US 11,982,698 B2 · Joint denoising and delay estimation for the extraction of pulse-width of signals in RF interference

Abstract

A feature detection system, the system comprising: at least one processor in operative communication with a signal source, said processor further comprising at least one non-transitory storage medium, wherein at least one non-transitory storage medium contains instructions configured to cause the processor to: apply a joint group sparse denoising and delay estimation approach to a signal received from said signal source; and output statistics regarding the signal, wherein the joint group sparse denoising and delay estimation approach comprises; using the following equation: { x * , τ * } = argmin x , τ ⁢ { 1 2 ⁢ ∑ j = 1 M  y j - x  2 2 + ∑ i = 0 N λ i ⁢ φ i ( D i l i ⁢ x ) } where: ϕi are regularization functions; ∥y−x∥22 is a data-fidelity term and, in embodiments, is chosen as the least-square term; li are real numbers; Di are operators, which may be linear filters that can be written in matrix form; λi are regularization parameters; and x*,τ* represent estimates of at least one transmitted pulse and associated delay, and solving the equation for multiple values of ϵ; choosing a vector, x, such that a cost function comprising the data fidelity term and regularization function is minimized; determining the ϵ that corresponds to the x that minimizes the cost function; and calculating the pulse width of the received signal, which corresponds to the desired estimate of the vector, x.

Claims20

Dependent claims

A (non-transitory) computer program product including one or more machine-readable mediums encoded with instructions that when executed by one or more processors cause a process to be carried out for feature detection, the process comprising:

applying a joint group sparse denoising and delay estimation approach to a signal received from said signal source;
and
outputting statistics regarding the signal,
wherein the joint group sparse denoising and delay estimation approach comprises:
using the following equation:
{
x
*
,
τ
*
}
=
argmin
x
,
ϵ
,
τ
⁢
{
1
2
⁢
∑
j
=
1
M

y
i
-
x

2
2
+
∑
i
=
0
N
λ
i
⁢
ϕ
i
(
D
i
l
i
⁢
x
)
}
where:
ϕi are regularization functions,
∥y−x∥22 is a data-fidelity term and, in embodiments, is chosen as the least-square term,
li are real numbers,
Di are operators, which may be linear filters that can be written in matrix form,
λi are regularization parameters, and
x*,σ* represent estimates of at least one transmitted pulse and associated delay, respectively;
solving the equation for multiple values of σ*;
choosing a vector, x, such that a cost function comprising the data fidelity term and regularization function is minimized;
determining the σ* that corresponds to the x that minimizes the cost function;
calculating the pulse width of the received signal, which corresponds to the desired estimate of the vector, x.

65 more elements

A method of extracting the pulse-width of signals, the method comprising:

receiving a first signal, yi, and a second signal, y2;
and
determining the pulse width of the signals using the following equations:
where:
{
x
*
,
τ
*
}
=
argmin
x
,
ϵ
,
τ
⁢
{
1
2
⁢
∑
j
=
1
M

y
i
-
x

2
2
+
∑
i
=
0
N
λ
i
⁢
ϕ
i
(
D
i
l
i
⁢
x
)
}
⁢
φ
G
(
x
)
=
∑
i
=
1
N
[
∑
k
=
0
K
-
1
V
k
⁢
❘
"\[LeftBracketingBar]"
x
⁡
(
i
+
k
)
❘
"\[RightBracketingBar]"
2
]
1
/
2
ϕi are regularization functions,
ϕG(X) represents a special case of a general sum of ϕi,
K represents a group size,
Vk is a window function,
∥y−x∥22 is a data-fidelity term,
li are real numbers,
Di are operators, which may be linear filters that can be written in matrix form,
λi are regularization parameters, and
x*,σ* represent estimates of at least one transmitted pulse and associated delay, respectively,
wherein determining the pulse width of the signals following receiving the first and second signals further comprises:
initializing K,λ,V, and P, where P represents a set of P delay values such that T={σ1, σ2 . . . σP};
for each feasible value of σp indexed by p from 1 to |P|, where p represents an index for the delay values:
shifting y2 by σp sample delays;
initializing the value of L=0;
setting xp(0)=0.5*(y1+ý2), where xp(L) represents an estimate of x at an Lth iteration;
setting y=xp(0);
and
setting h=DTy, where DT is a transpose of a first order difference operation;
then performing the following loop, which is repeated until convergence for L=1:
Nloop:
setting u=Dxp(L−1), where D is the first order difference operation and u is a temporary variable;
solving [M]n,n=Σj=0K−1|Σk=0K−1|Vku(n−j+k)|2]−5, where u is weighted by a window Vk;
solving
B
=
1
λ
⁢
M
-
1
+
D
⁢
D
T
,
where B is a constant matrix;
solving xp(L)=y−DT(B−1h);
evaluating
c
p
(
L
)
=
{
1
2
⁢

y
1
-
x

2
2
+
1
2
⁢

y
`
2
-
x

2
2
+
λ
⁡
(
φ
G
(
D
⁢
x
p
)
)
}
;
using the following equation:
x
p
*
=
argmin
p
⁢
c
p
,
from the set of cp where p
represents different delay values σp, choosing the index p* that corresponds to the minimum value of cp;
and
using xp, which represents a denoised pulse whose pulse width can be measured by the half point between its rise-time and fall-time, to determine the pulse width of at least one signal.

193 more elements

A method of extracting a pulse-width of a signal or signals in the presence of RF interference, the method comprising:

using a receiver and/or the following equation:
{
x
*
}
=
{
argmin
x
⁢
1
2
⁢

F
⁢
y
-
F
⁢
x
S

2
2
+
λ
⁢
❘
"\[LeftBracketingBar]"
DF
H
⁢
Fx
❘
"\[RightBracketingBar]"
}
obtaining y and S;
initializing the values of λ,
Y
~
=
Fy
S
,
X
~
1
=
Fy
S
,
and T=DFHSFDH;
repeating the previous steps until convergence for L=1:
Nloop−1;
evaluating
α
=
1
λ
⁢
diag
⁡
(
❘
"\[LeftBracketingBar]"
DF
H
⁢
S
⁢
X
~
L
❘
"\[RightBracketingBar]"
)
;
evaluating=α+T;
inverting β using a preconditioned gradient algorithm;
updating {tilde over (X)}L+1={tilde over (Y)}−(DFH√{square root over (S)})Tβ−1(DFH√{square root over (S)}){tilde over (Y)};
and
evaluating a pulse-width of the signal based on {tilde over (X)}*Nloop by calculating the time between the half value of the rising and trailing edge of the pulse,
wherein:
y represents noisy, base-band samples of a pulse,
S represents diag(p), where p represents power spectral density and P is a diagonal matrix whose elements have a one-to-one correspondence in the same ordered p,
λ is a regularization parameter,
{tilde over (Y)} represents a Fourier transform of received data normalized by a colored noise interference spectral pattern,
{acute over (X)}1 represents an initial guess for an estimate of the pulse,
Fy represents-,Fourier transform of the received channel data
T represents a constant that is equal to DFHSFDH, which is a left and right Fourier Transform and left and right difference filtered power spectrum of the colored noise,
D represents a difference filter,
FH represents an inverse Fourier Transform
F represents a forward Fourier Transform
DH represents a Hermitian transpose of the difference filter,
{tilde over (X)}L represents an ith iteration estimate of the Fourier transform of the pulse normalized by the colored noise interference spectral pattern,
α represents a matrix that is a function of ith estimate of the pulse weighted by its colored noise interference pattern, inverse Fourier transform, and the difference filter matrix, and
β represents a parameter that varies with each iteration of the algorithm and is the sum of T+α.

95 more elements

Dependencies are inferred from the claim text.

Joint denoising and delay estimation for the extraction of pulse-width of signals in RF interference

Life of this patent

Joint denoising and delay estimation for the extraction of pulse-width of signals in RF interference

Life of this patent

Abstract

Claims20