METHOD AND SYSTEM FOR LOCATING ONE OR MORE TRANSMITTERS IN THE
PRESENCE OF A NETWORK OF ANTENNAS WITH POLARIZATION DIVERSITY
5 The invention relates to a method and a system for locating one or
more fixed transmitters in the presence of a network of antennas with
polarization diversity on the basis of the movement of a moving carrier by
using measurements of direction vectors corresponding to the response of
the antenna network installed on the carrier to a transmitter having a direction
10 (9,~) and polarization p. The invention is applied to antenna networks where
the sensors (or antennas) have polarization diversity.
In the present description, the word "carrier" refers to an aircraft,
an aeroplane, or a vehicle equipped with a network of sensors and with a
device for processing the signals transmitted by the transmitters to be
15 located.
The words "transmitter" and "source" are used in the present
description to designate the same item.
In Figure 1, the transmitter 1 to be located is at the position
E(Xo,yo,zo) and the carrier 2, an aeroplane in this example, is at the position
20 Mk(Xk,Yk,Zk) at the time tk and receives the transmitter at the incidence
8k=(9(tk, E),A(tk. E) ) and with the polarization Pk. The incidence 8k of the
transmitter changes through time and depends on the position E of the
transmitter and also the trajectory D of the aeroplane. The incident
polarization Pk depends on the incidence 8k and on characteristic parameters
25 of the transmit antenna. More precisely, in the presence of a dipole, these
parameters are the 3 components of the orientation of the dipole. The carrier
is equipped with a sensor network Ci or an antenna network 3 associated
with a device 4 for processing the received signals, comprising, inter alia, a
processor.
30 The angles of incidences em=e(tk, E) and Am=~(tk. E) are defined
for an m-th transmitter Em in the reference point of the network of N antennas
2
or sensors Cl , ... CN, installed under the aeroplane as shown in Figure 2.
The antennas of the network receive the sources or transmitters
with a phase and an amplitude dependent on the angle of incidence of the
transmitters, on the position of the antennas of the receive network, and also
5 on the incident polarization which depends on the incidence and radio
characteristics of the transmit antenna.
The technical problem posed is that of estimating the position E of
a transmitter 1 on the basis of direction vectors ak measured in the carrier 2
at each time lk. A direction vector at the time tk is the response of the antenna
10 network 3 to the direction 8k and to the incident polarization Pk of the
transmitter.
The prior art describes different methods allowing the position of
the transmitters to be estimated on the basis of a flow of direction vectors
measured through time on a moving vehicle. These methods, such as those
15 described in the patents US 7400297 and US 7907089, US 7952 521,
assume that the position of the transmitters is fixed.
In the aforementioned patents, the methods assume that the
antenna network depends only on the position of the antennas and these
methods do not therefore allow the polarization of the incident wave to be
20 taken into account in the geo-Iocation process. The gao-location algorithm of
a transmitter implemented in these methods consists in constructing, on the
basis of the direction vectors measured through time, a large direction vector
of which the associated virtual network is of the size of the trajectory of the
aeroplane. The position of the transmitting source is then estimated with a
25 MUSIC antenna-processing algorithm known to the person skilled in the art.
These methods allow monopolarization transmitters to be geo-Iocated. They
do not address the problem in the case of receive networks with polarization
diversity, which are sensitive to the polarization of the transmit antenna which
influences the determination of the position of the transmitter.
30
3
The subject-matter of the invention relates to a method for
estimating the position Em of a transmitter comprising a transmit antenna on
the basis of a moving sensor network installed on a carrier, said transmitter
comprising a transmit antenna, comprising, in combination, at least the
5 following steps:
a) determining a set of direction vectors {a"'I,---,i"".} corresponding to the
response of the sensor network of the carrier to a transmitter having a
position EJII ,a direction (Elk, ~k) and a polarization Pk for (1~k~L),
b) constructing a normalized vector blPllc ,
10 corresponding to a noisy measurement Bark of the direction vector which is
the response of the antenna network at the time tk of a transmitter having a
position Em of which the transmit antenna is parameterized by the coefficients
em on the basis of estimated values of the direction vectors {a"", -.-, iJII/.} ,
c) constructing a "large observation vector" by considering L observations for
15 the transmitter haVing a position E", for L times 1k which is modelled by
[
b"'l] [b(E,tI'C)] hI. = : =b,.(E""clIl)+el. where b,.(Em,c..,)=. : .
blll
/. b(E,t,.,c)
Cm corresponds to the parameters of the antenna of the transmitter ~nd e" is the
measurement noise of the direction vectors of the sensor network,
d) determining the position Em of the transmitter by identifying the parameters
Em and c'" of the transmit antenna of the transmitter which, from a set of
parameters (E, c), maximize the correlation between the measurement bL of the
large observation vector and the modelled vector b/. (E,c) parameterized by the
possible values of position E and the parameters c of the transmit antenna of the
transmitter to be located:
4
According to one alternative embodiment. the method comprises a
step where the "large observation vector" is expressed using. on the one
hand. a vector vL(E, c,bI.) dependent on the positions of the transmitter and
the measurements of the vector VI. (E,b/.) and, on the other hand. the
5 parameters c for modelling the antenna of the transmitter.
Then, by modelling vI. (E, c,bI.) =V,. (E,bI.)C I the maximum of the criterion
dependent only on the possible values of position E for the transmitter is
estimated:
10
A
where bI. is the large observation vector. bI. (E, c) the modelled vector
parameterized by the possible values of position E and the parameters c of
15 the transmit antenna of the transmitter to be located,' superscript H
corresponds to the transpose. in order to determine the position Em of the
transmitter.
The criterion C/P' (E) is obtained, for example. by using the
properties on the quadratic forms of the Ferrara criterion.
s
According to one embodiment. the polarization vector is modelled
using a matrix of which the components correspond to the polarization
responses of an antenna modelled by 3 loops and 3 dipoles and a constant
vector of the parameters of the transmit antenna. and the relation is
5 expressed in the following manner:
Ex
Ey
Pk = U(ak)C where c= Ez
Mx
My
M:
where c is a constant vector dependent on the unknown parameters of the
transmit antenna and where U(e) is a matrix with a dimension of 2x6 of
which the components correspond to the known incidences.
The method may comprise a step of determining the parameters
10 of the transmit antenna on the basis of the knowledge of its position.
The invention also relates to a system for estimating the position
of a transmitter E on the basis of a moving sensor network installed on a
carrier. said transmitter comprising a transmit antenna. said carrier
comprising a device for processing the signals transmitted by the transmitter
15 suitable for carrying out the steps of the method presenting one of the
aforementioned characteristics.
The method and the system according to the invention are used,
for example, to locate transmitting sources in a communications network.
One of the objects of the method and the system according to the
20 invention is to take account of the fact that the incident polarization Pk of a
transmitter to be located varies through time since it depends on the
incidence 0J( of the source or transmitter which varies, in the case of a
transmitter with a fixed position and antenna. as a function of the movement
and possible variations in the attitude of the carrier.
25
Other characteristics and advantages of the present invention will
become evident from a reading of the description of an embodiment given by
way of illustration and in no way limiting, and the attached figures, in which:
• Figure 1 shows an example of the architecture of the system according
5 to the invention for the location of a transmitter from an aeroplane,
• Figure 2 shows a network of 5 antennas and the incidence of a
transmitter,
• Figure 3 shows the modelling of an antenna in a general manner,
• Figure 4 shows the polarization of an incident wave,
10 • Figures 5A and 58 show the electrical and magnetic components of the
vertical and horizontal polarization respectively,
• Figure 6 shows a diagram of a dipole having an orientation u in the
presence of a wave having a direction k,
• Figure 7 shows the diagram for a loop having an orientation u in the
15 presence of a wave having a direction k.
To provide a better understanding of the subject-matter claimed in
the present invention, the description which follows is given in association
with Figure 1 which shows a transmitter 1 of which the position E is to be
20 determined from a moving aeroplane 2 equipped with an antenna network 3
or sensor. network and a signal-processing device, for example a processor 4
suitable for carrying out the steps of the method according to the invention. In
this example embodiment, the position of the transmitter is referenced in a
diagram xo, Yo, Zo in the reference point of the aeroplane.
25 To carry out the method according to the invention, it is assumed
that the step of associating measured direction vectors for the same
transmitter has been previously performed by carrying out, for example, the
steps described in the patent US 7 907 089 allowing the association of the
vectors of each of the transmitters in a multi-transmitter context. This
30 therefore provides a set of groups, each of the groups comprising a
transmitter and a plurality of direction vectors for this same transmitter.
7
Moreover, the calibration table of the network is known, which
comes down to knowing the function a(e,p) which links a direction vector a to
the direction of arrival e and to the polarization p.
The parameters of the transmit antenna of the transmitter of which
5 the position is to be determined depend on the modelling of any given small
antenna, which may be reduced to three dipoles and three loops. Figure 3
then shows that an antenna can be parameterized according to its electrical
components (Ex,Ey,Ez) and its magnetic components (Mx,My,Mz). Under these
conditions, the polarization vector is written as follows:
10
15
20
Ex
Ey
( )
Ez
Pt =U at c wherec=
M;,;
My
M.
where c is a constant vector dependent on the unknown parameters of the
transmit antenna and where U(a) is a matrix with a dimension of 2x6, the
components of which correspond to the known incidences.
Noting that the first component of Pk is associated with the
polarization V and that the second component is associated with the
polarization H, the components of the first line of U(e) correspond to the
polarization response Vof the 3 dipoles and 3 loops of the modelling and the
second line corresponds to the polarization responses H of its loops and
dipoles. The first column of U(e) corresponds to the radiation of a dipole
having an orientation x, the second column to a dipole haVing an orientation y
and the third column to a dipole having an orientation z. The fourth, fifth and
,
sixth columns of U(e) correspond to the radiation diagrams of the loops
having orientations x, y and z respectively. In a general manner. the
components of the matrix U(a) correspond to the polarization response of
the transmitter.
(1) ,
(3),
8
The vector c is constant when the transmit antenna of the
transmitter is fixed. The components of c correspond to the weightings of a
channel formation for the transmission of a virtual network composed of 3
dipoles and three loops. The modelling of equation (1) will be explained in the
5 description below.
The antennas of the network of the aeroplane receive the sources
with a phase and an amplitude dependent on the incident angle of the
transmitters, on the position of the antennas, and on the incident polarization
which depends on the incidence and radio characteristics of the transmit
10 antenna of the transmitter.
In the presence of M transmitting sources, the signal at the output
of the network of N antennas of the aeroplane is written in the following
manner:
x(t+t.d =[ XI~t)]=fa(emklPmk) S.,,(t +Ik)+n(t+tk)
XN(t) lit-I
15 where xnCt) is the signal received on the n-th sensor en of the network of the
aeroplane, slit (I) is the signal of the m-th source, net) is the additional noise,
amk is the direction of arrival of the m-th transmitter at the time tic' Pmk is the
associated incident polarization (Figure 4) and a(elllk,Pmk) is the direction
vector of the m-th source at the time tk • The vector Pmk is the direction of the
20 electric field E which is included in the wave plane as shown in Figure 4.
According to Figure 4, the wave plane is perpendicular to the wave vector
k(e) which is written as follows:
[
U] {U=COS(8)cos(L\)
k(e)= v where v=sin(O)cos(L\)
W w=sin(L\)
where the incidence e = {8,L\} depends on the azimuth in the reference point
(2),
9
of the aeroplane. The polarization Pm. is then a function of the incidence 8 MI'
of the source at the time tk and also of the parameters em of the transmit
antenna according to (1). The direction vector a(E>mk,Pm.d of the m-th
source at the time I k is written as a function of the horizontal and vertical
5 components of PIIIk which are defined in equation (1) in the following manner:
a(S/Ilk,Pmk)=aH (8l1rk )Pmk.H +8v(E>mk)Pmk.v =D(E>/Ifk)PmkwherePmk =[Pmk.H] (4).
Prnk.1I
The vectors aH (E» and av (8) are the responses to a direction e of the
antenna network for linear polarizations (horizontal H and vertical V
respectively). A sensor network is said to have polarization diversity when the
matrix representing the response vectors of the antenna network D(E>ml:) has
10 the rank order of 2, the matrix comprising the components aH (e) and av(8)
of the response vectors of the antenna network. The vectors aH (8) and
av (8) are not co-linear, which allows the polarization diversity of the
transmitter to be exploited.
According to Figure 1, the relation between the incidence 8k of a
15 transmitter at the time tk and its position E is as follows:
r
Ut] -
k(e.)= ". =&..0- (a.)~
plane EM
~ k
k
where IIEM.:II is the norm of a vector EMk , E is the position of the
transmitter. M k is the position of the aeroplane at the time tk and
Raeroplene (Uk) is a rotation matrix dependent on the vector with an angle Uk of
which the components are the angles of pitch, roll and attitude at the time II"
20 The parameters M k and Uk are supplied, for example, by the navigation
(5) ,
10
system of the aeroplane or that of the vehicle or by any other suitable means.
According to the relations (3) and (5), the link between the azimuth and
elevation and the components of the wave vector is then:
{
81t =angle (ult +jVIt )
!:J./t =sin-I (wk
) (6) ,
Uk, Vk, Wk corresponding to the components of the wave vector for the time lie.
5 The relations (5) and (6) then define a function expressing the value of the
incidence as a function of the position of the transmitter E and the time
tic such that:
10
Moreover, the relation of equation (1) indicates that the
polarization vector is written as Plllic = U(81111c )c",.
Under these conditions, the direction vector amlc =a( <9Ink'Pmk )
depends on the position Em and on the electromagnetic parameters of the
transmit antenna cm and can be expressed as a function of the matrix
D(Smk) of the responses of the network to the reception at a direction E>mk
according to the respective polarizations V and H of the matrix U(f(Em,tlc )) ,
15 where U(8) contains the radiation diagrams in V and H in the direction S of
the 3 dipoles and 3 loops which are the virtual antennas of the model of the
transmit antenna:
allllt = a(8",/c,Pmk) = D(f(EIII,t/c ))U(f(E""l/c ))c",
= W(EIII,t/c )c",
where W(Em,lk) is a matrix representing the matrix of a transmission channel
between a network of 3 dipoles and 3 loops which are co-located (modelling
20 the transmit antenna) having a position Em and an antenna network on the
carrier at the time tk which is at the position Mk and has a known spatial
orientation defined by lXk.
(7) .
(8),
1]
The process of calculating the channel matrix W(E.t.<) for a
hypothetical position E of a transmitter is. for example. as follows:
Step A.1: calculating the wave vector k(8Jt) according to equation (5) on the
basis of the value of E and the orientation parameters Qk of the receive
5 network at the time tk which are supplied by a navigation system.
Step A.2: calculating the incidence 0k={Ok. dk } according to equations (6)
and (7). and, once this stage is performed, 0k=j{E. lk) is carried out,
Step A.3: calculating the matrix U(ek) with a dimension of 2x6 of which the
components are the radiation diagrams of the 3 dipoles and 3 loops of the
10 transmit antenna model according to the polarizations V and H in the
direction ek. The first line of U(ek) comprises the diagrams with polarization
V and the second line of the diagrams with polarization H.
Step A.4: calculating the matrix D(E>k)=[ ay(0k) aH(0k)] by reading from the
calibration table of the vectors av(e} and aH(0} for the direction e =0k.
15 Step A.5: calculating the matrix W(E,tk ) by carrying out W(Ettk )= D(0k)
U(e0·
The object of the method is notably to estimate the position Em of
a transmitter on the basis of a set of direction vectors {am,,··,allld estimated
on the basis of the time signal x (t +tk) at the output of the antenna
20 network of equation (2), knowing that sets of vectors {aml,···,a"'L} have
previously been produced for each of the transmitters m, by using methods
known in the prior art.
Location method for polarization diversity
The vectors all/k are incorrect estimates of the direction vectors
25 all/k of equation (8).
The writing model of the measured direction vector is then written
according to (8):
12
8",.. =a(Em,tk,c",) + em" where
in a general manner a(E,t,c) =W (E,t)c
where emk is an estimation and modelling noise and W(E,t) is a matrix
representing the aforementioned channel matrix. In this modelling step, the
parameters of the position E of the transmitter have been separated at a given
time t from the parameters c of the transmit antenna.
A In the method, a normalized vector bmk is then produced
corresponding to a noisy measurement amk of the direction vector which is the
response of the antenna network at the time lit to a transmitter having a position
Em of which the transmit antenna is parameterized by the coefficients Cm:
where no is a reference sensor set in advance by the method and 8[~ is the
i-th component of the vector 8.
The model of this vector is then:
(9) ,
(10)
5
.. ( ) _ () W(E,t)c bmk =b EIll,t.. ,c", +emk where b E,t,c = ( )
W"o E,t c
where Wno (E,t) is the no-th line of W(E,t) and emk is the noise vector at the
output of the normalization of equation (10). Its initial value is
em" ~ emk lam" [1lo].
The method will then construct a "large observation vector" by
using L measurements of normalized vectors:
(11)
[
it",.] [b(E,tl'C)] it/, = : =b/. (Em,cm)+eL where b/. (E""c.) = :
b"". b(E,ti.'c)
10 where e/. is the noise of the measurement of the direction vectors of the
network measured through time. It thus comprises the vectors em" of the
estimation and modelling noise of equation (11).
(12)
13
According to the model of equation (12), the joint estimation of the
position E", of the m-th transmitter with the parameters c... of the transmit
antenna is then carried out in the following manner:
(E""clIl ) = max JI• (E,c)
(E••cor )
/bL (E,C)"b,12
where J (E c) = .
L' (b/b/.)(bL (E,c)" bdE,c»)
This leads to identifying, from the set of positions E of the
5 transmitter and the parameters of the transmit antenna c the maximum value
of the criterion JL(E,c) of equation (13) or to identifying the parameters E",. C",
which, from the set of parameters E, c , maximize the correlation between the
measurement bL of the large observation vector and the vector b/. (E,c)
parameterized by E and c.
JO The criterion of equation (13) is multidimensional and may prove
to be difficult to implement.
One way to overcome this disadvantage is to construct a criterion
originating based on the principle of equation (13) which offers the advantage
of depending only on the position E of the transmitter.
15 According to one alternative embodiment, the method uses the
quadratic properties of the Ferrara principle described in the document by E.
R. Ferrara and T. M. Parks, entitled "Direction finding with an array of
antennas having diverse polarizations, "which appeared in the journal IEEE
Trans. Antennas. Propagation., vol. 31, pp. 231-236, Mar. 1983.
20 Assuming that e.,. is zero, it is known from (11) that:
" Wt(E)c {Wk(E)=W(E,tk ) bmJc = m m where
Wk (Em )Cm Wk (E) = W"o (E,tk )
From this last equation, it can be inferred that the vector
bk(E""c""bmk ) is an estimate of the vector b"'k associated with the
(13)
(14)
]4
....
normalized vector bmk corresponding to the measured direction vector RIllA:'
the response of the antenna network at the time tk to a transmitter having a
position Em having a transmit antenna of parameters Cm:
bmk ~ bk (Em,cm, bmk ) =Wk (Em)Wk (Em )# bmkW k (Em )cm
where W" (E)' designates the pseudo-inverse of Wk (E).
5 According to the model of equation (12) and the note of equation
(15), the joint estimation of the position EM of the m-th transmitter with the
parameters (III of the transmit antenna can be carried out via a second
approach, where:
(Em,cm ) = maxCL (E,c)
(I,e)
(15)
IbLHVL(E,c,bLt (16)
where CL(E,c) = H
(bLHbL ) ( VL (E,c,bL ) VL (E,c,bL ) )
and where the equivalent direction vector VL(E, c,bL) which models the
10 vector hi. where h,. =V,. (Em'(lN,b/.)+e/. is written by separating the
contributions of the positions E and the intrinsic parameters c of the antenna
of the transmitter in the following manner according to (15):
bl (E,c,bml )
where
... [ WI (E)W. (~)' b"'lw, (E) ]
V,. (E, bI. ) = :
W,. (E)WI. (E)' hml.wI. (E)
To construct the direction vector and separate the contributions, observations
IS b"'I"'" hm/. are added to the matrix.
(17)
(18)
•
15
According to equations (16)-(18), the criterion C,. (E,c) is written in the
following manner:
Q,(E)= VL(E.b{b~~:V/.(E,b,)
bl• bL
Q2(E)= V,. (E,bLf V,. (E,b,.)
(19)
According to the aforementioned Ferrara principle, the maximum
of the criterion Cr.{E,c) for a fixed position E is determined by varying the
5 values of c by:
(20)
where Amax (Q) designates the maximum characteristic value of Q.
Consequently, the algorithm alloWing the position of the transmitter E", to be
estimated then consists in identifying, from the set of possible positions E of
the transmitter, the maximum value of the criterion which maximizes the
to correlation between the measurement of the large observation vector bL and
the matrix VL (E,bI.) parameterized by E and the measurements bI. and is
expressed in the following manner:
Em =tnFC/"(E) where C,.opI(E)=Amax(Q2(EtQ.(E») (21)
According to one embodiment of the method according to the
invention, after having located a transmitter, its position is known. On the
15 basis of this position value, it is then possible to identify the value of the
components of the transmit antenna Cm of the located transmitter.
The estimated vector em of the components of the transmit
antenna is the characteristic vector associated with the maximum
characteristic value of the following matrix Q", :
(22).
16
The steps allowing the vector having a position Em to be
estimated on the basis of the direction vectors 81M measured through time for
(1~k,p) = uHE(0,p)=Pv x Gvdipok (0)+ PH xGHdipo/e (0) (25)
where P=[PH P"r,knOWing that Pv and PH are the components in
•
J8
polarization V and H respectively of the dipole. Figure 6 shows that the
voltage Vet) obtained at the two ends of the dipole is proportional to
Gdipoll! (0, p)
Example of an ideal loop
5 An ideal loop has the characteristic of being sensitive only to the
magnetic component. By using u to denote the unit vector giving the
orientation of the loop, the gains Gy'loop (e) and GHJoop (0) in polarization V
and H verify:
Gvloop (0)=kH(0t u and GH'loop (e)=-ky(et u (26)
where uHu =1. The gain of the dipole is then expressed as follows:
G100p (0,p)=uHH(0,p)=py xG/OOP (€»+PHXGHloop (0) (27)
10 where P= [PH py t, knowing that Pv and PH are the components in
polarization V and H respectively of the dipole. Figure 7 shows that the
voltage Vet) obtained at the two ends of the dipole is proportional to
Gdipoie (0, p).
General example
15 In the general example, it has been shown on the basis of
electromagnetic simulation that a small antenna comprises 3 dipoles and 3
orthogonal loops as shown in Figure 3. The gains Ex, Ey, Ez are the
electrical components according to the axes x, y and z and correspond to the
gains of the dipoles following these three axes. The gains Mx, My. Mz are the
20 magnetic components according to the axes x, y and z and correspond to the
gains of the dipoles according to these three axes. Any given antenna can
then be modelled as the channel pre-formation of a co-located network
comprising 3 dipoles and 3 loops.
Consequently. the gain of any given radiating element is written in
2S the following manner as a function of a direction 0 and a polarization p:
•
19
G(8,p) = ExG/i
polf1 (a,p) +EyG/lpo/e (e,p) +EzGzrlfpole (a,p)
+MxG/oop (e,p)+EyG}ooo (8,p)+EzGfoop (a,p)
where G/pole (8, p) ,G/,.,.,/e (0, p) and G/ipole (8, p) are the respective gains of
the dipoles having directions X, y and z which are known and
GlOOD (8, p) I G/pole ( 0,p) and Gzdipole (8, p) are the gains of the loops having
respective directions X, y and z which are also known. The expression (28) of
5 the gain can be written in the following manner:
Ex
Ey
G(e,p)=g(e,p)c whQl: c= ~
x
The polarization Pk of a wave transmitted by the antenna having gain
G(e,po = [1 If') in the direction 0 .. is expressed as follows:
(28)
(29)
p,=U(9,)c where U(e, )=[:~:::::~] .,=[~] and .,=m (30)
and the model of equation (1) is then validated with an expression of the
matrix Vee) as a function of e perfectly known.
10
The method and its associated system offer notably the following
advantages:
eretaining, in terms of performance, the advantages of gao-location of
the methods known from the prior art with a large incomplete
15 network;
etaking account of the case of an antenna network with polarization
diversity, the response of which depends on two orthogonal
polarizations which have been measured by a calibration process.

.. Claims
1 - Method for estimating the position Em of a transmitter comprising a
transmit antenna on the basis of a moving sensor network (3) installed on a
5 carrier (2), said transmitter comprising a transmit antenna, comprising, in
combination, at least the following steps:
a) determining a set of direction vectors {ill/l.···,imd corresponding to the
response of the sensor network of the carrier to a transmitter having a
position Em. direction (0k, ~) and polarization PIt for (1