Method and device for the relative positioning of a plurality of electronic apparatuses in communication with a communication device, and associated communication system
A method for relative positioning of electronic apparatuses in communication with a communication device establishing a set of communication channels through which the device exchanges electromagnetic signals with each electronic apparatus includes, for each electronic apparatus, estimating a vector for which the elements represent, respectively, transmission through the communication channels between the device and the respective electronic apparatus, for at least first and second electronic apparatuses, determining a minimum distance from the distances existing, for all possible phase-shift values, between a first vector having a predetermined norm which is colinear to the vector estimated for the first electronic apparatus, and a second vector having the predetermined norm which is colinear to the vector estimated for the second electronic apparatus and modified by applying a phase shift having a value among the possible values, and determining a position indicator for the first electronic apparatus based on the determined distance.
1 . A method for the relative positioning of a plurality of electronic apparatuses in communication with a communication device, the communication device establishing a set of communication channels through which the communication device exchanges electromagnetic signals with each of the electronic apparatuses, the method comprising:
for each of the electronic apparatuses, estimating a vector, the elements of the estimated vector respectively representing transmission through said communication channels between the communication device and the respective electronic apparatus;
for at least one pair of the electronic apparatuses comprising a first electronic apparatus and a second electronic apparatus, determining a minimum distance among the distances existing, for all the possible phase-shift values, between
a first vector having a predetermined norm and colinear to the vector estimated for the first electronic apparatus, and
a second vector having the predetermined norm, which is colinear to the vector estimated for the second electronic apparatus, and modified by application of a phase shift having a value among said possible values; and
determining a position indicator for the first electronic apparatus as a function of the determined distance.
2 . The positioning method according to claim 1 , wherein, for each of the electronic apparatuses, the vector is formed of complex numbers, the module and argument of which represent the attenuation and phase, respectively, of the transmission through a respective one of the communication channels between the communication device and the respective electronic apparatus.
3 . The positioning method according to claim 2 , wherein the minimum distance is determined by the following formula:
d
k
,
l
*
(
h
k
,
h
l
)
2
=
2
-
2
❘
"\[LeftBracketingBar]"
h
k
H
h
l
❘
"\[RightBracketingBar]"
h
k
2
h
l
2
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Math
.
16
]
with d* k,l being said minimum distance and h k and h l being the vectors associated with the first electronic apparatus and the second electronic apparatus, respectively.
4 . The positioning method according to claim 2 , further comprising determining a distance matrix, at least certain elements of the distance matrix being the minimum distances respectively determined for said at least one pair of electronic apparatuses.
5 . The positioning method according to claim 2 , wherein said position indicator for the first electronic apparatus is a coordinate vector.
6 . The positioning method according to claim 1 , wherein the minimum distance is determined by the following formula:
d
k
,
l
*
(
h
k
,
h
l
)
2
=
2
-
2
❘
"\[LeftBracketingBar]"
h
k
H
h
l
❘
"\[RightBracketingBar]"
h
k
2
h
l
2
[
Math
.
16
]
with d* k,l being said minimum distance and h k and h l being the vectors associated with the first electronic apparatus and the second electronic apparatus, respectively.
7 . The positioning method according to claim 6 , further comprising determining a distance matrix, at least certain elements of the distance matrix being the minimum distances respectively determined for said at least one pair of electronic apparatuses.
8 . The positioning method according to claim 6 , wherein said position indicator for the first electronic apparatus is a coordinate vector.
9 . The positioning method according to claim 1 , further comprising determining a distance matrix, at least certain elements of the distance matrix being the minimum distances respectively determined for said at least one pair of electronic apparatuses.
10 . The positioning method according to claim 9 , further comprising applying size reduction to said determined distance matrix.
11 . The positioning method according to claim 10 , wherein said position indicator for the first electronic apparatus is a coordinate vector.
12 . The positioning method according to claim 9 , wherein said position indicator for the first electronic apparatus is a coordinate vector.
13 . The positioning method according to claim 1 , wherein said position indicator for the first electronic apparatus is a coordinate vector.
14 . The positioning method according to claim 1 , wherein the first vector and the second vector are normalized in such a way that their associated predetermined norms are unitary.
15 . A device for the relative positioning of a plurality of electronic apparatuses in communication with a communication device, the communication device establishing a set of communication channels through which the communication device exchanges electromagnetic signals with each of the electronic apparatuses, the positioning device comprising:
one or more processors configured to:
estimate, for each of the electronic apparatuses, a vector, the elements of the estimated vector respectively representing transmission through said communication channels between the communication device and the respective electronic apparatus,
determine, for at least one pair of the electronic apparatuses comprising a first electronic apparatus and a second electronic apparatus, a minimum distance among the distances existing, for all the possible phase-shift values, between
a first vector having a predetermined norm and colinear to the vector estimated for the first electronic apparatus, and
a second vector having the predetermined norm, which is colinear to the vector estimated for the second electronic apparatus and modified by application of a phase shift having a value among said possible values, and
determine a position indicator for the first electronic apparatus as a function of the determined distance.
16 . A communication system comprising:
the communication device provided with the positioning device according to claim 8 , and
said plurality of electronic apparatuses in communication with the communication device.