METHOD FOR DETECTING AND CHARACTERISING A MOVING TARGET ON A
RADAR IMAGE
5 The invention relates to a method for detecting and characterizing (in terms of
position and speed) a moving target on a radar image representing reflectivity echoes of
an area illuminated by a radar beam. The invention is applicable, notably, to the
production of simultaneous high-resolution SAR-GMTI images using an aircraft equipped
with a radar antenna.
10
In this SAR-GMTI representation, the "image background" composed of the
fixed reflectors is provided by an SAR (Synthetic Aperture Radar) image, and on this
image background the position of each of the moving reflectors that is present and to be
detected (referred to as the "target" in the rest of the description for the sake of
15 convenience) in the area of interest is indicated by a blip to which is assigned a velocity
vector corresponding to the velocity vector of the moving target at the chosen reference
instant (generally the central instant of the illumination). The positioning of each target is
made possible by the GMTl (Ground Moving Target Indicator) mode.
20 The applicant has previously filed a French patent application under the
number 10/02083, describing a method of constructing focused radar images. By way of a
reminder, Figure 1 shows a step of data acquisition by a moving platform in SAR "Spot"
mode, that is to say a mode in which the antenna beam is permanently locked onto the
area to be imaged. A radar fixed on an aircraft 101 illuminates an imaged area 102 during
25 an illumination time Te with the antenna beam 103 locked onto the center 104 of said area
102 along the whole trajectory 105 of the aircraft 101. This time Te is inversely
proportional to the desired resolution along the transverse axis 106, while the resolution
along the radial axis 108 is inversely proportianal to the band emitted by the radar
antenna. The imaged area 102 is partitioned into a grid 110 of cells, with the aim of
30 associating at least one level of reflectivity with each of these cells.
The echoes backscattered by the area of ground illuminated by the radar beam
can be used to create an image along the radial axis 108 and the transverse axis 106,
referred to respectively hereafter as the "Range" axis 108 and the "Doppler" axis 106. This
image, referred to hereafter as the "range-Doppler" image, delivers for each cell NI within
35 the imaged area 102 a range value DM and a Doppler frequency value fM, these two
values DM and fM being referenced with respect to a given instant tref corresponding, for
example, to the elapsing of half the total illumination time.
By describing a given angular sector about the imaged area 102, the radar
periodically collects a series of N range profiles with a repetition frequency f, equal to
Nme. Each of the N range profiles provides a one-dimensional representation of the
imaged area 102 along the range axis 108. The range axis 108 is also divided into a
plurality of cells, the size of each of said cells preferably being slightly smaller than the
range resolution. For a given range cell, a spectrum analysis along the transverse axis
106 performed on the collected signal enables the different echoes contained in this cell to
be discriminated in Doppler. This spectrum analysis can be used to discriminate the .
echoes with the desired resolnltion if certain conditions are met.
The difficulty of generating an SAR-GMTI image is due to the fact that:
- in a conventional SAR mode (where the fixed reflectors are positioned in
azimuth according to a measurement of their Doppler frequency at a reference instant), &
the moving echoes appear in a different position from their real position in the imaged
scene: for these echoes, the Doppler frequency measurement can no longer be directly
related to an azimuth position. This is becauke the expression of the Doppler frequency of
the target requires knowledge not only of its' azimuth (or more precisely its angle with
respect to the velocity vector of the platform) but also of the radial velocity of the target,
which is not known in advance. Furthermore, the moving target is significantly
"defocused": its energy is dispersed over a considerable number of Doppler cells, or range
cells if the target is ambiguous in Doppler. Therefore a moving target does not benefit from
the high compression gain provided by SAR processing (with a wide transmission band
and long integration time), making it difficult to detect in all cases, including the case in
which the (ambiguous) Doppler image of the target belongs to the (ambiguous) Doppler
range covered by the set of fixed reflectors illuminated by the beam. In this case, we
speak of "endo-clutter" targets. These targets are slow or fast targets whose radial velocity
gives rise to a Doppler frequency shift corresponding to the repetition frequency of the
SAR mode' (the value of which defines the Doppler ambiguity).
-A conventional GMTl (Ground Moving Target Indicator) mode can be used to
detect and locate moving targets, but does not provide an "azimuth resolved"
representation of the area of ground illuminated by the radar beam. This is because the
integration times are generally too short to discriminate the fixed reflectors from the
ground in terms of the azimuth with satisfactory resolution.
In order to reduce-as far as possible the spectral spread of the "ground clutter"
(signals backscattered by the set of fixed reflectors on the ground illuminated by the radar
5 beam) and thereby reduce the number of endo-clutter targets (the detection of which is
problematic), GMTl acquisitions preferably make use of "in axis" acquisition geometries,
in which the platform velocity vector and the aiming vector guiding the radar beam are
collinear. However, these configurations are prohibited for SAR, because they prevent
any azimuth discrimination of the fixed reflectors illuminated by the beam. The
10 conventional solution, in which the area of interest is imaged with an SAR mode
(unaimed) and the detections obtained with a GMTl mode aimed along the axis are then
superimposed on it, has a major drawback in that the platform is required to switch
between SAR acquisition and GMTl acquisition.
15 To summarize, the conventional solutions for positioning on an SAR image
blips associated with moving targets present in the area of interest generally consist in
performing two separate acquisitions, namely an SAR acquisition and a GMTl acquisition.
The detections obtained from the GMTl mode are located and then superimposed on the
SAR image, using the location provided by the SAR mode for each of the fixed reflectors
20 imaged.
,
In order to avoid the problem of endo-clutter targets, the GMTl acquisition is
performed by prioritizing "in axis" aiming, unlike the SAR acquisition which must always be
performed in an unaimed way. However, this configuration is demanding in terms of time,
25 since it requires the platform to switch between the two acquisitions in order to position
itself correctly relative to the area of interest illuminated by the beam.
If the GMTl acquisition is not performed in the axis but with "identical unaiming"
to the SAR acquisition, the problem of the detection and location of the endo-clutter
30 targets arises. This problem is conventionally resolved by techniques of the STAP (Space
Time Adaptive Process) type. However, these techniques require a large number of
receiving channels to be effective.
Furthermore, STAP techniques do nothing to resolve the problem of "focusing"
targets and generally use integration times which are much shorter than those provided by
35 SAR acquisition.
Where the characterization of the velocity vector associated with the target is
concerned, conventional GMTI modes provide, at best, an estimate of the radial
component of this vector.
5
The object of the invention is to provide in a natural way an SAR representation
of the area of interest, to detect moving targets including endo-clutter targets, and to focus
them and position the targets on the SAR image and characterize their velocity vector.
10 More specifically, the invention relates to a method for detecting and
characterizing a moving target on a radar image representing the reflectivity echoes of an
area illuminated by a radar beam of a platform formed by a repetition of radar acquisitions.
According to the invention, the method comprises the following steps:
15 a first step of eliminating the stationary fixed echoes with high reflectivity
measured on the radar image, %
a second step of reducing the integration time by extracting the cefitral
temporal illumination portion on the radar image,
a third step of focusing the echo of the moving target by applying a correction of
20 the range migration and the Doppler migration of the moving target on the radar image,
a fourth step of extracting the moving target from the radar image, I
a fifth step of calculating the position of the target and the components of the
velocity vector of the target, including at least the component projected on the route of the
platform.
2 5
Advantageously, the first step of eliminating the stationary fixed echoes
comprises the following steps:
- reduction of the reflectivity of the moving echoes, consisting in retaining, for
each pixel of the radar image, the minimum reflectivity for the whole set of repeated radar
30 acquisitions, and
- detection of the fixed echoes by a thresholding operation.
Advantageously, in the third step the range migration of a target is corrected by
testing a number of possible ranks of Doppler ambiguity for the target.
Advantageously, in the third step the Doppler migration of a target is corrected
by testing a number of quadratic phase law hypotheses to compensate the residual phase
characterizing the residual Doppler migration of the moving target, the quadratic term of
this residual phase being defined by the following formula:
Advantageously, the third step comprises filtering of the defocused points.
Advantageously, the fourth step comprises an operation of thresholding pixels
10 of the radar image.
Advantageously, the fifth step comprises the calculation of the radial
component of the velocity vector of the moving target according to the following relation:
Advantageously, the fifth step comprises the calculation of the component of
the velocity vector of the moving target projected along the route of the aircraft according
to the following relation:
20
The phase of detecting moving targets of the identification method according to
the invention on a radar image can be executed using a single receiving channel.
Furthermore, the method according to the invention enables profitable use to
be made of the integration times which are much longer than those conventionally used in
a GMTl mode, so that the focused targets benefit from a compression gain (and therefore
from a signal to noise ratio) close to that provided by the completeness of SAR acquisition.
These high signal to noise ratios also provide an improvement in the final quality of the
positioning of the targets on the SAR image.
Moreover, the method provides a complete estimate, in two dimensions, of the
velocity vector associated with the target.
The invention will be more clearly understood and other advantages will be
apparent from the following description provided in a non-limiting way with reference to
the following drawings:
5 Figure 1 shows an illustration of a phase of acquisition of data by a movable
platform (prior art);
Figure 2a shows a raw range-Doppler radar image representing the moving
targets and the fixed stationary echoes.
Figure 2b shows a range-Doppler radar image after partial processing
10 according to the method with the fixed stationary echoes erased.
Figure 3 shows a range and temporal radar image showing the moving targets.
Figure 4 shows a range-Doppler radar image after partial processing according
to the method following partial temporal extraction of the repetitions.
Figure 5 is a flow diagram showing the steps of the method according to the
15 invention.
Figure 6 is a geometric diagram representing an SAR acquisition by a platform
aimed at a moving target.
Figure 7 is a range-Doppler radar image resulting from the use of the method
according to the invention and representing a moving target identified by location and by
20 velocity behavior.
The invention is applicable to moving platforms such as aircraft or satellites
with on-board radar devices for the surveillance of an area of interest.
The invention can be used to obtain a synthetic image showing the moving
25 targets with which is associated a movement vector representing their direction of
movement and a quantification of the velocity of movement. An image of this type is
obtained on the basis of the method according to the invention. Figure 7 is a schematic
representation of a radar image 50 obtained by the method of the invention. This image
represents a moving target echo 21 and the movement vector 52. The image shows, on
30 the axis 11, the range with respect to the receiving channels of the platform, and, on the
axis 12, the Doppler frequency of the fixed reflectors that are imaged. On this image, the
moving target is positioned at the location of the fixed reflector characterized by the same
azimuth and the same range as the moving target at the central instant of illumination.
The object of the method according to the invention is to provide an SAR image
of an area of interest from a single radar acquisition, and to superimpose blips on this
image corresponding to the position of the moving targets present in the imaged area.
More specifically, these blips 51 provide the estimated position of the moving
targets at a given instant (corresponding to the central instant of the acquisition). For a
given target, in addition to the position information, the invention allows the delivery of an
estimate 52 of the velocity vector of the target at the same reference instant.
For each of the moving targets detected in this way, the method subsequently
provides a characterization in terms of position and velocity. The position information
(referenced with respect to the central instant of illumination) is obtained according to the
platform-target range read on the range-Doppler image, and according to an angle error
measurement performed on the refocused moving target. The latter measurement
requires the use of two azimuth receiving channels. The method of locating the moving
target does not limit the scope of the invention. The velocity vector of the target (at the
central instant of illumination) is the sum of two components. The radial component is
calculated according to the Doppler frequency of the target (this frequency being
determined unambiguously at the end of h e detection step) and the angular position
found by means of the angle error measurement. The component along the platform route
I is deduced directly from the quadratic phase term characterizing the Doppler migration of
the target during illumination. This quadratic term is known as a result of the use of the
method of the invention when the phase law for refocusing the moving target has been
determined.
The waveform used is that of an SAR metric or submetric resolution mode
using the highest possible repetition frequency in order to enlarge the Doppler clear area
to the maximum and increase the width of the Doppler ambiguity.
An advantage of the invention is that it allows the detection of slow moving
targets (whose Doppler frequency is within the Doppler range covered by the fixed ground
echoes) with a single receiving channel. For this purpose, the basic principle is that of
making profitable use of the high compression gain provided by the SAR acquisition (high
range resolution and long acquisition time by comparison with a conventional GMTl
mode) and discriminating the fixed echoes from the moving echoes according to the
manner of their range and Doppler migration over time.
Thus, in the "raw" SAR image generated in such a way as to focus the canonic
fixed reflectors in the area of interest, the fixed echoes with a high ERS (equivalent radar
surface) have their energy concentrated in a very small surface area (because of the fine
resolution). Conversely, the moving echoes are significantly defocused (because of the
long integration time of SAR) and their energy is therefore diluted over a large number of
pixels: they do not benefit from the gain in azimuth compression provided by SAR.
The method according to the invention is applied by means of a radar device
coupled to electronic and data processing resources for carrying out SAR imaging (ideally
with metric-class resolution), including at least two azimuth receiving channels.
These electronic and data processing resources for an SAR imaging
application may be on board the platform or located at a remote station. In the latter case,
the platform also has means for transmitting the measured data toward the remote station.
In the case of an application for an aircraft as shown in Figure 1, the two receiving
channels may be, for example, two antenna panels positioned on a surface of the platform
facing in a direction which is not collinear with the trajectory of the platform. The purpose
of this is to be able to discriminate in Doppler (and therefore in azimuth) the fixed ground
echoes illuminated by the radar beam, thus allowing an SAR image to be created.
By acquiring radar images as shown in Figure 1, it is possible to obtain a raw
range 1 I -Doppler 12 image 10 of the area of interest. In this raw range-Doppler image 10
of the area of interest, the two targets 13 and 14 appear significantly defocused.
Furthermore, since the two targets 13 and 14 have been assigned a non-zero radial
velocity, their position on the SAR image does not correspond to their real positioning on
the ground. However, by way of illustration, two significantly different values of radial
velocity have been chosen for these two synthetic targets, as follows.
The first target 13 is assigned a very slow radial velocity, making it
non-ambiguous in Doppler: the Doppler frequency of the target (or more precisely the
Doppler range covered by the target on the image) is read correctly on the range-Doppler
SAR image. For a given reflector (fixed or moving), knowledge of the Doppler frequency at
the central instant of illumination makes it possible to determine without error the linear
term of the range migration associated with this reflector during the illumination.
Therefore, as the target is unambiguous in Doppler, the SAR process applies a first-order
range'migration correction to it. The residual range migration term no longer contains a
linear term and is therefore spread over a very small (or ever1 negligible) number of range
cells. This phenomenon can be seen in the SAR image below, in which the unambiguous
moving point target 13 is virtually concentrated in a single range cell.
On the other hand, the second target 14 is assigned a high radial velocity,
making it ambiguous in Doppler: the Doppler frequency of the target read correctly on the
5 SAR (range-Doppler) image 10 differs from the actual Doppler frequency of the target.
This difference is a multiple of the repetition frequency of the waveform of the SAR mode.
Therefore, unlike the non-ambiguous target, the ambiguous target continues to have a
very high residual range migration, spread over a significant number of range cells.
However, knowledge of the ambiguity rank of the target is sufficient for the determination
10 of the linear term of this residual range migration. This phenomenon is visible in the
Range-Time signal obtained by applying to the range-Doppler image 10 an inverse FTF
(Fourier transform function) along the Doppler axis. This Range-Time signal is
represented in Figure 3.
15 Starting with a raw range-Doppler image as shown in Figure 2a, the method 80
shown schematically in Figure 5 comprises a first step 81 of eliminating the stationary
fixed echoes 15 with high reflectivity measured on the radar image 10.
On the raw SAR range-Doppler image 10, the significant fixed ERS echoes 15
illuminated by the main lobe of the antenna'beam are focused and benefit from the high
20 compression gain of the SAR process. They are therefore above the mean level of the
"image background" (composed of turf and bitumen in the chosen example) and are
concentrated in a small number of pixels by comparison with the total number of pixels
covered by the area illuminated by the main lobe.
2 5 The contribution of these echoes may therefore be subtracted by setting the
pixels of the range-Doppler image, where their energy is concentrated, to zero. This
operation of zero setting, commonly referred to as "blanking", of a limited number of pixels
does not significantly degrade the signals obtained from the moving echoes, since these
echoes are defocused and their energy is therefore diluted over a very large number of
30 pixels.
The detection of the highly reflective fixed echoes is not simply a matter of
thresholding on the range-Doppler image. Processing in this way would have the
undesirable effect of also detecting (and suppressing) the moving echoes with a very high
ERS, or those whose defocusing was not sufficiently marked (slow targets, for example).
35
An effective solution has been described in a patent application by the present
applicant, filed in 2001 under publication number FR2833713. This method consists in
performing a preliminary operation of filtering the non-stationary points on the raw
range-Doppler image 10, in order to filter the various moving echoes and prevent them
5 from exceeding the detection threshold.
The principle of this filtering consists, in a first stage, in applying different
corrections required to obtain an SAR image focused at any point. A stationary reflector is
viewed at a fixed range and at a fixed Doppler frequency throughout the illumination.
Consequently, the generation of a "film" composed of SAR images resulting from a
10 division of the complete illumination time into sub-illuminations enables the
non-stationarity to be highlighted. In each image of the film, a stationary reflector 15 is
seen at an identical range-Doppler position and with the same reflectivity. Conversely, a
non-stationary reflector 13 or 14 (particularly a moving reflector) will be positioned
differently according to the images and/or will fluctuate in amplitude.
15 Therefore the filtering of the non-stationary points 13 or 14 consists in retaining,
for each of the pixels, the minimum reflectivity on the set of the range-Doppler images of
the film.
The amplitude of the non-stationary echoes is thus significantly attenuated. On
the other hand, the azimuth resolution of this filtered image is degraded, because the
20 duration of a sub-illumination is small relative to the complete illumination.
In order to retain the optimal azimuth resolution corresponding to the complete
illumination, a minimum value seeking operation is finally performed between the
last-mentioned image and the full-resolution raw image.
The image of Figure 2B represents a diagram of a radar image obtained as a
25 result of the first step of the method. In this range 11 - Doppler 12 image 20, the stationary
fixed echoes 15 have been removed and all that are left are the non-stationary echoes 13
and 14 representing the moving targets.
The method comprises a second step 82 of reducing the integration time.
30 Reducing the integration time is useful in two ways. In the first place, it makes it easier to
verify the hypothesis that the target is moving in a uniform rectilinear way; secondly, the
computation load decreases significantly. The size of signals is limited and the number of
phase rules to be tested during the subsequent steps for correcting Doppler migration is
also reduced, because it is proportional-to the square of the integration time (reducing the
35 integration tim6 limits the residual Doppler migration while also characterizing it with a
coarser Doppler cell size).
This reduction of the integration time is achieved by the following operations:
- Returning to the time domain by applying an inverse FTF along the Doppler
axis on the range-Doppler image 20 from which the fixed echoes with a significant ERS
have been stripped.
- Temporal de-weighting: the strong echoes are set to zero in a weighted
range-Doppler image, in order to concentrate the energy of these echoes in a minimum
number of pixels without parasitic energy dissipation in the secondary lobes. On return to
the time domain, the effect of this weighting must be eliminated.
- Extraction of the central temporal portion.
The image of Figure 3 represents a Range 31 - Time 32 image 30. The echoes
moving at a slow radial velocity are represented by the line 34, and the echoes moving at
a higher movement velocity are represented by the line 33.
The image 40 of Figure 4 represents a diagram of the range 41 - Doppler 42
image with degraded azimuth resolution obtained by performing an FTF on the reduced
integration time corresponding to the extracted temporal portion. In this image 40, the
defocusing of the targets 43 and 44 now covers a significantly smaller number of pixels
compared with the original raw range-Doppler image 10.
The method 80 then comprises a third step 83 of focusing the echo of the
moving target by calculating a correction of the range migration and the Doppler migration
of the moving target on the radar image.
Focusing consists in re-concentrating the energy of the signal backscattered by
a target into the smallest possible number of range-Doppler cells, to allow detection on a
residual noise composed of thermal noise only (clear area), or composed of thermal noise
and weakly reflective non-focused echoes (endo-clutter area).
Focusing enables the target to benefit from a high compression gain, in terms
of both range (because of the wide band emitted) and Doppler (because of the long
integration time), provided that its residual range migration and residual Doppler migration
can be corrected.
Correction of the linear term of the range migration of the target during
acquisition is initially performed during the generation of the SAR image: the correction
rule applied is that which is applied to a fixed echo which, at the central instant of
illumination, is located at the same range as the moving echo and has the same
ambiguous Doppler frequency as the moving target.
Since the linear term of the range migration depends solely on the
(non-ambiguous) Doppler frequency of the echo at the instant in question (in this case the
5 central instant of the illumination), the residual range migration of the target can therefore
be7ully characterized simply on the basis of knowledge of its Doppler ambiguity rank.
The concept of a Doppler ambiguity rank will now be summarized briefly. Since
the signal is sampled at a frequency Fr, it is impossible to distinguish between a signal
10 with a Doppler frequency of fd and a signal with a Doppler frequency of fd + Fr or fd + 2Fr,
or fd + 3Fr, etc. The terms "Doppler ambiguity" and "Doppler ambiguity rank" are both
used. However, this does not cause any problems in the restricted context of SAR
imaging. In fact, because the geometry of the problem is known (position of the platform,
velocity of the platform, beam aiming direction, position of the points on the ground
15 illuminated by the radar beam, etc.), the ambiguity rank of the fixed ground echoes
illuminated by the radar beam is also known. On the other hand, this ambiguity rank is
initially unknown in the case of a moving echo whose velocity is initially unknown. By
default, when the SAR image is generated, it is hypothesized that the received echoes
have a Doppler frequency in the range from fdO - Fr12 to fdO + Frl2, where fdO denotes the
20 Doppler frequency of the central point of the imaged area (this Doppler frequency fdO is
known from the acquisition geometry).
It is therefore possible to correct the linear term of the residual range migration
of the target by making different hypotheses about its ambiguity rank. For the classes of
25 velocity searched for, and with an SAR mode operating with a high repetition frequency,
the ranks can be limited to +I and -1.
In the non-ambiguous image, the target which is non-ambiguous in Doppler is
already satisfactorily corrected. Its residual range migration does not exceed one range
cell.
3 0 When the ambiguity rank 1 is tested, it is the ambiguous target that has its
energy re-concentrated over a restricted range interval: its residual range migration is less
than the size of the cell. For a radial resolution of the metric or slightly submetric class, and
after the integration time has been reduced, the quadratic term characterizing the residual
range migration can beconsidered to be less than the size of the range cell.
At this stage in the method, for a given moving target, there is a range-Doppler
image (associated with a Doppler ambiguity rank) for which the range migration of the
target has been compensated. In this image, the residual migration of the target can now
be considered as a Doppler migration. Because of the reduced integration time, this
5 residual Doppler migration can be characterized by a quadratic phase term in the time
domain (higher-order terms cause negligible defocusing).
The final step for re-concentrating the energy of the target is therefore to test
different hypotheses concerning the defocusing "width", by varying the quadratic term of
the residual phase error in the time domain.
10 Thus the range-Doppler image on which the non-ambiguous target has been
refocused belongs to the set af images associated with the zero ambiguity rank. For the
target which is ambiguous in Doppler, the image on which the energy of the target has
been concentrated in a limited number of range-Doppler pixels belongs to the set of
images associated with the rank +I.
15
The method 80 then comprises a fourth step 84 of extracting the moving target
from the radar image. After focusing, the targets benefit from high compression gain and
can therefore be detected by simple thresholding on a residual noise composed, in the
worst case, of weakly reflective defo~used~~rouenchdo es. However, in order to avoid
20 parasitic detection of the same target in a number of range-Doppler images, it is
preferable to apply a preliminary filtering of the non-stationary points to each of these
irnages (a procedure identical to that used to filter highly reflective ground echoes). At the
end of this filtering, only the focused targets are retained.
The method 80 also comprises a fifth step 85 of calculating the position of the
target and the components of the velocity vector of the target, particularly the component
projected on the route of the platform. Figure 6 is a diagram showing the acquisition
geometj between a platform and the moving target and the velocity vectors of the moving
30 target and the platform. First of all, the following notation will be described:
All the quantities (positions, velocities, bearings, etc.) are shown with reference
to the central instant of illumination:
- P : position of the platform
+
- V : velocity vector of the platform
- C : position of the target
- Vc : velocity vector of the target
II + II
R c = ~ ~ p c ~ ~
- Rc : Platform-Target range:
+
- Uc : unit vector pointing at C: IPCI
. .
- 'CR : component of the target velocity vector along the radial axis: VCR= Vc. U c
5 - : component of the target velocity vector along the aircraft route:
+
- Gc : bearing of the target
- ' c : location of the target
- fdC : Doppler frequency of the target
- fd 0: Doppler frequency of the ground point located at the center of the beam
b
- fr : repetition frequency of the SARIGMTI mode
- M c : "apparent" position of the target= position of the ground point located at
the same distance as the target and for which:
the non-ambiguous Doppler is in the range from f d O - f , I 2 , f d O + f r / 2 ,
15 the ambiguous Doppler is equal to the ambiguous Doppler of the target.
- G~ : 'apparent" bearing of the target = bearing of the point Mc
- f d M : Doppler frequency of the point Mc
- kamb : Doppler ambiguity rank of the target C: kamb = CfdC - fdM'/fr ,
- Te : illumination time (integration time for the SAR)
The reference instant t=O corresponds to the central instant of illumination:
The Platform-Target range over time is written:
Consequently,
and therefore:
(expression of the form J1 + where x << 1)
1 1
.ll+x=l+-x--xi +0(x3)
By limited expansion: 2 8
10 Therefore,
At the instant t=O, the Doppler frequency of the moving target is written:
15 Finally, the position of the target is found by the following formula:
The phase of the signal backscattered by the target C over time is written:
The Doppler migration of the target C during the illumination is characterized by
the quadratic term (PC (4.
This quadratic term is therefore written thus:
When the range-Doppler image is generated (with correction of the range
migration and Doppler migration using correction rules adapted to the fixed reflectors of
5 the imaged area), the migration correction applied to the moving target is identical to the
correction applied to the fixed reflector Mc. The reader is reminded that Mc denotes the
"apparent" position of the target.
The Doppler migration of Mc is characterized by the following quadratic phase:
10
Rc = ~~~=c ~~ 1 11 ~ ~ ~ where
15
Consequently, on the final range-Doppler image (where each fixed reflector is
focused), the residual defocusing of the moving target is characterized by the phase term:
hr,, 6) = h.c (t)- 2 w (t)
The residual defocusing is therefore written thus:
4n (;q2-( q2 AT
d2,c,M(f)= _tX x t2 - -(2 f , + ~kam bx f r ) x kambx fr x t2
2Rc 2Rc
If the moving target is assumed to be moving much more slowly than the
platform, this expression finally becomes:
25
component of the velocity
Defocusing due to the Doppler
ambiguity rank of tire target (term
which can be compensated by making
a hypothesis on the value of the
ambiguity rank)
At the end of the target extraction step 104, the following characteristics are
10 known for each detected target:
Platform-Target range Rc at the central instant of illumination.
Non-ambiguous Doppler frequency f d c = f d M + knmb f r .
First characterization of the phase rule 42,c1M(t) for an integration time shorter
than the complete illumination time. This first characterization can be refined by increasing
15 the integration time. Thus the step of refocusing the target is reiterated over a longer a
integration time. The accuracy of the estimate of the quadratic phase term can thus be
improved: for a given target, the first rough estimate performed with a limited integration
time enables the "fine" focusing to be initialized. The next focusing tests are carried out
with a finer interval (according to a reduced number of hypotheses) around the initial
20 value. At t'he end of this step, the final focusing of the target can be achieved by using a
local autofocus of the PGA (Phase Gradient Autofocus) type. In this way it is possible to
access the fine knowledge of the phase rule of the moving target over time.
The angular location of the target can then be estimated by an azimuth angle
error measurement (using two receiving channels), carried out on the refocused moving
25 target. The high compression gain obtained by focusing the target over a long integration
time with final radial resolution makes it possible to reduce the standard deviation of the
noise in this angle error measurement.
Therefore, in a fifth step 105, the method calculates the position of the target
and the components of the velocity vector of the target as a function of at least the route of
30 the platform on the radar image and the platform-target radial component.
+
At this stage, therefore, it is possible to estimate the vector Uc pointing toward
the moving target at the central instant of illumination, according to the knowledge of the
angular location of the target, the range R c , the relative Platform-Target altitude and the
aircraft attitudes and the information relating to the antenna aiming.
When the position of the target at the central instant of illumination has been
5 estimated, it is also possible to characterize its velocity vector thus:
When the position of the target and its non-ambiguous Doppler frequency are
known, the radial component of its velocity vector can be estimated according to the
following relation:
When the phase of the target over time is known, it is possible to deduce the
component "CV of the velocity vector projected along the route of the aircraft, by using the
following relation:
aL
15 The final result, therefore, is an SAR image on which the various detected
moving targets are repositioned, with a velocity vector assigned to each one. This result is
illustrated by the schematic range-Doppler image 50 of Figure 7.

19
CLAIMS
I . A method (80) for detecting and characterizing a moving target (1 3; 14) on a
radar image representing the reflectivity echoes of an area illuminated by a radar beam of
a platform (1 01) formed by a repetition of radar acquisitions (103), characterized in that it
comprises the following steps:
a first step (81) of eliminating the stationary fixed echoes with high reflectivity
measured on the radar image,
a second step (82) of reducing the integration time by extracting the central
temporal illumination portion on the radar image,
a third step (83) of focusing the echo of the moving target by applying a
correction of the range migration and the Doppler migration of the moving target on the
radar image,
a fourth step (84) of extracting the moving target from the radar image, a%
a fifth step (85) of calculating the position of the target and the components of
the velocity vector of the target, including at least the component projected on the route of
the platform.
2. The method as claimed in claim 1, characterized in that the first step (81) of
eliminating the stationary fixed echoes comprises the following steps:
- reduction of the reflectivity of the moving echoes, consisting in retaining, for
each pixel of the radar image, the minimum reflectivity for the whole set of repeated radar
acquisitions, and
- detection of the fixed echoes by a thresholding operation.
3. The method as claimed in claim 1, characterized in that, in the third step
(83), the range migration of a target is corrected by testing a number of possible ranks of
Doppler ambiguity for the target.
4. The method as claimed in claim 1, characterized in that, in the third step
(83), the Doppler migration of a target is corrected by testing a number of quadratic phase
law hypotheses to compensate the residual phase characterizing the residual Doppler
migration of the moving target, the quadratic term of this residual phase being defined by
the following formula:
Where:
-+
- V : velocity vector of the platform
- C : position of the target
+
- : velocity vector of the target
- : Platform-Target range:
- fdC : Doppler frequency of the target.
5. The method as claimed in either one of claims 3 and 4, characterized in that
the third step (83) comprises filtering of the defocused points.
10
6. The method as claimed in claim 1, characterized in that the fourth step (84)
comprises an operation of thresholding pixels of the radar image.
7. The method as claimed in claim 1, characterized in that the fifth step (85)
1s comprises the calculation of the radial component of the velocity vector of the moving h
target according to the following relation:
20 Where:
'CR : component of the target velocity vector along the radial axis.
8. The method as claimed in claim 1, characterized in that the fifth step (85)
comprises the calculation of the radial component of the velocity vector of the moving
25 target along the aircraft route according to the following relation:
Where:
- 'CV : component of the target velocity vector along the aircraft axis,
30 - kamb: Doppler ambiguity rank of the target
- Mc: apparevt position of the target, that is to say the position of the ground
point located at the same distance as the target,
- fr : repetition frequency. ,
Dated this (q.08.2013
OF EMFRY SSAGAIP
ATTORNEY FOR TEE APPLICANT[S]