Tracking a target using doppler shift
For tracking a target, a method receives a combined signal comprising a target signal reflected by a target and a transmitter signal not reflected by the target, wherein the transmitter signal is comprised of a plurality of orthogonal frequency division multiplexing (OFDM) subcarrier signals. The method calculates a signal Fourier transform for the combined signal to obtain the complex symbols. The method estimates a sequence of channel state information. The method estimates CSI over for non-pilot OFDM subcarriers of the combined signal to obtain CSI for a sequence of M OFDM symbols. The method computes a CSI Fourier transform for the sequence of CSI for a plurality of OFDM subcarriers. The method estimates a CSI Doppler frequency by matching a Fourier transform template to the CSI Fourier transform. The method computes each of a target position and a target velocity vector for the target.
1 . A method comprising:
receiving a combined signal comprising a target signal reflected by a target and a transmitter signal not reflected by the target, wherein the transmitter signal is comprised of a plurality of orthogonal frequency division multiplexing (OFDM) subcarrier signals;
calculating a signal Fourier transform for the combined signal to obtain the complex symbols z m [n], where where n is the pilot subcarrier index, m is an OFDM symbol index;
estimating a sequence of channel state information (CSI) c m,n for pilot indices of the pilot subcarrier index for the OFDM subcarrier signals of the combined signal as ĉ m,n =(z m [n]/pilot m (n)) estimating CSI over for non-pilot OFDM subcarriers of the combined signal to obtain CSI for a sequence of M OFDM symbols;
computing a CSI Fourier transform for the sequence of CSI for a plurality of OFDM subcarriers;
estimating a mean Fourier transform by averaging the CSI Fourier transform of the CSI over at least one OFDM subcarriers;
estimating a CSI Doppler frequency by matching a central lobe template of a Fourier transform to the CSI Fourier transform indicating stationary components, and wherein a side lobe template is matched to side lobes of the Fourier transform indicative of Doppler frequency components; and
computing each of a target position and a target velocity vector for the target within a field of interest from the CSI Doppler frequency.
2 . The method of claim 1 , wherein the target position and/or the target velocity vector are determined based on the equation:
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wherein f d,i,j denotes Doppler frequency determined at receiver j from a signal transmitted at transmitter i, and wherein x (t) and y (t) are a position of the target at time t, x Rj (t) and y Rj (t) are a position of a receiver j at time t, x T,i (t) and y T,i (t) are a position of a transmitter i at time t, v x (t) and v y (t) are a velocity of the target ( 105 ) at the time t, fc is a carrier frequency of the combined signal ( 106 ).
3 . The method of claim 1 , wherein the central lobe is offset by a carrier offset frequency.
4 . The method of claim 1 , wherein the match between the frequency interval and the estimated frequency interval is identifyied using an extended Kalman filter.
5 . The method of claim 1 , wherein the CSI Doppler frequency is refined using a Viterbi algorithm.
6 . The method of claim 1 , wherein the CSI Doppler frequency is calculated using a complex ambiguity function.
7 . The method of claim 1 , wherein the OFDM symbols transmitted on OFDM subcarrier signals are estimated as
a
^
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,
n
=
Q
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z
m
[
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n
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,
wherein
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[
n
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represents quantizing
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n
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m
,
n
)
to a nearest point in the signal space and where ĉ m,n is the estimated CSI.
8 . An apparatus comprising:
a processor executing code stored on a memory to perform:
receiving a combined signal comprising a target signal reflected by a target and a transmitter signal not reflected by the target, wherein the transmitter signal is comprised of a plurality of orthogonal frequency division multiplexing (OFDM) subcarrier signals;
calculating a signal Fourier transform for the combined signal to obtain the complex symbols Z m [n], where where n is the pilot subcarrier index, m is an OFDM symbol index;
estimating a sequence of channel state information (CSI) c m,n for pilot indices of the pilot subcarrier index for the OFDM subcarrier signals of the combined signal as
c
^
m
,
n
=
(
z
m
[
n
]
pilot
m
(
n
)
)
;
estimating CSI over for non-pilot OFDM subcarriers of the combined signal to obtain CSI for a sequence of M OFDM symbols;
computing a CSI Fourier transform for the sequence of CSI for a plurality of OFDM subcarriers;
estimating a mean Fourier transform by averaging the CSI Fourier transform of the CSI over at least one OFDM subcarriers;
estimating a CSI Doppler frequency by matching a central lobe template of a Fourier transform to the CSI Fourier transform indicating stationary components, and wherein a side lobe template is matched to side lobes of the Fourier transform indicative of Doppler frequency components; and
computing each of a target position and a target velocity vector for the target within a field of interest from the CSI Doppler frequency.
9 . The apparatus of claim 8 , wherein the target position and/or the target velocity vector are determined based on the equation:
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d
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i
,
j
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x
(
t
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x
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)
]
i
=
1
,
2
,
…
,
I
,
j
=
1
,
2
,
…
,
J
.
wherein f d,i,j denotes Doppler frequency determined at receiver j from a signal transmitted at transmitter i, and wherein x (t) and y (t) are a position of the target at time t, x Rj (t) and y Rj (t) are a position of a receiver j at time t, x T,i (t) and y T,i (t) are a position of a transmitter i at time t, v x (t) and v y (t) are a velocity of the target ( 105 ) at the time t, fc is a carrier frequency of the combined signal.
10 . The apparatus of claim 8 , wherein the central lobe is offset by a carrier offset frequency.
11 . The apparatus of claim 8 , wherein the match between the frequency interval and the estimated frequency interval is identifyied using an extended Kalman filter.
12 . The apparatus of claim 8 , wherein the CSI Doppler frequency is refined using a Viterbi algorithm.
13 . The apparatus of claim 8 , wherein the CSI Doppler frequency is calculated using a complex ambiguity function.
14 . The apparatus of claim 8 , wherein the OFDM symbols transmitted on OFDM subcarrier signals are estimated as
a
^
m
,
n
=
Q
(
z
m
[
n
]
c
^
m
,
n
)
,
wherein
Q
(
z
m
[
n
]
c
^
m
,
n
)
represents quantizing
(
z
m
[
n
]
c
^
m
,
n
)
to a nearest point in the signal space and where ĉ m,n is the estimated CSI.
15 . A computer program product comprising a non-transitory computer storage medium storing code executable by a processor to perform:
receiving a combined signal comprising a target signal reflected by a target and a transmitter signal not reflected by the target, wherein the transmitter signal is comprised of a plurality of orthogonal frequency division multiplexing (OFDM) subcarrier signals;
calculating a signal Fourier transform for the combined signal to obtain the complex symbols Z m [n], where where n is the pilot subcarrier index, m is an OFDM symbol index;
estimating a sequence of channel state information (CSI) c m,n for pilot indices of the pilot subcarrier index for the OFDM subcarrier signals of the combined signal as
c
^
m
,
n
=
(
z
m
[
n
]
pilot
m
(
n
)
)
;
estimating CSI over for non-pilot OFDM subcarriers of the combined signal to obtain CSI for a sequence of M OFDM symbols;
computing a CSI Fourier transform for the sequence of CSI for a plurality of OFDM subcarriers;
estimating a mean Fourier transform by averaging the CSI Fourier transform of the CSI over at least one OFDM subcarriers;
estimating a CSI Doppler frequency by matching a central lobe template of a Fourier transform to the CSI Fourier transform indicating stationary components, and wherein a side lobe template is matched to side lobes of the Fourier transform indicative of Doppler frequency components; and
computing each of a target position and a target velocity vector for the target within a field of interest from the CSI Doppler frequency.
16 . The computer program product of claim 15 , wherein the target position and/or the target velocity vector are determined based on the equation:
f
d
,
i
,
j
(
x
(
t
)
,
y
(
t
)
,
v
x
(
t
)
,
v
y
(
t
)
)
=
-
f
c
c
[
(
v
x
(
t
)
,
v
y
(
t
)
)
·
(
(
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x
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j
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t
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x
(
t
)
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y
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t
)
)
-
(
x
R
,
j
(
t
)
,
y
R
,
j
(
t
)
)
]
i
=
1
,
2
,
…
,
I
,
j
=
1
,
2
,
…
,
J
.
wherein f d,i,j denotes Doppler frequency determined at receiver j from a signal transmitted at transmitter i, and wherein x (t) and y (t) are a position of the target at time t, x Rj (t) and y Rj (t) are a position of a receiver j at time t, x T,i (t) and y T,i (t) are a position of a transmitter i at time t, v x (t) and v y (t) are a velocity of the target ( 105 ) at the time t, fc is a carrier frequency of the combined signal ( 106 ).
17 . The computer program product of claim 15 , wherein the central lobe is offset by a carrier offset frequency.
18 . The computer program product of claim 15 , wherein the match between the frequency interval and the estimated frequency interval is identifyied using an extended Kalman filter.
19 . The computer program product of claim 15 , wherein the CSI Doppler frequency is refined using a Viterbi algorithm.
20 . The computer program product of claim 15 , wherein the CSI Doppler frequency is calculated using a complex ambiguity function.