Determining a position of a mobile receiver
View Patent ↗The invention relates to a method and to a mobile receiver for determining a position of a mobile receiver RX, which moves in an unknown but at least quasi-stationary environment, on the basis of signals s(kT) which are emitted by a transmitter TX positioned at an unknown position and immobile in the environment, wherein the receiver RX receives as reception signal q ( k , τ ) = ∑ i = 0 N ( k ) - 1 S i ( τ ) a signal s(kT) which is emitted by the transmitter TX and which is transmitted via N(k) transmission paths as signal components s i (τ), where k:=time step, τ:=time delay, and i=0, . . . , N(k)−1, wherein, as interactions: reflections of the signal components s i (τ) at reflectors and scatterings of the signal components s i (τ) at scatterers are taken into account on the transmission paths, wherein on the basis of the reception signals q(k,τ) the following are determined: a position r u (k) and a velocity v u (k) of the receiver RX, and for each of the N(k) transmission paths, in each case a position r v,i (k) of a virtual transmitter vTX i , and a transmission path distance d v,i between the transmitter TX and a last scatterer SCATTER i lying on the i-th transmission path, provided that such a scatterer SCATTER i is present, wherein: a signal component s i (τ) of the signal s(kT) that is transmitted on the i-th transmission path no longer experiences further scattering between the last scatterer SCATTER i and the receiver RX, and, it is assumed that each signal component s i (τ) received by the receiver RX is emitted by an assigned virtual transmitter vTX i and has reached the receiver RX directly without interaction, and at least the determined position r u (k) of the receiver RX and/or the velocity v u (k) of the receiver RX are/is provided and/or output for further evaluations.
1. A method for determining the position of a mobile receiver RX, which moves in an unknown but at least quasi-stationary environment, on the basis of signals s(τ) which are emitted by a transmitter TX positioned at an unknown position and immobile in the environment, wherein the receiver RX receives a signal s(τ) emitted by the transmitter TX, which is transmitted via N(k) transmission paths as signal components s i (τ), as reception signal
q
(
k
,
τ
)
=
∑
i
=
0
N
(
k
)
-
1
s
i
(
τ
)
,
where k:=time step, τ:=time delay, and i=0, . . . , N(k)−1, wherein, as interactions: reflections of the signal components s i (τ) at reflectors and scatterings of the signal components s i (τ) at scatterers are taken into account on the transmission paths, the method comprising:
determining, on the basis of the reception signals q(k,τ) a position r u (k) and a velocity v u (k) of the receiver RX, and for each of the N(k) transmission paths in each case a position r v,i (k) of a virtual transmitter vTX i , and a transmission path distance d v,i between the transmitter TX and a last scatterer SCATTER i lying on the i-th transmission path, provided that such a scatterer SCATTER i is present, wherein:
a signal component s i (τ) of the signal s(kT) that is transmitted on the i-th transmission path no longer experiences further scattering between the last scatterer SCATTER i and the receiver RX, and,
for the virtual transmitters vTX i , it is assumed that each signal component s i (τ) received by the receiver RX is emitted by an assigned virtual transmitter vTX i and has reached the receiver RX directly without interaction; and
providing or outputting at least the determined position r u (k) of the receiver RX and/or the velocity v u (k) of the receiver RX for further evaluations.
2. The method according to claim 1 , wherein the method further comprises using a simultaneous localization and mapping (SLAM) algorithm to determine the position r u (k) and the velocity v u (k) of the receiver RX, and the positions r v,i (k) of the virtual transmitters vTX i and the transmission path distances d v,i .
3. The method according to claim 1 , wherein the method further comprises:
defining a state vector X(k) where:
X ( k )=[ r u ( k ) T ,v u ( k ) T ,x v,0 ( k ) T , . . . ,x v,N(k)−1 ( k ) T ] T , (1)
where:
r u (k): position of the receiver RX at time step k,
v u (k): velocity vector of the receiver RX at time step k, and
x y,i (k)=[r v,i (k) T , d v,i ] T : state vector of the virtual transmitter vTX i at time step k, wherein r v,i (k) T is the position of the transmitter vTX i and d v,i is the transmission path distance; and
representing a temporal change of the state vector X(k) according to:
X ( k )= f k ( X ( k− 1), w ( k− 1)), (2)
where:
f k : linear or nonlinear function of X(k−1), and
w(k−1): noise term.
4. The method according to claim 1 , wherein the method further comprises:
defining a state vector X(k) where:
X ( k )=[ r u ( k ) T ,v u ( k ) T ,x v,0 ( k ) T , . . . ,x v,N(k)−1 ( k ) T ] T , (1)
where:
r u (k): position of the receiver RX at time step k:
v u (k): velocity vector of the receiver RX at time step k, and
x y,i (k)=[r v,i (k) T , d v,i ] T : state vector of the virtual transmitter vTX i at time step k, wherein r v,i (k) T is the position of the transmitter vTX i and d v,i is the transmission path distance; and
representing a temporal change of the state vector x v,i (k) according to:
X v,i ( k )= x v,i ( k− 1)+ w i ( k− 1), (3)
where:
w i (k−1): noise term, and therefore the position of the respective virtual transmitter remains approximately the same.
5. The method according to claim 3 , wherein the method further comprises determining the state vector X(k) by a recursively defined sequential Bayes filter.
6. The method according to claim 1 , wherein the method further comprises:
applying the following for the reception signals q(k,τ):
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i
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-
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i
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where:
s(kT): signal transmitted by the transmitter TX at time kT,
q(k,τ): signal received by the receiver RX,
α i (k): amplitude, and
n q (k): noise term at time step k.
7. The method according to claim 1 , wherein the method further comprises using a super resolution algorithm in order to estimate a time delay τ i (k) of the i-th signal component s i (τ) at the receiver RX.
8. The method according to claim 1 , wherein the method further comprises:
using the following distance model for the i-th signal component s i (τ):
d i ( k )=∥ r u ( k )− r v,i ( k )∥+ d v,i +n d ( k )= cτ i ( k ), (5)
where
d i (k): estimated propagation distance of the signal component s i (τ) from the virtual transmitter vTx i ,
c: speed of light, and
n d (k): noise term.
9. The method according to claim 1 , wherein the method further comprises predetermining, at the beginning of the process, for the position r u (k) and the velocity v u (k) of the receiver RX, a start position r u (k=0) and a start velocity v u (k=0).
10. A mobile receiver RX, which is movable in an unknown but at least quasi-stationary environment and set up and designed for determining a position of the receiver RX on the basis of signals s(kT) which are emitted by a transmitter TX positioned at an unknown position and immobile in the environment, wherein the receiver RX receives a signal s(kT) emitted by the transmitter TX, which is transmitted via N(k) transmission paths as signal components s i (τ), as reception signal
q
(
k
,
τ
)
=
∑
i
=
0
N
(
k
)
-
1
s
i
(
τ
)
,
where k: time step, τ=time delay, and i=0, . . . , N(k)−1, wherein, as interactions, reflections of the signal components s i (τ) at reflectors and scatterings of the signal components s i (τ) at scatterers are taken into account on the transmission paths, the mobile receiver comprising:
an evaluation means designed and set up so that on the basis of the reception signals q(k,τ) the following are determined: a position r u (k) and a velocity v u (k) of the receiver RX, and for each of the N(k) transmission paths in each case: a position r v,i (k) of a virtual transmitter vTX i , and a transmission path distance d v,i between the transmitter TX and a last scatterer SCATTER i lying on the i-th transmission path, provided that such a scatterer SCATTER i is present, wherein:
a signal component s i (τ) of the signal s(kT) that is transmitted on the i-th transmission path no longer experiences further scattering between the last scatterer SCATTER i and the receiver RX, and,
for the virtual transmitters vTX i , it is assumed that each of the signal components s i (τ) received by the receiver RX is emitted by an assigned virtual transmitter vTX i and has reached the receiver RX directly without interaction; and
an output means to provide and/or output at least the determined position r u (k) of the receiver RX and/or the velocity v u (k) of the receiver RX for additional evaluations.
11. The mobile receiver according to claim 10 , wherein the evaluation means uses a simultaneous localization and mapping (SLAM) algorithm to determine the position r u (k) and the velocity v u (k) of the receiver RX, and the positions r v,i (k) of the virtual transmitters vTX i and the transmission path distances d v,i .
12. The mobile receiver according to claim 10 , wherein the evaluation means is further designed and set up to:
define a state vector X(k) where:
X ( k )=[ r u ( k ) T ,v u ( k ) T ,x v,0 ( k ) T , . . . ,x v,N(k)−1 ( k ) T ] T , (1)
where:
r u (k): position of the receiver RX at time step k,
v u (k): velocity vector of the receiver RX at time step k, and
x y,i (k)=[r v,i (k) T , d v,i ] T : state vector of the virtual transmitter vTX i at time step k, wherein r v,i (k) T is the position of the transmitter vTX i and d v,i is the transmission path distance; and
represent a temporal change of the state vector X(k) according to:
X ( k )= f k ( X ( k− 1), w ( k− 1)), (2)
where:
f k : linear or nonlinear function of X(k−1), and
w(k−1): noise term.
13. The mobile receiver according to claim 12 , wherein the state vector X(k) is determined by a recursively defined sequential Bayes filter.
14. The mobile receiver according to claim 10 , wherein the evaluation means is further designed and set up to:
define a state vector X(k) where:
X ( k )=[ r u ( k ) T ,v u ( k ) T ,x v,0 ( k ) T , . . . ,x v,N(k)−1 ( k ) T ] T , (1)
where:
r u (k): position of the receiver RX at time step k,
v u (k): velocity vector of the receiver RX at time step k, and
x y,i (k)=[r v,i (k) T , d v,i ] T : state vector of the virtual transmitter vTX i at time step k, wherein r v,i (k) T is the position of the transmitter vTX i and d v,i is the transmission path distance; and
represent a temporal change of the state vector x v,i (k) according to:
X v,i ( k )= x v,i ( k− 1)+ w i ( k− 1), (3)
where:
w i (k−1): noise term, and therefore the position of the respective virtual transmitter remains approximately the same.
15. The mobile receiver according to claim 14 , wherein the state vector X(k) is determined by a recursively defined sequential Bayes filter.
16. The mobile receiver according to claim 10 , wherein the evaluation means is further designed and set up to:
apply the following for the reception signals q(k,τ):
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k
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τ
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=
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i
=
0
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k
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-
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i
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where:
s(kT): signal transmitted by the transmitter TX at time kT,
q(k,τ): signal received by the receiver RX,
α i (k): amplitude, and
n q (k): noise term at time step k.
17. The mobile receiver according to claim 10 , wherein the evaluation means is further designed and set up to use a super resolution algorithm in order to estimate a time delay τ i (k) of the i-th signal component s i (τ) at the receiver RX.
18. The mobile receiver according to claim 10 , wherein the evaluation means is further designed and set up to:
use the following distance model for the i-th signal component s i (τ):
d i ( k )=∥ r u ( k )− r v,i ( k )∥+ d v,i +n d ( k )= cτ i ( k ), (5)
where
d i (k): estimated propagation distance of the signal component s i (τ) from the virtual transmitter vTx i ,
c: speed of light, and
n d (k): noise term.
19. The mobile receiver according to claim 10 , wherein the evaluation means is further designed and set up to predetermine, at the beginning of the process, for the position r u (k) and the velocity v u (k) of the receiver RX, a start position r u (k=0) and a start velocity v u (k=0).
20. The mobile receiver according to claim 10 , wherein the evaluation means is further designed and set up to predetermine, at the beginning of the process, for the position r u (k) and the velocity v u (k) of the receiver RX, a probability distribution for a start position r u (k=0) and a start velocity v u (k=0).
21. The method according to claim 4 , wherein the state vector X(k) is determined by a recursively defined sequential Bayes filter.
22. The method according to claim 1 , wherein the method further comprises predetermining, at the beginning of the process, for the position r u (k) and the velocity v u (k) of the receiver RX, a probability distribution for a start position r u (k=0) and a start velocity v u (k=0).