the Strait of Hormuz

Its advantages are listed below:

� sharp land-sea boundary,

� decent resolution (90m),

� free and easily downloadable on the Internet by 5°x5° tiles,

� low memory size (approximately 50MB after processing for the whole world, storingin Tagged Image File Format),

� fast post-processing (thresholding).

However, some drawbacks remain:

� geographic coverage not global (see 3.4),

� requires to fill an order to download all the tiles.

37

Figure 3.4: Land and sea coverage of the SRTM DTM. Areas in pale green and whiteare not covered by the DTM. (source [20])

3.3 Algorithm implementation

The algorithm is based on two different stages. The first stage corresponds to a non-coherent mode, a mask is created by comparing the radar and navigation data to theDTM. Secondly, this processing is adapted to the coherent mode.

This first stage consists mainly in a change of coordinates, and is further detailed in thefollowing section. The objective is to determine for each range cell if it is located onthe land or on the sea, using the DTM. The second stage adapts the created mask toremove the influence of the land on the coherent processing chain.

3.4 Change of coordinates

The change of coordinates is the main part of the spatial mask creation. Indeed, thegeographic position of each cell is known from the radar data in a local spherical coor-dinate system. The corresponding reference frame is the body frame, shown in Figure3.5 and defined as (MO,xr,yr, zr), where MO is the plane’s center of gravity, xr is theunit vector directed towards the plane’s nose, yr is directed towards the end of the rightwing, and zr is chosen such that (xr,yr, zr) forms a right-handed triad.

However, the DTM coordinates are expressed in the geodetic coordinate system. Fora point T located on the Earth, its longitude α and geodetic latitude φ are defined asshown in Figure 3.6. The longitude is the angle between the prime meridian and themeridian going through T in the equatorial plane. The geodetic latitude is the anglebetween the equatorial plane and the normal to the Earth surface at T . Since the Earth

38

Towardsplane nose

Towards planeright wing

xr

zryr

D

βr

εr

T

MO

Figure 3.5: Spherical coordinate system in the body frame. The target T has coordinates(βr, εr, D). βr is the relative bearing, εr the relative elevation and D the distance to theradar.

is ellipsoidal, this normal does not go through the Earth center, hence the differencewith the geocentric latitude. This difference is illustrated in Figure 3.7. For a sphericalEarth approximation, the relation φ = φ holds.

The overall change of coordinates process, from the spherical coordinates in the bodyframe, to the geodesic coordinate system, is detailed in Figure 3.8.

3.4.1 Spherical coordinates to cartesian, body frame

The first change of coordinates, from spherical coordinates (βr, εr, D) to cartesian coor-dinates (xr, yr, zr) in the body frame is obtained using the following relations

xr = D cos εr cosβr

yr = D cos εr sinβr

zr = D sin εr

(3.1)

3.4.2 Body frame to local Earth frame

Secondly, the change of reference frame from the body frame to the local Earth frameis obtained using the information about the aircraft navigation angles (βp, εp,Θ), alsocalled Tait-Bryan angles [5]. βp is the plane’s heading, εp the plane’s elevation, and Θ

39

T

α

φ

Primemeridian

Figure 3.6: Geodetic coordinate system. The point T located on the ellipsoidal Earthsurface has coordinates (α, φ).

T

φ φ

Figure 3.7: Difference between geodetic latitude φ and geocentric latitude φ.

Sphericalcoordinates,body frame

Cartesiancoordinates,body frame

Cartesian coor-dinates, localEarth frame

Cartesiancoordinates,

geocentric frame

Geodeticcoordinates

Change ofcoordinates

Change ofreference frame

Change ofreference frame

Change ofcoordinates

Figure 3.8: The different reference frames and coordinate systems used

40

zl zYP

;el

nl

−zl

zl

xYβp

xYP

yYP

−zYP

zYP

εp

MO

(a) Illustration of the Tait-Bryan angles, withyaw and pitch only.

zl zYPzr

el

nl

−zl

zl

xYβp

yYP

−zYP

zYP

εp

xr

yr

zr

−zr

Θ

MO

(b) Illustration of the Tait-Bryan angles, withyaw, pitch and roll.

Figure 3.9: Illustration of the Tait-Bryan angles, with an intermediary figure withoutroll. (M0;nl, el, zl) is the local Earth frame, and (MO,xr,yr, zr) the body frame.

the bank. They are commonly referred to respectively as yaw, pitch and roll. Thesethree angles are described in Figure 3.9. The local Earth frame is centred on the plane,nl is pointing towards North, el towards East, and zl downwards. (MO;xYP ,yYP , zYP)is the body frame for yaw and pitch only ; (MO;xY ,yY , zY) is the body frame for yawonly. The different relations between these frames are described as follows

(nl,xY) = βp

(el,yY) = βp

zY = Zl

(xY ,xYP) = εp

yYP = xY(zY , zYP) = εp

xr = xYP(yr,yYP) = Θ

(zr, zYP) = Θ

(3.2)

The corresponding rotation matrices are detailed below

RY =

1 0 00 cos(βp) −sin(βp)0 sin(βp) cos(βp)

RP =

cos(εp) 0 −sin(εp)0 1 0

sin(εp) 0 cos(εp)

RR =

cos(Θ) −sin(Θ) 0sin(Θ) cos(Θ) 0

0 0 1

(3.3)

Using (3.3), this change of frame can be expressed easily. For a point T defined by its

41

L

xe

ye

ze

MO

elnl

zl

αp

φp

Primemeridian

O

P

Figure 3.10: Illustration of the geocentric frame (O;xe,ye, ze) and the local Earth frame(M0;nl, el, zl), with M0 located by its GPS coordinates (αp, φp) and its altitude h =LM0.

coordinate vector ur in the body frame, the corresponding coordinate vector ul in thelocal frame is obtained as follows

ul = RYRPRR ur (3.4)

This comes from the Tait-Bryan angles decomposition. Note that these matrices are notcommutative.

3.4.3 Local Earth frame to global Earth frame

Thirdly, the coordinates will be expressed relatively to the global Earth frame (or geocen-tric frame) (O;xe,ye, ze), as shown in Figure 3.10. This change of frame is composed oftwo steps, a translation and rotations. These transformations will be respectively repre-sented by the matrices t and R, such that, for a point T defined by its coordinate vectorul in the local Earth frame, the corresponding coordinate vector ue in the geocentricframe is

ue = Rul + t (3.5)

This step depends on the ellipsoid model used. The model used for the GPS system,and also the most commonly used one, is the WGS84 (World Geodetic System 1984 ).It is generally defined by two parameters, (ae, fe), ae being the major semi-axis and fe

42

the flattening. The other two parameters of the ellipse, the minor semi-axis be and theeccentricity ee can be derived from ae and fe

be = ae(1− fe), e2e = fe(2− fe) (3.6)

The translation t depends on the aircraft position in the geodetic system (αp, φp, h),which is acquired by GPS. φp is the aircraft latitude, αp its longitude, and h its altitude.With the notations of Figure 3.10, and with PL = N and LM0 = h, the translation isshown in [19] to be equal to

t =

(N + h) cosφp cosαp(N + h) cosφp sinαp

(N(1− e2e) + h) sinφp

(3.7)

As shown in [19], N can then be expressed as

N =ae√

1− e2e sin2 φp

(3.8)

The rotation is composed of a first rotation R1 of φp+ π2 along el, followed by a rotation

R2 of αp along the rotated axis ze. This yields

R = R2R1

R1 =

− sinφp 0 − cosφp0 1 0

cosφp 0 − sinφp

R2 =

cosαp − sinαp 0sinαp cosαp 0

0 0 1

(3.9)

3.4.4 Global Earth frame to geodetic coordinates

The last step consists of a change of coordinates, from the cartesian coordinates in theglobal Earth frame to the geodetic system. This step proves to be challenging if thepoint is not located directly on the Earth surface, and involves a fixed point iterationin that case (see [19]). However, the formulas are straightforward in the case of a pointlocated on the Earth surface. Finally, for a point defined in the global Earth frame bythe coordinates (xe, ye, ze) , its geodetic latitude φ and longitude α are

φ = arctan

(ze

(1− e2e)√x2e + y2

e

), α = arctan

(yexe

)(3.10)

43

3.5 Approximations

The whole change of coordinates process involves many steps, and many computations,which leads to an inconveniently high computation time. Different approaches have beencompared to optimise the change of coordinates computation time, in order to allow areal-time processing.

44

Chapter 4

Results

4.1 Datasets

The algorithm improvement is assessed on two different datasets called TO26 andTO63. These are real data obtained during two different flights near Lorient in France.The aircraft trajectory is depicted in Figure 4.1 by arrows of different color for eachflight: the trajectory (in red) corresponding to the TO63 dataset is perpendicular tothe coast while the other trajectory (in yellow), corresponding to the TO26 dataset, isparallel to it. The scanned sector covers an area of approximately 60° by 4.7km. Bothdatasets include approximately 20 scans of the same sector.

However, even if the datasets have been created from real data, the field reality is

Figure 4.1: Illustration of the aircraft trajectory for the two flights near Lorient, inFrance

45

unknown, so these datasets are not enough to assess precisely the algorithm efficiency.Thus, synthetic targets will be added to these datasets.

4.2 Detections

The first results obtained are visible at the end of the signal processing chain, and consistof all the detections obtained for one scan. Figure 4.2 shows the results obtained for theTO63 dataset. The land represented here is the land corresponding to the DTM used,so it can differ from the reality due to imprecisions (on the radar measurements, thesignal processing or the DTM). Three observations can be made instantly. Firstly, allthe detections on the land have disappeared after using the DTM algorithm. Secondly,there is no change for the areas in the open sea, all the detections remain, and noneappears.

The exact same observations can be made in Figure 4.3. Here, the number of detectionsafter DTM processing is more than halved, which will induce a significant improvementon the processing time required for tracking.

46

14 NM

16 NM

18 NM

−30 °

0 °

30 °

(a) Detections for TO63, without DTM processing.

14 NM

16 NM

18 NM

−30 °

0 °

30 °

(b) Detections for TO63, with DTM processing

Figure 4.2: Comparison between the detections for one scan for the dataset TO63 withand without DTM processing. The sea is in grey, and the land in black ; the red crossesrepresent the detections.

47

4 NM

6 NM

8 NM

60 °

90 °

120 °

(a) Detections for TO26, without DTM pro-cessing.

4 NM

6 NM

8 NM

60 °

90 °

120 °

(b) Detections for TO26, with DTM pro-cessing

Figure 4.3: Comparison between the detections for one scan for the dataset TO26 withand without DTM processing. The sea is in grey, and the land in black ; the red crossesrepresent the detections.

48

4.3 Tracks

The final results concern the tracks. They are obtained by gathering the detections ofall the scans for each dataset: if a detection is coherent throughout several consecutivescans, a track will be opened.

Figure 4.4 shows the results for the TO63 dataset. Figure 4.4a shows many tracks onthe land, which are unwanted. All these tracks located on the land have disappearedafter DTM processing, and all the tracks located on the sea remain.

14 NM

16 NM

18 NM

0 °

30 °−30 °

(a) Tracks for TO63, without DTM processing.

14 NM

16 NM

18 NM

−30 °

0 °

30 °

(b) Tracks for TO63, with DTM processing

Figure 4.4: Comparison between the tracks for TO63 with and without DTM processing.The sea is in grey, and the land in black ; the red circles represent the tracks, and thegreen line their trajectory over all scans.

49

4 NM

6 NM

8 NM

60 °

90 °

120 °

(a) Tracks for TO26, without DTM

60 °

90 °

120 °

4 NM

6 NM

8 NM

(b) Tracks for TO26, with DTM processing

Figure 4.5: Comparison between the tracks for TO26 with and without DTM processing.The sea is in grey, and the land in black ; the red circles represent the tracks, and thegreen line their trajectory over all scans.

Figure 4.5 shows the results for the TO26 dataset. Again, Figure 4.5a shows manytracks on the land, which are unwanted, and only one track on the sea. All these trackslocated on the land have disappeared after DTM processing, the track located on thesea remains.

50

Conclusion

A state-of-the-art of land and sea clutter is offered in this thesis, leading to the propo-sition of a knowledge-aided algorithm using DTM to enhance detection performance ofcoherent radars in coastal areas.

The proposed algorithm aims at removing the influence of the land echoes on the Dopplerspectrum. For this purpose, the DTM is used to determine for each radar cell if it islocated on land or sea. A change of coordinates establishes the geographic location ofthe cells, allowing a comparison with the DTM.

The resulting information is used to remove the influence of the land cells on the Dopplerspectrum, using the coherent model for land clutter described previously in the state-of-the-art.

The performance of the proposed algorithm is assessed on real data. A comparison withthe same detector without the use of this algorithm shows that all the detections locatedon the land are discarded.

51

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