CLAIMS
1 - A method for determining the optimal position of identical sensors within a communications array of dimension d-D (1≤d≤3) intended to perform goniometry measurements, said goniometry measurements minimizing the ambiguities, by taking account of parameters of a specification comprising single-source performance of the array as represented by uncertainty ellipses or an interval for the case of one-dimensional arrays, the footprint resulting from the size of a sensor array, the resolving power in the presence of two sources, characterized in that it comprises at least the following steps:
0 - initializing to 0 an array index i and to I the number of arrays available,
1 - randomly picking an array having a structure of N sensors disposed in initial positions pd,n (1≤n≤N),
2 - determining the matrix Dppdirectional obeying the uncertainty ellipse
given in the specification or the interval for one-dimensional arrays, the axes of the uncertainty ellipse in the space of the angles of azimuth and of elevation being defined by the minimum and maximum standard deviations σθmin=θdirectional = minθσθ
and σθmax=θdirectional π/2 = maxθσθ in azimuth knowing that σθ= √E[(θm -θm)2]) and by
the standard deviation in elevation σΔ= √E[(Δm-Δm)2] , said determination comprising the following steps:
3 - calculating the correlation matrix Dpp of the positions pd,n of the sensors of an initial d-D array
(Equation Removed)
where d is the dimension of the array of sensors and n the index of the sensor,
4 - determining the values σd,1=σθmin |cos(Δm)| and
σd,d = σθmax |cos(Δm |) (σ3,2 = σΔ for the 3-D arrays with d=3) of the axes of
the uncertainty ellipse in the space of the wave vector on the basis of σθmin
and σθmax which are the axes of the uncertainty ellipse in the space of the
azimuth and of the elevation or corresponding to the interval in the one-dimensional case, with d = 1, 2 or 3,
where σθmin and σθmax are the minimum and maximum values of the azimuthal
precision at the elevation Δm as well as a precision σΔ at Δm = 0.,
5 - calculating the size of each array Di by taking account of the
axes of the uncertainty ellipses σd,i in the space of the wave vector which
depend on the axes of the ellipse in the space of the azimuth and of the
elevation which are given in the specification:Di =((√α/8N)σd,i)λ for
1≤i≤d,
with N the number of sensors, a a parameter dependent on the type of performance as indicated in Table-1, λ the wavelength
6 - determining the correlation matrix Dppdirectional by using
(Equation Removed)
where (D,) and h, are respectively the eigenvalues and eigenvectors
of Dppdirectional and the hi depend on θdirectional
7 - determining the position pd,n of each sensor n of the directional
array, by performing pdndirectional =(Dppdirectional)1/2 Dpp -1/2(pd,n-p)
8 - testing whether the values of the positions of the sensors satisfy
the technical conditions given in the specification and if not, varying the value of i
to i+1, i=i+1 and if i≤l then returning to the step of drawing an initial array.
2 - The method as claimed in claim 1, characterized in that for an array
of dimension 2 in which the uncertainty ellipse is characterized by its major axis and
its minor axis, said method comprising the following steps:
determining the values of σd,1 = σθmin |cos(Δm)| and σd,2=σΔmax|cos(Δm)|
σθmin ≤ σθ ≤ σθmax with (Equation Removed)
determining the sizes
Di =((√α/8N)/σd,i)λ of the array for 1 ≤i≤2 and determining the correlation matrix Dppdlrectional
Dppdlrectional = (Equation Removed)

on the basis of θdirectional =θm -π/2, determining the positions of the sensors of the directional array
P2,ndirectional =(Dppdirectional )1/2 Dpp -1/2 (P2,n -p)
3 - The method as claimed in claim 1, characterized in that for an array
of sensors in 3 dimensions, the uncertainty ellipse corresponds to an ellipsoid which
contains 3 axes and two angles and said method comprises at least the following
steps:
determining the values of σd,1 = σθmin |cos(Δm)|, σd,2 = σΔ and σd,3 = σθmax |cos(Δm)|
(Equation Removed)
where σΔ is the standard deviation in azimuth given in the specification at Δ=Δm,
on the basis of the specification giving the directional azimuth θdirectionaol =θm -π/2 for
which the azimuthal precision crg is a minimum
determining the sizes Di = ((√α/8N)/σd,i)λ of the array for 1≤i≤3
determining the value of the matrix
Dppdirectional _(Equation Removed)

and, on the basis of said matrix, determining the position of the sensors of the directional array
P3,n directional =(Dpp directional )1/2 Dpp -1/2 (p3,n -p)
4 - The method as claimed in claim 1, characterized in that the array is a one-dimensional linear array of sensors, the uncertainty ellipse being in this case characterized by the standard deviation and the bias of the precision in estimating the component of the wave vector projecting on a line and in that it comprises at least the following steps, in the case where the azimuth is fixed:
Calculation of σd,1 = σΔ |sin(Δm)cos(θ0)| by using the data of the table
(Table Removed)
Calculation of the array sizes D1 by performing D1 =((√α/8N)/σd,1)λ Calculation of the correlation matrix
Dpp directional=(D1)2
Calculation of the position of the sensors of the directional array by performing
(Equation Removed)
5 - The method as claimed in claim 1, characterized in that it comprises a step in the course of which omnidirectionality and resolving power criteria are determined on the basis of the position pd,n of the sensors of an array whether it be the array drawn initially or else the directional array defined by taking account of the covariance matrix Dpp of the positions of the sensors and of
(Equation Removed)
on the basis of Qpp and of Dpp determining the value of Qpp decomposing the matrix Qpp into eigenelements thereby leading to
(Equation Removed)

determining the criterion, for omnidirectionality in resolution
(Equation Removed)
determining the resolving power Rpower = min|Qi -1|
comparing these two values with values given in the specification and if the values determined do not satisfy the criterion of the specification, choosing a new array and repeating the various steps of calculating the position of the sensors and omnidirectionality and resolving power criteria, for arrays of dimension 1, 2 or 3.
6 - The method as claimed in claim 1, characterized in that it comprises a step in the course of which the arrays are, ranked as a function of a degree of ambiguity by executing the following steps: ,.
Initializing a set ψ containing arrays and their characteristics,
Determining, for an array, the criterion η1ambig of the robustness to
ambiguities of order 1 on the basis of the knowledge of the frequency fmax
(Equation Removed)
where λmax -cl fmm knowing that f≤fmax. with Δk corresponding to a distance
(Equation Removed)
where 0d = [0 • • • 0]T. Knowing that kd (Θ1)H kd (Θ1) ≤ 1 and that kdHkd ≤ 1
Ranking the elements contained in ψ according to the level of the ambiguities of order 1 such that ultimately
ψ={(ηambig(k),pd,n (k)) for (1≤k≤K) with η1ambig(1) ≥---≥η1ambig(K)}
Ranking from the array most robust to ambiguities of order 1 to the least robust
array by executing the following steps
Storage of the nb best arrays in relation to the ambiguities of order 1 such that
ψopt ψ with ψopt ={(η1ambig(k),pd,n(k)) for (1≤k ≤ nb)}
Repeating said steps for all the arrays i=1,... l
Calculation of the ambiguities of order P of the arrays of ψopt according to
the criterion of robustness to ambiguities of order P ΗP (λ)k for the wavelength λ satisfying
PR(ΗF(λ)k < ΗP (λ)) = Pfa for 1≤k≤nb (67)
where Pr(.) is a probability and where pfa typically equals 5% to obtain ψopt={(η1ambig(k),ηp(c/fmax)(k) ,Pd,n(k)) for (1≤k≤nb)}. Ranking of the elements of ψopt according to the level of the ambiguities of order P such that ultimately
ψopt={(η1ambig(k),ηp(c/fmax)(k) ,Pd,n(k)) for (1≤k≤nb)} with ηP(1) ≥ •••≥ηP(nb)}: Ranking from the array most robust to ambiguities of order P to the least robust array.
7 - The method as claimed in one of claims 1 to 6, characterized in that
the array of sensors is an array comprising two V-shaped branches over which are
distributed, the two branches forming an angle 5.
8 - The method as claimed in one of claims 1 to 6, characterized in that
the array of sensors is an array for which the distribution of the sensors is disposed
on a double circle.
9 - The method as claimed in one of claims 1 to 6, characterized in that
the initial array is a d-D sensor array, the distribution of whose sensors follows a
Gaussian law.
10 - The method as claimed in one of claims 1 to 6, characterized in that
the initial array is an array of sensors of dimension d-D, the sensors being
distributed according to a uniform law.
11 - The use of the method as claimed in one of claims 1 to 8,
characterized in that it operates in the UHF or VHF band.