Adaptive optimization of estimation of the angle of arrival of a signal received by an array of antenna elements
View Patent ↗A parameter of interest of a signal, such as the angle of arrival of a target signal received by an antenna system having an array of antenna elements, is estimated by (a) obtaining disparate observations of the target signal received by the antenna system; (b) with a computer, processing the disparate observations of the target signal to determine a subset of a set of possible further obtained disparate observations of the target signal for processing to enable an optimal estimation of the angle of arrival of the target signal; (c) obtaining the subset of further disparate observations of the signal; and (d) processing the obtained subset of further obtained disparate observations to obtain the optimal estimate of the parameter of interest.
1. A method of estimating the angle of arrival of a target signal received by an antenna system, comprising the steps of:
(a) obtaining disparate observations of a target signal received by an antenna system; and
(b) with a computer, processing the obtained disparate observations of the signal to select a subset of said disparate observations of the signal for processing to enable an optimal estimation of the angle of arrival of the signal.
2. A method according to claim 1 , further comprising the steps of:
(c) subsequent to step (b), obtaining the subset of said disparate observations of the signal; and
(d) with a computer, processing the subsequently obtained subset of said disparate observations to obtain the optimal estimate of the angle of arrival of the signal.
3. A method according to claim 1 , where step (b) comprises the steps of:
(c) processing the disparate observations of the signal to provide a plurality of estimates of the angle of arrival of the signal; and
(d) processing the plurality of estimates to determine the subset in accordance with which of the estimates is an optimal estimation of the angle of arrival of the signal.
4. A method according to claim 3 , wherein step (c) comprises the step of:
(e) using maximum-likelihood processing to estimate the angle of arrival of the target signal.
5. A method according to claim 4 , wherein step (e) comprises the step of:
(f) making the maximum-likelihood-estimation of the angle of arrival φ of the target signal in accordance with the equation:
φ MLE =argmin φ ∥y−Xz∥ 2
wherein
y=Xz+v
X
=
(
ⅇ
ⅈ
cos
(
ϕ
+
τ
1
)
ⅇ
ⅈcos
(
ϕ
+
τ
2
)
ⅇ
ⅈ
cos
(
ϕ
+
τ
3
)
ⅇ
ⅈcos
(
ϕ
+
τ
4
)
)
z is a vector of length two that represents unknown modulation of the target signal,
v is random noise, and
T is determined by the particular disparate observation of the target signal.
6. A method according to claim 3 , wherein step (d) comprises the step of:
(e) using minimization of variance of the estimates of the angle of arrival as a criterion for determining which of said estimates is an optimal estimation of the angle of arrival.
7. A method according to claim 6 , wherein step (e) comprises the step of:
(f) determining said variance for a particular said estimate by using a Cramer-Rao bound derived from a prior said determination of a said particular estimate as an optimal estimation of the angle of arrival.
8. A method according to claim 7 , wherein step (f) comprises the step of:
(g) determining the variance bound for said particular estimate of the angle of arrival by using the equations:
Var{α i }≧φ i,z .
φ=γ −1
γ
i
,
j
=
-
E
{
∂
2
∂
α
i
∂
α
j
log
p
(
y
|
α
)
}
wherein i and j are indices for a matrix of possible values of γ,
α
=
(
ϕ
,
Re
z
0
,
Im
z
0
,
Re
z
1
,
Im
z
1
,
…
)
,
E
{
∂
2
∂
α
i
∂
α
j
log
p
(
y
|
α
)
}
=
1
σ
2
Re
{
(
Xz
)
*
∂
2
∂
α
i
∂
α
j
Xz
}
-
k
2
σ
2
∂
2
∂
α
i
∂
α
j
z
2
X
=
(
ⅇ
ⅈcos
(
ϕ
+
τ
1
)
ⅇ
ⅈ
cos
(
ϕ
+
τ
2
)
ⅇ
ⅈcos
(
ϕ
+
τ
3
)
ⅇ
ⅈcos
(
ϕ
+
τ
4
)
)
z is a complex vector of length two that represents unknown modulation of the target signal,
T is determined by the particular disparate observation of the target signal,
σ 2 is the variance of distribution of random noise, and
k is a scalar.
9. A method according to claim 8 , wherein step (b) comprises the step of:
(h) determining said optimal estimation in accordance with the equation:
X =argmin x ψ 0,0
wherein ψ 0,0 is the inverse matrix of the variance bound matrix for said particular estimate of the angle of arrival.
10. A method according to claim 8 , wherein step (b) comprises the step of:
(h) determining said optimal estimation in accordance with the equation:
X =argmax x {μ′ 2k+0 (φ)−μ′ 2k+1 (φ)} 2 ∀k
wherein μ′ i (φ) is a linear combination of two translated sinusoidal functions of φ.
11. A method according to claim 1 , wherein step (a) comprises the step of:
(c) obtaining the disparate observations from different antenna elements of the antenna system.
12. A method according to claim 1 , wherein step (a) comprises the step of:
(c) obtaining the disparate observations from different elements of a commutated antenna array of the antenna system.
13. A method according to claim 1 , wherein step (a) comprises the step of:
(c) obtaining the disparate observations at different times.
14. A method according to claim 1 , wherein step (a) comprises the step of:
(c) obtaining the disparate observations at different frequencies.
15. A method according to claim 1 , wherein step (a) comprises the step of:
(c) obtaining the disparate observations by using different CDMA signal access codes.
16. A system for estimating the angle of arrival of a target signal received by an antenna system, comprising the steps of:
means for obtaining disparate observations of a target signal received by an antenna system; and
a computer adapted for processing the obtained disparate observations of the signal to select a subset of said disparate observations of the signal for processing to enable an optimal estimation of the angle of arrival of the signal.
17. A nontransitory computer readable storage medium for use with a computer in a system for estimating the angle of arrival of a target signal received by an antenna system, wherein the system comprises: means for obtaining disparate observations of the signal; and a computer,
wherein the computer readable storage medium contains computer executable program instructions for causing the computer to perform the step of:
(a) with a computer, processing the obtained disparate observations of the signal to select a subset of said disparate observations of the signal for processing to enable an optimal estimation of the angle of arrival of the signal.
18. A nontransitory computer readable storage medium according to claim 17 , wherein the means for obtaining disparate observations of the signal are adapted for subsequently obtaining the subset of said disparate observations of the signal; and wherein the computer readable storage medium further contains computer executable program instructions for causing the computer to perform the step of:
(b) processing the subsequently obtained subset of said disparate observations to obtain the optimal estimate of the angle of arrival of the signal.
19. A nontransitory computer readable storage medium according to claim 17 , wherein the computer readable storage medium contains computer executable program instructions for causing the computer to perform step (a) by performing the steps of:
(b) processing the disparate observations of the signal to provide a plurality of estimates of the angle of arrival of the signal; and
(c) processing the plurality of estimates to determine the subset of further obtained disparate observations in accordance with which of the estimates is an optimal estimation of the angle of arrival of the signal.
20. A nontransitory computer readable storage medium according to claim 19 , wherein the computer readable storage medium contains computer executable program instructions for causing the computer to perform step (b) by performing the step of:
(d) using maximum-likelihood processing to estimate the angle of arrival of the signal.
21. A nontransitory computer readable storage medium according to claim 20 , wherein the computer readable storage medium contains computer executable program instructions for causing the computer to perform step (d) by performing the step of:
(e) making the maximum-likelihood-estimation of the angle of arrival φ of the target signal in accordance with the equation:
φ MLE =argmin φ ∥y−Xz∥ 2
wherein
y=Xz+v
X
=
(
ⅇ
ⅈ
cos
(
ϕ
+
τ
1
)
ⅇ
ⅈ
cos
(
ϕ
+
τ
2
)
ⅇ
ⅈ
cos
(
ϕ
+
τ
3
)
ⅇ
ⅈ
cos
(
ϕ
+
τ
4
)
)
z is a complex vector of length two that represents unknown modulation of the signal,
v is random noise, and
T is determined by the particular disparate observation of the signal.
22. A nontransitory computer readable storage medium according to claim 19 , wherein the computer readable storage medium contains computer executable program instructions for causing the computer to perform step (c) by performing the step of:
(d) using minimization of variance of the estimates of parameter of interest as a criterion for determining which of said estimates is an optimal estimation of the parameter of interest.
23. A nontransitory computer readable storage medium according to claim 22 , wherein the computer readable storage medium contains computer executable program instructions for causing the computer to perform step (d) by performing the step of:
(e) determining said variance for a particular said estimate by using a Cramer-Rao bound derived from a prior said determination of a said particular estimate as an optimal estimation of the parameter of interest.
24. A nontransitory computer readable storage medium according to claim 23 , wherein the computer readable storage medium contains computer executable program instructions for causing the computer to perform step (e) by performing the step of:
(f) determining the variance bound for said particular estimate of the angle of arrival by using the equations:
Var{α i }≧ψ i,i
ψ=γ −1
γ
i
,
j
=
-
E
{
∂
2
∂
α
i
∂
α
j
log
p
(
y
|
α
)
}
wherein i and j are indices for a matrix of possible values of γ,
α
=
(
ϕ
,
Re
z
0
,
Im
z
0
,
Re
z
1
,
Im
z
1
,
…
)
,
E
{
∂
2
∂
α
i
∂
α
j
log
p
(
y
|
α
)
}
=
1
σ
2
Re
{
(
Xz
)
*
∂
2
∂
α
i
∂
α
j
Xz
}
-
k
2
σ
2
∂
2
∂
α
i
∂
α
j
z
2
X
=
(
ⅇ
ⅈ
cos
(
ϕ
+
τ
1
)
ⅇ
ⅈ
cos
(
ϕ
+
τ
2
)
ⅇ
ⅈ
cos
(
ϕ
+
τ
3
)
ⅇ
ⅈ
cos
(
ϕ
+
τ
4
)
)
z is a complex vector of length two that represents unknown modulation of the target signal,
T is determined by the particular disparate observation of the target signal,
σ 2 is the variance of distribution of random noise, and
k is a scalar.
25. A nontransitory computer readable storage medium according to claim 24 , wherein the computer readable storage medium contains computer executable program instructions for causing the computer to perform step (a) by performing the step of:
(g) determining said optimal estimation in accordance with the equation:
X =argmin x ψ 0,0
wherein ψ 0,0 is the inverse matrix of the variance bound matrix for said particular estimate of the angle of arrival.
26. A nontransitory computer readable storage medium according to claim 24 , wherein the computer readable storage medium contains computer executable program instructions for causing the computer to perform step (a) by performing the step of:
(g) determining said optimal estimation in accordance with the equation:
X =argmax x {μ′ 2k+0 (φ)−μ′ 2k+1 (φ)} 2 ∀k
wherein μ′ i (φ) is a linear combination of two translated sinusoidal functions of φ.