Estimation of multiple angles of arrival of signals received by an array of antenna elements
View Patent ↗A computer estimates multiple angles of arrival of a target signal received by an array of commutated antenna elements. In one aspect, samples of a received target signal obtained from an array of communicated antenna elements and from an element in an array of reference antenna elements are processed to make maximum-likelihood-estimations of multiple angles of arrival at which signals are received by the array of commutated antenna elements; and a display is mapped over time and frequency of the estimations, with the angle of arrival for a particular sample being represented by a variable given display feature.
1. A method of estimating multiple angles of arrival of a target signal received by an array of commutated antenna elements, comprising the steps of:
(a) obtaining samples of the received signal from the array of commutated antenna elements and from an element in an array of reference antenna elements;
(b) with a computer, processing the obtained samples of the received signal to estimate multiple angles of arrival of a target signal received by the array of commutated antenna elements; and
(c) mapping a display over time and frequency of said estimations, with the angle of arrival for a particular sample being represented by a variable color;
wherein step (b) comprises the step of:
(d) making maximum-likelihood-estimations φ MLE of the multiple angles of arrival at which the target signal is received by the array of commutated antenna elements in accordance with the following computer processing step:
ϕ
_
0
←
argmax
ϕ
Color
_
*
A
(
A
*
diag
(
Energy
_
)
A
)
-
1
A
*
Color
_
A
n
←
a
_
k
n
(
ϕ
_
)
Color
_
n
←
∑
k
∈
R
n
y
C
,
k
y
R
,
k
_
Energy
_
n
←
∑
k
∈
R
n
y
R
,
k
y
R
,
k
_
wherein φ 0 approaches φ MLE , the subscript i denotes the iteration number, y C denotes an individual sample of the received target signal obtained from a single commutated antenna array element, y R denotes a sample of the received target signal obtained from the reference antenna array element; n ranges over time and frequency, the vector a k n ( φ ) is the nth row of the matrix A, Color is a vector with tuples that are the color sequence of the target, the tuple Color n denotes the n th color in the color sequence measured using the n th commutated element, R n denotes the set of all k for which the n th commutated element was used, the vector Energy is similarly defined and measures the energy sequence of the target, the n th row and the i th of column of the matrix A is the response of the n th element of the commutated array to a signal from angle φ , with the n th row being given by a k n ( φ ) for some k n , diag(Energy) denotes a diagonal matrix where the diagonal elements are given by the vector Energy and the other elements are zero.
2. A method of estimating multiple angles of arrival of a target signal received by an array of commutated antenna elements, comprising the steps of:
(a) obtaining samples of a received target signal from an array of commutated antenna elements and from an element in an array of reference antenna elements;
(b) with a computer, processing the obtained samples of the received target signal to make maximum-likelihood-estimations of multiple angles of arrival at which signals are received by the array of commutated antenna elements; and
(c) mapping a display over time and frequency of said estimations, with the angle of arrival for a particular sample being represented by a variable given display feature.
3. A method according to claim 2 , wherein the variable display feature is color so that an estimation over time of the angle of arrival for a particular sample within a band of frequencies is displayed as a sequence of colored rectangles.
4. A method according to claim 3 , wherein the displayed color is argColor{R i }, wherein Color (R i ) is determined in accordance with: Color(R i )=Σ n∈R i y C,n y R,n ; and wherein y C denotes an individual sample of the received target signal obtained from a single commutated antenna array element, y R denotes a sample of the received target signal obtained from a reference antenna array element; and n ranges over time and frequency.
5. A method according to claim 3 , wherein step (c) comprises the step of:
(d) displaying said estimations in separate columns of colored rectangles for each set of the sequentially obtained samples.
6. A method according to claim 3 , further comprising the step of:
(d) constructing a classifier that labels a subset of rectangles as either a target instance or not.
7. A method according to claim 3 , wherein step (c) comprises the step of:
(d) clustering displayed indicia for multiple estimations of the angle of arrival for signals received from multiple targets in accordance with similarities and differences in rectangle color-sequence patterns.
8. A method according to claim 2 , further comprising one of more of the following steps:
(d) processing the display to determine that a target signal is being received by the array of commutated antenna elements;
(e) processing the display to estimate parameters of said received target signal;
(f) associating multiple displayed rectangles with a single received target signal.
9. A method according to claim 2 , further comprising at least one of the following steps:
(d) processing the displayed estimations to determine that a target signal is being received by the array of commutated antenna elements;
(e) processing the displayed estimations to estimate parameters of the received target signal;
(f) processing the estimations to associate multiple displayed estimations with a single received target signal.
10. A method of estimating multiple angles of arrival of a target signal received by an array of commutated antenna elements, comprising the steps of:
(a) obtaining samples of a received signal from an array of commutated antenna elements and from an element in an array of reference antenna elements;
(b) with a computer, processing the obtained samples of the received target signal to make maximum-likelihood-estimations of multiple angles of arrival at which signals are received by the array of commutated antenna elements;
(c) mapping a display of a distributions of said estimations over the angle of arrival for arbitrarily numbered received target signals; and
(d) identifying the angle of arrival that is most prevalent in this distribution as a reflected angle.
11. A non-transitory computer readable storage medium for use with a computer in a system for estimating multiple angles of arrival of a target signal received by an array of commutated antenna elements, wherein samples of a received target signal are obtained from an array of commutated antenna elements and from an element in an array of reference antenna elements; a computer is adapted for processing the obtained samples of the received signal to estimate multiple angles of arrival of a target signal received by the array of commutated antenna elements, and for mapping a display over time and frequency of said estimations, with the angle of arrival for a particular sample being represented by a variable color; and
wherein the computer readable storage medium contains computer executable program instructions for causing the computer to make maximum-likelihood-estimations φ MLE of the multiple angles of arrival at which the target signal is received by the array of commutated antenna elements in accordance with the following computer processing step:
ϕ
_
0
←
argmax
ϕ
Color
_
*
A
(
A
*
diag
(
Energy
_
)
A
)
-
1
A
*
Color
_
A
n
←
a
_
k
n
(
ϕ
_
)
Color
_
n
←
∑
k
∈
R
n
y
C
,
k
y
R
,
k
_
Energy
_
n
←
∑
k
∈
R
n
y
R
,
k
y
R
,
k
_
wherein φ 0 approaches φ MLE , the subscript i denotes the iteration number, y C denotes an individual sample of the received target signal obtained from a single commutated antenna array element, y R denotes a sample of the received target signal obtained from the reference antenna array element; n ranges over time and frequency, the vector a k n ( φ ) is the nth row of the matrix A, Color is a vector with tuples that are the color sequence of the target, the n th tuple Color n denotes the n th color in the color sequence measured using the n th commutated element, R n denotes the set of all k for which the n th commutated element was used, the vector Energy is similarly defined and measures the energy sequence of the target, the n th row and the i th of column of the matrix A is the response of the n th element of the commutated array to a signal from angle φ , with the n th row being given by a k n ( φ ) for some k n , diag(Energy) denotes a diagonal matrix where the diagonal elements are given by the vector Energy and the other elements are zero.
12. A non-transitory computer readable storage medium for use with a computer in a system for estimating multiple angles of arrival of a target signal received by an array of commutated antenna elements, wherein samples of a received target signal are obtained from an array of commutated antenna elements and from an element in an array of reference antenna elements; and
wherein the computer readable storage medium contains computer executable program instructions for causing the computer to perform the steps of:
(a) processing the obtained samples of the received target signal to make maximum-likelihood-estimations of multiple angles of arrival at which signals are received by the array of commutated antenna elements; and
(b) mapping a display over time and frequency of said estimations, with the angle of arrival for a particular sample being represented by a variable given display feature.
13. A non-transitory computer readable storage medium for use with a computer in a system for estimating multiple angles of arrival of a target signal received by an array of commutated antenna elements, wherein samples of a received target signal are obtained from an array of commutated antenna elements and from an element in an array of reference antenna elements; and
wherein the computer readable storage medium contains computer executable program instructions for causing the computer to perform the steps of:
(a) with a computer, processing the obtained samples of the received target signal to make maximum-likelihood-estimations of multiple angles of arrival at which signals are received by the array of commutated antenna elements;
(b) mapping a display of a distributions of said estimations over the angle of arrival for arbitrarily numbered received target signals; and
(c) identifying the angle of arrival that is most prevalent in this distribution as a reflected angle.