Computer implemented method for estimating interferers of radiofrequency system, computer program, and device
A method comprising: Obtaining observations Z_n, and building an observation vector Z=[Z_1, . . . , Z_n, . . . , Z_N], Defining a latent variable V_n, to build a vector of latent variables V=[V_1, . . . , V_n, . . . , V_N], and Implementing a Dirichlet process involving a Gibbs sampling with a Markov chain, the sampling being repeated as follows until convergence: For n−1, . . . , N, if the observation Z_n is associated to a source, remove observation Z_n from a source corresponding to latent variable V_n, and retrieve a position posterior of this source as the observation Z_n is belonging to this source; Draw a new value of latent variable V_n, based on a conditional probability; Associate the observation Z_n to the source, and update the posterior distribution of the position for the source, and, upon convergence of the algorithm, operating a separation of the interfering sources into K independent measurement sets, and an estimation of each source position.
1 . A computer implemented method for estimating interferers of a radiofrequency system embarked in a moving vehicle, the method comprising:
obtaining a trajectory of the moving vehicle at each time n, with a non-overlapping condition between the interferers considered as K independent active sources of interference having respective positions θ=[θ 1 , . . . , θ k , . . . , θ K ],
obtaining observations Z n corresponding to measurement, measured by an interface of the radiofrequency system in the moving vehicle, of interference from time instant 1 to N, and building an observation vector Z=[Z 1 , . . . , Z n , . . . , Z N ],
defining a latent variable V n indicating which source is activated at moment n, to build a vector of latent variables V=[V 1 , . . . , V n , . . . , V N ], and
implementing a Dirichlet process involving a Gibbs sampling with a Markov chain defined by vector V=[V 1 , . . . , V n , . . . , V N ], the sampling as follows, being repeated until convergence:
for n=1, . . . , N,
if the observation Z n is already associated to a source, remove observation Z n from its current associated source corresponding to latent variable V n , and retrieve a position posterior of this source as the observation Z n is no longer belonging to this source,
draw a new value of latent variable V n , based on a conditional probability P(V n =k|V −n , Z −n , Z n ) depending on whether a source k pre-existed or not,
Associate the observation Z n to the source corresponding to latent variable V n , and update the posterior distribution of the position for the source corresponding to latent variable V n ,
and, upon convergence of the algorithm, operating thereby:
a separation of interfering sources into K independent measurement sets related respectively to the K interfering sources, and
an estimation of each source position with the interfering sources thus separated.
2 . The method of claim 1 , wherein a probability is evaluated to identify which source an observation Z n belongs to, said probability being given by:
P
(
V
n
❘
"\[RightBracketingBar]"
V
-
n
,
Z
-
n
,
Z
n
)
∝
P
(
Z
n
❘
"\[RightBracketingBar]"
V
-
n
,
Z
-
n
,
V
n
)
P
(
V
n
❘
"\[RightBracketingBar]"
V
-
n
)
=
P
(
V
n
❘
"\[RightBracketingBar]"
V
-
n
)
∫
p
(
z
n
(
Vn
)
-
n
(
V
n
)
,
θ
V
n
)
·
p
(
θ
V
n
❘
"\[RightBracketingBar]"
Z
-
n
(
V
n
)
)
d
θ
V
n
where ( ) −n refers to an index other than n, a probability
p
(
Z
n
(
V
n
)
-
n
(
V
n
)
,
θ
V
n
)
being a conditional probability of an observation Z n to be associated to the source corresponding to latent variable V n , given other measurement Z −n already associated to this source.
3 . The method of claim 2 , wherein the posterior distribution of the position is updated progressively to estimate the source's position by implementing:
P
(
θ_
(
V_n
)
❘
"\[RightBracketingBar]"
Z_
(
-
n
)
∧
(
(
V_n
)
)
,
Z_n
∧
(
(
V_n
)
)
)
=
(
P
(
Z_n
∧
(
(
V_N
)
)
❘
"\[RightBracketingBar]"
Z_
(
-
n
)
∧
(
(
V_n
)
)
,
θ_
(
V_n
)
)
P
(
θ_k
⊣
❘
"\[RightBracketingBar]"
Z_
(
-
n
)
∧
(
(
V_N
)
)
)
)
/
(
P
(
Z_n
∧
(
(
V_n
)
)
❘
"\[RightBracketingBar]"
Z_
(
-
n
)
∧
(
(
V_
n
)
)
)
)
where ( ) −n refers to an index other than n.
4 . The method of claim 3 , wherein the probability
p
(
Z
n
(
V
n
)
-
n
(
V
n
)
,
θ
V
n
)
is expressed as:
p
(
Z
n
(
V
n
)
-
n
(
V
n
)
,
θ
V
n
)
=
1
2
π
σ
(
n
❘
"\[RightBracketingBar]"
-
n
)
(
V
n
)
2
e
-
(
z
n
-
μ
(
n
❘
"\[RightBracketingBar]"
-
n
)
(
V
n
)
)
2
2
σ
(
n
❘
"\[RightBracketingBar]"
-
n
)
(
V
n
)
2
.
5 . The method of claim 4 , wherein the terms
μ
(
n
❘
"\[RightBracketingBar]"
-
n
)
(
V
n
)
and
σ
(
n
❘
"\[RightBracketingBar]"
-
n
)
(
V
n
)
are calculated as follows:
{
μ
n
❘
-
n
(
V
n
)
=
μ
n
(
V
n
)
+
∑
n
❘
-
n
(
V
n
)
∑
-
n
(
V
n
)
-
1
(
Z
-
n
(
V
n
)
-
μ
-
n
(
V
n
)
)
σ
n
❘
-
n
(
V
n
)
2
=
σ
2
-
∑
n
❘
-
n
(
V
n
)
∑
-
n
(
V
n
)
-
1
∑
-
n
❘
n
(
V
n
)
,
where:
μ
n
(
V
n
)
denotes a mean in a gaussian distribution for the observation Z n , and expressed as
μ
n
(
V
n
)
=
a
+
b
log
T
n
-
θ
V
n
∑
(
n
❘
"\[RightBracketingBar]"
-
n
)
(
V
n
)
denotes a correlation matrix between observation n and the other observation than n of source V n ,
∑
-
n
(
V
n
)
denotes an auto-correlation matrix of observations other than n of source V n ,
μ
-
n
(
V
n
)
denotes the mean at observations other than n of source V n ,
∑
(
-
n
❘
"\[RightBracketingBar]"
n
)
(
V
n
)
denotes the correlation matrix between observations other than n and observation n of source V n .
6 . The method according to claim 2 , wherein the conditional probability p(V n =k|V −n ) is given by:
p
(
V
n
=
k
❘
V
-
n
)
=
N
k
+
α
K
N
-
1
+
α
where N k is a number of observations associated to a source corresponding to V n , N is a total number of observations, a being a concentration parameter.
7 . The method of claim 6 , wherein the number of possible interferers K is unknown and:
the conditional probability for an observation to belong to a pre-existing source k is given by:
p
(
V
n
=
k
❘
V
-
n
)
=
N
k
N
-
1
+
a
and the conditional probability for an observation to belong to a new source k′ is given by:
p
(
V
n
=
k
′
❘
V
-
n
)
=
α
N
-
1
+
a
.
8 . The method of claim 2 , wherein the conditional probability equals to:
b
N
k
N
-
1
+
α
∫
p
(
Z
n
(
k
)
-
n
(
k
)
,
θ
k
)
·
p
(
θ
k
❘
"\[RightBracketingBar]"
Z
-
n
(
k
)
)
d
θ
k
,
for an existing source k,
or to
b
α
N
-
1
+
α
∫
p
(
Z
n
❘
θ
)
·
G
0
(
θ
)
d
θ
,
for a new source,
where b is an appropriate normalizing constant making the above given probabilities sum to one.
9 . The method according to claim 1 , wherein the Dirichlet process involves a Dirichlet mixture model defined as:
{
Z
n
❘
V
n
,
θ
∼
N
(
μ
n
(
V
n
)
,
σ
n
2
(
V
n
)
)
@
V
n
∼
Discrete
(
p
1
,
…
,
p
K
)
p
∼
Dirichlet
(
α
/
K
)
θ
k
∼
G
0
Where G 0 is a base distribution of position of a source.
10 . The method according to claim 1 , comprising further an estimation of a likelihood p
p
(
Z
n
(
V
n
)
-
n
(
V
n
)
,
θ
V
n
)
,
as a function of a mobile vehicle position T n , given by:
p
(
Z
n
(
V
n
)
-
n
(
V
n
)
,
θ
V
n
)
=
A
·
exp
(
-
B
(
∑
n
c
n
log
(
θ
-
T
n
)
-
h
′
)
2
)
.
11 . The method according to claim 10 , wherein position θ is discretized into discrete values in a discrete space Ω θ , each value of position θ in said discrete space being associated with a probability.
12 . The method according to claim 10 , wherein a continuous position determination is performed by partitioning a space around the mobile vehicle position into sub-partitions s=1, . . . , S, each sub-partition being represented by a center C s , the mobile vehicle position T n being in sub-partition s, and the likelihood being given by:
p
(
Z
n
(
V
n
)
-
n
(
V
n
)
,
θ
V
n
)
=
A
exp
(
-
B
(
∑
n
c
n
log
(
θ
-
T
n
)
-
h
′
)
2
)
≈
A
exp
(
-
B
(
∑
s
w
s
log
(
θ
-
C
s
n
)
-
h
′
)
2
)
Where
C
s
i
is determined by
C
s
n
=
arg
min
C
s
-
C
s
❘
"\[RightBracketingBar]"
,
And a base distribution G 0 is given by
G
0
(
θ
)
=
A
0
exp
(
-
B
0
(
∑
s
w
s
0
log
(
θ
-
C
s
)
-
h
0
′
)
2
)
.
13 . Computer program comprising instructions for performing the method according to claim 1 when such instructions are executed by a processing circuit.
14 . Device comprising a processing circuit configured to implement the method according to claim 1 .