System and method for improving the accuracy of time of arrival measurements in a wireless ad-hoc communications network
View Patent ↗A system and method for improved Time Of Arrival (TOA) distance measurements between nodes of a wireless ad-hoc network. Specifically, the present invention is a system and method of distance estimation using square-root raised-cosine pulse shaping and chip matched filters on direct sequence spreading waveforms, the multiplication of which produces raised-cosine filtered pulse responses. The responses are used to identify a time when a function is at a maximum, corresponding to the actual signal reception time. The system and method produces a raised-cosine filtered pulse response and an auto-correlation function based on a received signal. A peak value of the auto-correlation function is calculated based on a quadratic approximation, which is corrected using a signal sampling phase offset detected between the raised-cosine filtered pulse response and the calculated peak value. The calculated peak value is then corrected to represent an actual reception time for received signals.
1. A method to determine signal propagation time between nodes in an ad-hoc communications network, said nodes being adapted to transmit and receive signals to and from other nodes in said ad-hoc network, the method comprising:
controlling a first node of said plurality to receive at least one signal communicated from a second node, and to calculate a response based on said signal;
controlling said first node to calculate an auto-correlation function of said response, and to calculate an approximate peak value of a quadratic approximation based on said auto-correlation function;
controlling said first node to determine a signal sampling phase offset between said response and said approximate peak value and in response, to calculate an actual peak value of said response; and
controlling said first node to calculate an actual reception time for said at least one signal at said first node based on said actual peak value, and to determine, based on said actual reception time, a signal propagation time.
2. A method as claimed in claim 1 , further comprising:
controlling said first node to calculate said response based on an application of a square-root raised-cosine pulse shaping and chip-matched filter on a direct sequence spreading waveform of said signal to produce at least one square-root raised cosine function.
3. A method as claimed in claim 2 , wherein:
said response comprises a superposed multiplication of each said square-root raised cosine function.
4. A method as claimed in claim 1 , further comprising: controlling said first node to calculate said auto-correlation function of said response wherein said auto-correlation function is based on the following equation:
p
RC
(
t
)
=
[
cos
(
πα
[
t
2
T
c
]
)
(
1
-
[
2
α
(
t
2
T
c
)
]
2
)
sin
(
π
(
t
2
T
c
)
)
(
π
(
t
2
T
c
)
)
]
2
wherein T c is a chip period value and α is an alpha filter parameter.
5. A method as claimed in claim 1 , further comprising:
controlling said first node to calculate said approximate peak value of said quadratic approximation wherein said quadratic approximation is based on the following equation:
Y=A ( t 2 )+ B ( t )+ C.
6. A method as claimed in claim 1 , further comprising:
controlling said first node to calculate said approximate peak value of said quadratic approximation wherein said approximate peak value is based on the following equation:
δ
=
-
1
2
(
y
+
-
y
-
y
+
+
y
-
-
2
y
0
)
wherein y − , y + and Y 0 are a first, second and third equidistant point located on said quadratic approximation.
7. A method as claimed in claim 1 , further comprising:
controlling said first node to calculate said sampling phase offset wherein said sampling phase offset is based on the following equation:
δ′=δ( a−b |δ|)
wherein δ is said approximate peak value of said quadratic approximation, and δ′ is said sampling phase offset; and
controlling said first node to calculate said actual peak value of response based on said approximate peak value and said sampling phase offset.
8. A system to determine signal propagation time between nodes in an ad-hoc communications network, said nodes being adapted to transmit and receive signals to and from other nodes in said ad-hoc network, the system comprising:
a controller, adapted to control a first node of said plurality to receive at least one signal communicated from a second node, and to calculate a response based on said signal;
said controller being further adapted to control said first node to calculate an auto-correlation function of said response, and to calculate an approximate peak value of a quadratic approximation based on said auto-correlation function;
said controller being further adapted to control said first node to determine a signal sampling phase offset between said response and said approximate peak value and in response, to calculate an actual peak value of said response; and
said controller being further adapted to control said first node to calculate an actual reception time for said at least one signal at said first node based on said actual peak value, and to determine, based on said actual reception time, a signal propagation time.
9. A system as claimed in claim 8 , wherein: said controller is adapted to control said first node to calculate said response based on an application of a square-root raised-cosine pulse shaping and chip-matched filter on a direct sequence spreading waveform of said signal to produce at least one square-root raised cosine function.
10. A system as claimed in claim 9 , wherein:
said response comprises a superposed multiplication of each said square-root raised cosine function.
11. A system as claimed in claim 8 , wherein:
said controller is adapted to control said first node to calculate said auto-correlation function of said response wherein said auto-correlation function is based on the following equation:
p
RC
(
t
)
=
[
cos
(
πα
[
t
2
T
c
]
)
(
1
-
[
2
α
(
t
2
T
c
)
]
2
)
sin
(
π
(
t
2
T
c
)
)
(
π
(
t
2
T
c
)
)
]
2
wherein T c is a chip period value and α is an alpha filter parameter.
12. A system as claimed in claim 8 , wherein:
said controller is adapted to control said first node to calculate said approximate peak value of said quadratic approximation wherein said quadratic approximation is based on the following equation:
Y=A ( t 2 )+ B ( t )+ C.
13. A system as claimed in claim 8 , wherein:
said controller is adapted to control said first node to calculate said approximate peak value of said quadratic approximation wherein said approximate peak value is based on the following equation:
δ
=
-
1
2
(
y
+
-
y
-
y
+
+
y
-
-
2
y
0
)
wherein y − , y + and y 0 are a first, second and third equidistant point located on said quadratic approximation.
14. A system as claimed in claim 8 , wherein:
said controller is adapted to control said first node to calculate said sampling phase offset wherein said sampling phase offset is based on the following equation:
δ′=δ( a−b |δ|)
wherein δ is said approximate peak value of said quadratic approximation, and δ′ is said sampling phase offset; and
controlling said first node to calculate said actual peak value of said response based on said approximate peak value and said sampling phase offset.
15. A computer-readable medium of instructions, adapted to determine signal propagation time between nodes in an ad-hoc communications network, said nodes being adapted to transmit and receive signals to and from other nodes in said ad-hoc network, comprising:
a first set of instructions, adapted to control a first node of said plurality to receive at least one signal communicated from a second node, and to calculate a response based on said signal;
a second set of instructions, adapted to control said first node to calculate an auto-correlation function of said response, and to calculate an approximate peak value of a quadratic approximation based on said auto-correlation function;
a third set of instructions, adapted to control said first node to determine a signal sampling phase offset between said response and said approximate peak value and in response, to calculate an actual peak value of response; and
a fourth set of instructions, adapted to control said first node to calculate an actual reception time for said at least one signal at said first node based on said actual peak value, and to determine a signal propagation time based on said actual reception time.
16. A computer-readable medium of instructions as claimed in claim 15 , wherein:
said first set of instructions is adapted to control said first node to calculate said response based on an application of a square-root raised-cosine pulse shaping and chip-matched filter on a direct sequence spreading waveform of said signal to produce at least one square-root raised cosine function.
17. A computer-readable medium of instructions as claimed in claim 16 , wherein:
said response comprises a superposed multiplication of each said square-root raised cosine function.
18. A computer-readable medium of instructions as claimed in claim 15 , wherein:
said second set of instructions is adapted to control said first node to calculate said auto-correlation function of said response wherein said auto-correlation function is based on the following equation:
p
RC
(
t
)
=
[
cos
(
πα
[
t
2
T
c
]
)
(
1
-
[
2
α
(
t
2
T
c
)
]
2
)
sin
(
π
(
t
2
T
c
)
)
(
π
(
t
2
T
c
)
)
]
2
wherein T c is a chip period value and α is an alpha filter parameter.
19. A computer-readable medium of instructions as claimed in claim 15 , wherein:
said second set of instructions is adapted to control said first node to calculate said approximate peak value of said quadratic approximation wherein said quadratic approximation is based on the following equation:
Y=A ( t 2 )+ B ( t )+ C.
20. A computer-readable medium of instructions as claimed in claim 15 , wherein:
said second set of instructions is adapted to control said first node to calculate said approximate peak value of said quadratic approximation wherein said approximate peak value is based on the following equation:
δ
=
-
1
2
(
y
+
-
y
-
y
+
+
y
-
-
2
y
0
)
wherein y − , y + and Y 0 are a first, second and third equidistant point located on said quadratic approximation.
21. A computer-readable medium of instructions as claimed in claim 15 , wherein:
said third set of instructions is adapted to control said first node to calculate said sampling phase offset wherein said sampling phase offset is based on the following equation:
δ′=δ( a−b |δ|)
wherein δ is said approximate peak value of said quadratic approximation, and δ′ is said sampling phase offset; and
said third set of instructions being further adapted to control said first node to calculate said actual peak value of said response based on said approximate peak value and said sampling phase offset.
22. A method as claimed in claim 1 , wherein said response is a raised-cosine filtered pulse response.
23. A system as claimed in claim 8 , wherein said response is a raised-cosine filtered pulse response.
24. A computer-readable medium of instructions as claimed in claim 15 , wherein said response is a raised-cosine filtered pulse response.