METHOD OF MULTI-TRANSMITTER AND MULTI-PATH AOA-TDOA
LOCATION COMPRISING A SUB-METHOD FOR SYNCHRONIZING AND
EQUALIZING THE RECEIVING STATIONS
The invention relates to a method and a system making it possible to locate several transmitters in the presence of reflectors on the basis of several receiving stations with synchronization of the receiving stations.
The invention relates to the location of several transmitters in the presence of reflectors on the basis of several stations. Figure 1 gives an exemplary location system with 2 receiving stations with position A1 and A2 in the presence of two transmitters with position E1 and E2 and a reflector at R1. According to Figure 1, the station at Ai receives the direct path of the transmitter Em at the incidence θmi0 and the reflected path associated with the reflector Rj at the incidence θmiJ. Location of the transmitters requires not only the estimation of the incidence angles θmj ( AOA abbreviation of "Angle of Arrival") but also the estimation of the associated TDOAs or time differences of arrival τmi1j-τmi2j. between the stations Ai1 and Ai2. Figure 2 shows that the AOA/TDOA location of a transmitter at E1 with the stations with position A1 and A2, consists in firstly estimating its direction θ so as to form a straight line and then in estimating the time difference of arrival Δτ12 of the signal transmitted between the two stations so as to form a hyperbola H. The transmitter is then situated at the intersection of the straight line D of direction 6 and of the hyperbola H.
Knowing that a receiving station is composed of one or more receivers, the invention also relates to the processing of antennas which processes the signals of several transmitting sources on the basis of multi-sensor reception systems. In an electromagnetic context the sensors Ci are antennas and the radio-electric sources propagate in accordance with a given polarization. In an acoustic context the sensors Ci are microphones and the sources are
sound sources. Figure 3 shows that an antenna processing system is composed of a network of sensors receiving sources with different angles of arrival θmp. The elementary sensors of the network receive the signals from the sources possibly being either the direct path transmitted by a transmitter or its reflected path with a phase and an amplitude depending in particular on their angles of incidence and the position of the reception sensors. In Figure 5 is represented a particular network of sensors where the coordinates of each sensor are (x„,y„). The angles of incidence are parametrized in 1D by the azimuth θm and in 2D by the azimuth θm and the elevation Δm. According to Figure 4, 1D goniometry is defined by techniques which estimate solely the azimuth by assuming that the waves from the sources propagate in the plane of the sensor network. When the goniometry technique jointly estimates the azimuth and the elevation of a source, it corresponds to 2D goniometry. The main objective of antenna processing techniques is to utilize the spatial diversity which consists in using the position of the antennas of the network to better utilize the differences in incidence and in distance of the sources. One of the technical problems to be solved in this field is that of the location of transmitters consisting in determining their coordinates, which will be envisaged in 2 dimensions or 2D, in the plane and/or in 3 dimensions or 3D, in space, on the basis of measurements of AOA and/or TDOA type. Multi-transmitter location requires a transmitter-based association of the parameters of AOA/TDOA type, hence joint estimation of the AOA/TDOA parameters.
The field of AOA estimation in the presence of multi-transmitters and multi-paths on the basis of a multi-channel receiving station is very vast, That of TDOA estimation is just as wide as that of AOA with in particular the techniques according prior art. However, most of the time the measurement is performed on the basis of two signals arising from two single-channel stations. These techniques are then not very robust in multi-transmitter or multi-path situations. This is why prior art propose TDOA techniques making it possible to
separate the sources on the basis of a priori knowledge about their cyclic characteristics.
AOA/TDOA joint estimation has generated a large number of references such as described in prior art. These works are much more recent than the previous ones on TDOA and are due essentially to the advent of cellular radio-communications systems as indicated explicitly in documents of prior art. Unlike the previous references for TDOA, the processings are performed with multichannel receiving stations. However, the objective is to carry out the parametric analysis of a multi-path channel from a single transmitter Ei to a multi-channel receiving station at A1. The jointly estimated parameters are then the angles of arrival θ11J and the time deviations τ11j -τ11j, between the paths of this same transmitter due to reflectors at Rj and Rj-. This kind of system does not make it possible to carry out the location of the transmitter at E1 such as is envisaged in Figure 1, unless the positions of the reflectors at Rj and Rj, are known. The joint estimation of the parameters (θ11j,τ11j-τ11j) is very often envisaged on the basis of the knowledge of a pilot signal such as the TSC sequence codes (Training Sequence Code) for GSM (Global System Mobile) or the spreading codes for signals of CDMA (Code Division Multiple Access) type. TOA (Time Of Arrival) estimation techniques have been envisaged for locating mobiles in cellular radio-communications systems and for locating radio-navigation receivers of GPS/GALILEO type for the Global Positioning System. These estimation techniques are performed on the basis of the knowledge of a pilot signal and can be carried out with multi-channel receiving stations. Location often requires'the demodulation of transmitted signals which returns, for example, the position of the satellites in GPS/GALILEO and allows location of the receiver on the basis of the knowledge of the position of the satellites as well as the estimation of the TOA on each of the satellites. The TOA estimation and location techniques then require an accurate knowledge of the operation and characteristics of the radio-navigation or radio-communications system but
they do not make it possible to carry out location in the general case without a priori knowledge of system type or of signal type.
The location of a transmitter on the basis of the AOA/TDOA parameters has spawned a significant bibliography. These data processing techniques are generally suited to mono-transmitter situations and sometimes envisage problems with tracking when the transmitter is in motion or else one of the receiving stations is intentionally in motion. In this field numerous references use Kalman filtering. However, these location techniques do not deal with the case of TDOA measurements performed on asynchronous receiving stations. In poor art the authors propose a direct estimation of the position of the transmitters on the basis of the set of signals originating from all the reception channels of all the stations. In this paper, the authors deal with the problem of multi-sources through algorithms know of prior art. It directly estimates the positions of the transmitters through an antenna processing approach. However, it assumes that all the signals have the same bandwidth and that the signals originating from the various stations are synchronous. This approach does not, however, make it possible to deal with the problem of the multi-paths generated by reflectors and the problem of asynchronism between the various stations.
The subject of the invention relates to a method for locating one or more transmitters Ei in the potential presence of obstacles Rp in a network comprising at least one first receiving station A and one second receiving station B asynchronous with A characterized in that it comprises at least the following steps:
• The identification of a reference transmitter of known position E0 by a calculation of the AOA-TDOA pair (θref,Δτref) on the basis of the knowledge of the position EO of the reference transmitter and of those of the stations at A and B,
• An estimation of the direction of arrival of the transmitter or transmitters and of the reflectors (or estimation of the AOA) on the first station A,
• The separation of the signals received on the first station A by spatial filtering in the direction of the source (transmitters and/obstacles),
• The separation of the incidences originating from the transmitters from those originating from the obstacles by inter-correlating the signals arising from the spatial filtering at A.
• The estimation of the time difference of arrival or TDOA of a source (transmitters and/obstacles) by inter-correlating the signal of the source
(transmitters and/obstacles) received at A with the signals received on the second receiving station B: for each transmitter source Ei (or obstacles Rj) a pair (AOA.TDOA) is then obtained,
• A synthesis of the measurements of the pairs (AOAi, TDOAi) of each source (Ei, Rp) so as to enumerate the sources and to determine the means and standard deviation of their AOA and TDOA parameters,
• The determination of the error of synchronism between the receiving stations A and B by using the reference transmitter Eo, and then the correction of this error on all the TDOAi of the pairs (AOAi, TDOAi) arising from the synthesis,
• The determination of the orientation error of the network at A by using the reference transmitter E0, and then the correction of this error on all the AOAi of the pairs (AOAi, TDOAi) arising from the synthesis,
• The location of the various transmitters on the basis of each pair (AOAi, TDOAi).
Other characteristics and advantages of the present invention will be more apparent on reading the description which follows of an exemplary embodiment given by way of wholly non-limiting illustration, accompanied by the figures which represent:
o Figure 1, a location system comprising receiving stations at Ai and transmitters at Em,
o Figure 2, an example of AOA/TDOA location in the presence of a
transmitter, o Figure 3, a diagram of a transmitter propagating toward a network of
sensors, o Figure 4, the incidences (θm, Δm of a source, o Figure 5, an example of a network of sensors with position (xn, yn), o Figure 6, a system for location on the basis of the stations A and B in the
presence of several transmitters and paths, o Figure 7, the distortion of the signal transmitted between the receivers at A and at B, o Figure 8, the MUSIC criterion in the presence of coherent multi-paths
(red curve) and of non-coherent sources (green curve), for directions
of multi-paths θ11=100° and θ12=200°, the network of N=5 sensors is
circular with a radius of 0.5A., o Figure 9, an exemplary elementary Goniometry method taking
situations of coherent paths into account, o Figure 10, an illustration of an elementary AOA-TDOA estimation
method, o Figure 11, a representation of the technique for the AOA-TDOA
location of the transmitter at the position E, and o Figure 12, the AOA-TDOA location uncertainty ellipse.
Figure 6 represents a location system according to the invention comprising for example the following elements:
o M transmitters Em of unknown positions, o P reflectors Rp of unknown positions,
o a multi-channel receiving station at A. The station A comprises a network of sensors since it affords the goniometry function. The orientation of the antenna of the goniometer at A is for example known approximately to
within Δθ=15°. This corresponds to the typical accuracy of a magnetic
compass, o a single- or multi-channel receiving station at B having at least one
reception sensor, o a reference transmitter at E0 whose position is known. The signal
transmitted by this transmitter possesses a transmit band of the same
order of magnitude as that of the receivers at A and B. The various parameters of the location system are given in Figure 6. In this system, one of the objectives of the location is to determine the position of the M transmitters Em of unknown positions. To summarize, the method according to the invention executes at least the following steps:
• A goniometry (or estimation of the AOA) of the transmitters Em and of the reflectors Rp on the station A,
• A separation of the signals transmitted by spatial filtering in the direction of the source (transmitter or reflector),
• The estimation of the time difference of arrival or TDOA of a source by inter-correlating the signal of a source at the output of the spatial filtering at A with the signals received at B: for each source (transmitter Ei or reflector Rj) an (AOA, TDOA) pair is obtained. This inter-correlation technique making it possible to estimate the TDOA, will be performed jointly with the remote "gauging" of the receivers at B, for example.
• A synthesis of the measurements of the (AOA, TDOA) pairs of each source will be performed so as to enumerate the transmitters Em and the reflectors Rp corresponding to the obstacles and to give statistics, such as the means and standard deviation associated with the accuracy of estimation of the AOA and TDOA parameters.
• The identification of the reference transmitter EO by an AOA technique from among the (AOA, TDOA) pairs arising from the synthesis. Knowing the position of the reference transmitter E0, the calculation of the error of synchronism between the stations A and B and then the correction of this error on all the TDOAs of the (AOA, TDOA) pairs arising from the synthesis.
Knowing the position of the reference transmitter E0, the calculation of the orientation error of station A and then the correction of this error on all the AOAs of the (AOA, TDOA) pairs arising from the synthesis.
• The location of the various transmitters and reflectors on the basis of each
(AOA, TDOA) pair and the establishment of the uncertainty ellipse on the
basis of the measurements of standard deviation of these parameters for
each of the transmitters and reflectors.
• The calibration error impacting on the goniometry is known,
• The number K of time slices of duration T over which a joint estimation of the AOA-TDOA parameter pairs will be performed is chosen.
The method implemented by the invention is described in more detail
hereinafter.
Modeling of the Signal on station A
In the presence of M transmitters and P obstacles or reflectors, the signal
received as output from the N sensors at A may be written in the following
manner according to Figure 6.
(Figure Remove)
where sm(t) is the signal of the m-th transmitter,θmd and θpr are respectively the directions of arrival of the direct path and of a reflected path and τrm is the Time Of Arrival (TOA) of the m-th transmitter such that
(Figure Remove)
where [AB| is the distance between the points A and B. The signal bp(t) is associated with the p-th obstacle and satisfies:
(Figure Remove)
where τmp is the TOA of the multi-path of the m-th source such that:
(Figure Remove)
and pmp is the attenuation of the multi-path of the m-th source caused by the p-th obstacle. The signal of the direct path sm(t-τm) is correlated with the signal bp(t) originating from the obstacle in the following manner
(Figure Remove)
where rsm(τ) = E[sm(t)sm(t-τ)*] is the auto-correlation function of the signal sm(t) and rmp is a normalized coefficient between 0 and 1 giving the degree of correlation between sm(t-τm) and b (t). When the passband of the m-th transmitter equals Bm, the function rSm (τ) can be written
(Figure Remove)
when M=P=1, the expression for rs1b1 may be written in the following manner according to (2)(4)(5)(6)
(Figure Remove)
where sinc(x) = sin(x)/x. When x is small the latter function becomes sinc(x)≈ 1-x2/6. Under these conditions and according to (5)(7), the correlation level rmp depends on the distance Dmp: rmp ≈1-(πBmDmplc)2 /6 in the following manner:
Inversely
(Figure Remove)
By using the above expressions, the multi-
paths can be classed into the following three categories: Decorrelated cases: rmp ≈ 0 such that Dmp >clBm
Correlated cases: 0 < rmp < rmax such tha
(Figure Remove)
Coherent case: rmp > rmax such that
(Figure Remove)
In practice rmax=0.9 is a typcal correlation value for separating the cases of coherent multi-paths from the cases of correlated multi-paths. The following chart then gives the inter-path distance limits for obtaining coherent paths.

I Bm (MHz) 1300kHz |1MHz |10MHz I
Limit distance for
obtaining coherent paths < 246m < 74rr< \<7m

Chart 1 - Distance limit for obtaining coherent paths Modeling of the Signal on station B
The expression for the signal received on the sensors or receivers of station B
is similar to that of equation (1). However:
• The angles of incidence of the transmitters Em and of the obstacles or reflector Rp are different: θmd' and θpr' instead of θmd and θpr • The instants of arrival (TOA) of the transmitters Em and of the obstacles Rp are different: τm' and τmp' instead of τm and τmp where
(Figure Remove)
Moreover, the signal of the direct path at the output of the receivers B may be written sm(t-τm'). Noting that this signal may be written sm(t-τm) at the output of the receivers of station A, the difference between the signals sm(t) and sm '(t) is due to the difference in the frequency templates (term known in the art) of the receivers of the stations A from those of the station B. This distortion caused by receivers of different nature is illustrated in Figure 7.
To be more precise, in the presence of M transmitters and P obstacles or reflectors, the signal received as output from the N sensors at B may be written in the following manner according to Figure 6
(Figure Remove)
where sm'(t) is the signal of the m-th transmitter,θmd and θpr ' are respectively the directions of arrival of the direct path and of the reflected path and τm ' is the Time Of Arrival (TOA) of the m-th transmitter, the expression for which is given by equation (8). The signal bp'(t) is associated with the p-th obstacle and satisfies
(Figure Remove)
where τmp' is the TOA of the multi-path of the m-th source of equation (8) and pmp'is the attenuation of the multi-path of the m-th source caused by the p-th obstacle (or reflector).
Elementary modules for AOA and TDOA estimation Goniometry or Estimation of the angle of arrival AOA
The goniometry or AOA estimation algorithms must process the case of multi-transmission. With the objective of additionally taking into account the problem of multi-paths, the method can implement two different algorithms:
• The MUSIC scheme in the absence of coherent multi-paths
• The coherent MUSIC scheme (More generally, this involves the auto-calibration algorithm know by the man of the art) in the presence of coherent paths, applied when the MUSIC scheme does not lead to satisfactory results.
It will be considered that it is necessary to apply the Coherent MUSIC scheme when for example the estimated correlation τmp between the paths is larger than τmax possibly typically being fixed at 0.9. It will also be decided to apply coherent MUSIC when the MUSIC scheme has failed.
On output from the goniometry the sources (transmitters and obstacles) are identified either as direct path or as secondary path by a temporal criterion: The path in the lead over the others is the direct path. The MUSIC [1] and Coherent MUSIC [4] algorithms are based on the properties of the covariance matrix Rx =- E[x(t)x(t)H] of the observation vector x(t) of equation (1) where E[.] is the mathematical expectation and H the conjugation
and transposition operator. According to (1), the covariance matrix may be written
(Figure Remove)
And where
(Figure Remove)
The two schemes are based on the decomposition into eigenelements of Rx where the σvectors ek are the eigenvectors associated with the eigenvalue Xk where (λ 1, ≥λ2 ≥...≥N). K is defined as being the rank of the matrix Rx such that λ1 ≥...≥ΛK≥σ2=λK+I...=λN. The two schemes will be differentiated by:
o The structure of the eigenvectors ek of the signal space (1≤k≤K)
o The value K of the rank of the matrix Rx. The two schemes have in common that they utilize the orthogonality between the eigenvectors of the signal space (1≤k≤K) and the eigenvectors of the noise space (K+1≤k threshold_1st, the azimuth θm is not associated with a direction of arrival. The presence of coherent paths is then detected when the number K of minima satisfying JMUSIC(θk)< threshold_1 st is less than the rank K of the covariance matrix Rx.
Detection of coherent sources by estimating the inter-correlation level In this case where K=M+P, the K estimated incidences satisfy JMUSIC(θ)< threshold_1st. However, it is known moreover that the more significant the level of correlation between the sources, the larger the variance of the estimates θm. The objective is then to estimate the covariance matrix of the sources Rs of equation (11) on the basis of the estimates of the matrix A as well as the noise level a2. On the basis of the covariance matrix Rx(T0) and of the estimates θ1...θk , the steps of the method are as follows:
Step A.1: On the basis of the result of EVD o

(Figure Remove)
which is
used to construct IIA, calculation of an estimate of the noise level
(Figure Remove)
Step A.2: Calculation of an estimate of the denoised covariance matrix Ry =A Rs AH by performing
(Figure Remove)
Step A.3: On the basis of the estimate A=[a(θ1) ••• a(θk)]of the matrix of
direction vectors, deduction of an estimate of the covariance matrix of the sources
(Figure Remove)
Step A.4: Calculation of the maximum correlation rmax between the paths i.e.
(Figure Remove)
The estimated correlation rmp between the paths is larger than rmax possibly
typically being fixed at 0.9.
The coherent MUSIC technique will be used when rmax >rmax. A typical value of
rmax is 0.9.
Case of coherent path and application of Coherent MUSIC
In this case the rank of the matrix Rx satisfies K•••>θ1 where the θi vary between 0 and 360°. The criterion
JMC(θ,I) is moreover normalized between 0 and 1 since it satisfies
0≤MC(θ)<1. Just as for MUSIC the elimination of the poor /-tuples will be
done by way of a threshold of good goniometry "threshold_1sf. Consequently,
to be valid, the /-tuples θk =[θk1---θk1] must satisfy JMC(θk)< threshold_1st. If
the number of good /-tuples is less than K, the coherent MUSIC scheme is
repeated for/=/+1.
The steps of coherent MUSIC are then as follows:
Step B.1: Initialization to /=2
Step B.2: Calculation of the criterion of equation (23) for all the θ = [θ1•••θ1]
satisfying θ1>, >• • • >θ1 knowing that the θi, vary between 0 and 360°.
Step B.3: Search for the K /-tuples satisfying JMC (θk) < threshold_1st.
Step B.4: If Kτm', the method will retain the TDOA τm -τm' knowing that it satisfies τm -τm' <τm -τmp'.
• When(Equation Removed)
the observation vector is constructed
(Equation Removed)
The TDOA τmp-τmp' will correspond to a maximum correlation between the signals bp(t) and xB(t + τ). The multi-channel correlation criterion of equation (35) is constructed with x(t) = bp(t) and y(t) = xB(t). The correlation criterion cxy(τ) also contains P other correlation maxima in τmp-τm'. Knowing that
τmp'>τm', the method will retain the TDOA of interest τmp-τmp' knowing that it
satisfies τmp-τmp'<τmp-τm'.
According to the above description the method for associating the angles of
arrival and time differences of arrival TDOA is as follows:
Step E.1: Estimation of the signal S(t) on the basis of the incidences {θ1•••θM+p}
and of the signal x(t) of equation (1) according to the method of steps C.1 and
C.2 described previously.
Step E.2: i=1 ψd = Ø and ψr =Ø
Step E.3: On the basis of the i-th component si(t) of s(t) construction of the
vectors x(t) = [st(t + LTe) ••• si(t - LT)]T and y(t) = xB(t) and then
construction of the criterion cxy(τ) of equation (35).
Step E.4: Search for the P maxima Δτk of the criterion cxy(τ) such that
cxy(Δτk)>η.
Step E.5: If θt ε{θ1d.•••.θMd} this corresponds to the presence of a direct path and
(Equation Removed)
Step E.6: If θi ε{θ1r.•••θPr} corresponds to the presence of a multi-path and
(Equation Removed)
Step E.7: i= i +1 and if i ≤ then return to step E.3. Location Module
Location of a source (transmitter-obstacle) on the basis of a pair of AOA-TDOA
parameters
The AOA-TDOA parameter pairs (θmd, Δτmd) and (θpr, Δτpr) make it possible to
locate respectively the transmitters Em and the reflectors (or obstacles) at Rp.
According to Figure 11, the method must determine the position of the
transmitter knowing that its direction of arrival is 0 and that the TDOA between
the two asynchronous stations A and B is Δτ. It is therefore necessary to solve the following equation system
(Equation Removed)
which has solution M = Em according to Figure 4. The coordinates (xm,ym) of Em then satisfy
(Equation Removed)
where c is the speed of light, (xA,yA) the coordinates of A and |AB| the
distance between A and B.
The uncertainty ellipse for the location of the transmitter at Em is constructed on
the basis of a knowledge of the standard deviation σΔτ and of the mean Δτ of
the TDOA Δτ as well as of the standard deviation and of the mean 9 of the
estimation of the angle of incidence "AOA" θ. The parameters of this ellipse are
illustrated in Figure 12.
The equation of the uncertainty ellipse is then

(Equation Removed)
for 0