Method and device for updating coefficient vector of finite impulse response filter
A method and a device for updating a coefficient vector of a finite impulse response filter are provided. The update method includes: obtaining an updated step-size diagonal matrix for a coefficient vector of the FIR filter; and obtaining an updated coefficient vector of the FIR filter based on the updated step-size diagonal matrix.
1. A method for updating a coefficient vector of a finite impulse response (FIR) filter, comprising:
obtaining an updated step-size diagonal matrix for a coefficient vector of the FIR filter; and
obtaining, based on the updated step-size diagonal matrix, an updated coefficient vector of the FIR filter;
wherein the obtaining the updated step-size diagonal matrix for the coefficient vector of the FIR filter comprises: updating, based on an end moment of pre-learning and a pre-defined updating period, a step-size diagonal matrix used to update the coefficient vector of the FIR filter, to obtain the updated step-size diagonal matrix;
wherein the updating, based on the end moment of the pre-learning and the pre-defined updating period, the step-size diagonal matrix used to update the coefficient vector of the FIR filter, to obtain the updated step-size diagonal matrix, comprises:
obtaining, a coefficient vector of the FIR filter at an updating moment of the step-size diagonal matrix;
obtaining, based on the coefficient vector of the FIR filter at the updating moment of the step-size diagonal matrix, an estimated value of an attenuation factor of a step-size diagonal matrix of an exponentially weighted step-size normalized least mean square (ES-NLMS) algorithm; and
obtaining, based on the estimated value of the attenuation factor, an updated step-size diagonal matrix of the ES-NLMS algorithm at the updating moment of the step-size diagonal matrix.
2. The method according to claim 1 , wherein in a case that the updating moment is the end moment of the pre-learning, the obtaining the coefficient vector of the FIR filter at the updating moment of the step-size diagonal matrix comprises: obtaining, the coefficient vector of the FIR filter at the end moment of the pre-learning, according to the following formula
h
→
(
k
+
1
)
=
h
→
(
k
)
+
α
e
(
k
)
x
→
T
(
k
)
·
x
→
(
k
)
+
δ
(
k
)
x
→
(
k
)
;
wherein {right arrow over (h)}(k+1) is the coefficient vector of the FIR filter at a (k+1) th moment; {right arrow over (h)}(k) is a coefficient vector of the FIR filter at a k th moment; α is a learning rate constant, and 0<α<2; e(k) is an error signal at the k th moment; {right arrow over (x)}(k) is a far end received signal vector, {right arrow over (x)}(k)=[x(k), x(k−1), . . . , x(k−L+1)] T , x(k−n) is a far end received signal at a (k−n) th moment, n=0, 1, . . . , L−1, L is the quantity of coefficients of the filter, and T is a transpose operator; e(k)=y(k)−ŷ(k)+n(k); y(k) is an echo signal; ŷ(k) is an estimation of the echo signal; n(k) is an ambient noise signal received by a microphone; δ(k) is a time-varying regularization factor; (k+1) is a time index of a signal sample at the end moment of the pre-learning.
3. The method according to claim 1 , wherein in a case that the updating moment is a moment corresponding to the pre-defined updating period of the step-size diagonal matrix after the pre-learning is ended, the obtaining the coefficient vector of the FIR filter at the updating moment of the step-size diagonal matrix comprises: obtaining, the coefficient vector of the FIR filter at the moment corresponding to the pre-defined updating period of the step-size diagonal matrix after the pre-learning is ended, according to the following formula
h
→
(
k
+
1
)
=
h
→
(
k
)
+
A
^
e
(
k
)
x
→
T
(
k
)
·
x
→
(
k
)
+
δ
(
k
)
x
→
(
k
)
;
wherein {right arrow over (h)}(k+1) is the coefficient vector of the FIR filter at a (k+1) th moment; {right arrow over (h)}(k) is a coefficient vector of the FIR filter at a k th moment; Â is the step-size diagonal matrix before updating; δ(k) is a time-varying regularization factor; {right arrow over (x)}(k) is a far end received signal vector, and {right arrow over (x)}(k)=[x(k), x(k−1), . . . , x(k−L+1)] T , x(k−n) is a far end received signal at a (k−n) th moment, n=0,1, . . . ,L−1, L is the quantity of coefficients of the filter, and T is a transpose operator; e(k) is an error signal at the k th moment, and e(k)=y(k)−ŷ(k)+n(k); y(k) is an echo signal; ŷ(k) is an estimation of the echo signal; n(k) is an ambient noise signal received by a microphone; (k+1) is a time index of a signal sample at the moment corresponding to the pre-defined updating period of the step-size diagonal matrix after the pre-learning is ended, and (k+1−T 0 ) is a positive integer multiple of T 1 ; T 0 is the end moment of the pre-learning, and T 1 is the pre-defined updating period for updating the step-size diagonal matrix.
4. The method according to claim 1 , wherein the obtaining, based on the coefficient vector of the FIR filter at the updating moment of the step-size diagonal matrix, the estimated value of the attenuation factor of the step-size diagonal matrix of the ES-NLMS algorithm comprises: obtaining the estimated value of the attenuation factor according to the following formula
γ
^
=
∑
i
=
0
L
-
2
{
h
i
+
1
(
k
)
h
i
(
k
)
}
L
-
1
;
wherein {circumflex over (γ)} is the estimated value of the attenuation factor; h i (k) is an (i+1) th component of a coefficient vector of the FIR filter at a k th moment; h i+1 (k) is an (i+2) th component of the coefficient vector of the FIR filter at the k th moment; i is an index variable of coefficients of the filter, i=0, 1, 2, . . . , L−2, and L is the quantity of the coefficients of the filter; k is the updating moment of the step-size diagonal matrix.
5. The method according to claim 1 , wherein the obtaining, based on the estimated value of the attenuation factor, the updated step-size diagonal matrix of the ES-NLMS algorithm at the updating moment of the step-size diagonal matrix comprises: obtaining, the updated step-size diagonal matrix of the ES-NLMS algorithm at the updating moment of the step-size diagonal matrix, according to the following formula
A
^
=
[
α
^
1
α
^
2
0
0
⋱
α
^
L
]
;
wherein  is the updated step-size diagonal matrix of the ES-NLMS algorithm; {circumflex over (α)} i is an i th element on a main diagonal of the step-size diagonal matrix, and {circumflex over (α)} i =α{circumflex over (γ)} i−1 ; α is a learning rate constant, and 0<α<2; {circumflex over (γ)} is the estimated value of the attenuation factor; i is an index variable of coefficients of the filter, i=1, 2, . . . , L, and L is the quantity of the coefficients of the filter.
6. The method according to claim 1 , wherein the obtaining, based on the updated step-size diagonal matrix, the updated coefficient vector of the FIR filter comprises: obtaining the updated coefficient vector of the FIR filter according to the following formula
h
→
(
k
+
1
)
=
h
→
(
k
)
+
A
^
e
(
k
)
x
→
T
(
k
)
·
x
→
(
k
)
+
δ
(
k
)
x
→
(
k
)
;
wherein {right arrow over (h)}(k+1) is the coefficient vector of the FIR filter at a (k+1) th moment; {right arrow over (h)}(k) is a coefficient vector of the FIR filter at a k th moment; Â is a step-size diagonal matrix of the ES-NLMS algorithm; δ(k) is a time-varying regularization factor; {right arrow over (x)}(k) is a far end received signal vector, {right arrow over (x)}(k)=[x(k), x(k−1), . . . , x(k−L+1)] T , x(k−n) is a far end received signal at a (k−n) th moment, n=0, 1, . . . , L−1, L is the quantity of coefficients of the filter, and T is a transpose operator; e(k) is an error signal at the k th moment, and e(k)=y(k)−ŷ(k)+n(k); y(k) is an echo signal; ŷ(k) is an estimation of the echo signal; n(k) is an ambient noise signal received by a microphone; k is a time index of a signal sample, k≥T 0 , and T 0 is an end moment of pre-learning.
7. The method according to claim 2 , wherein the manner of obtaining the time-varying regularization factor comprises:
obtaining a received signal power of the microphone; and
obtaining, based on the received signal power of the microphone, the time-varying regularization factor.
8. The method according to claim 7 , wherein the obtaining the received signal power of the microphone comprises: obtaining the received signal power of the microphone according to the following formula
σ
d
2
(
k
)
=
{
β
a
t
t
a
c
k
·
σ
d
2
(
k
-
1
)
+
(
1
-
β
a
t
t
a
c
k
)
·
❘
"\[LeftBracketingBar]"
d
(
k
)
❘
"\[RightBracketingBar]"
2
,
if
❘
"\[LeftBracketingBar]"
d
(
k
)
❘
"\[RightBracketingBar]"
2
>
σ
d
2
(
k
-
1
)
β
d
e
c
a
y
·
σ
d
2
(
k
-
1
)
+
(
1
-
β
d
e
c
a
y
)
·
❘
"\[LeftBracketingBar]"
d
(
k
)
❘
"\[RightBracketingBar]"
2
,
if
❘
"\[LeftBracketingBar]"
d
(
k
)
❘
"\[RightBracketingBar]"
2
≤
σ
d
2
(
k
-
1
)
;
wherein σ d 2 (k) is the received signal power of the microphone at the k th moment; β attack and β decay are recursive constants, and 0≤β attack <β decay <1; σ d 2 (k−1) is a received signal power of the microphone at the (k−1) th moment; d(k) is a received signal of the microphone at the k th moment; |·| is a modulus operator for a complex number; k is a time index of a signal sample.
9. The method according to claim 7 , wherein the obtaining the time-varying regularization factor based on the received signal power of the microphone comprises: obtaining the time-varying regularization factor according to the following formula
δ( k )=max{ L·σ d 2 ( k ),δ min };
wherein δ(k) is the time-varying regularization factor at the k th moment; σ d 2 (k) is the received signal power of the microphone at the k th moment; δ min is a pre-defined positive constant; L is the quantity of the coefficients of the filter.
10. A device for updating a coefficient vector of a finite impulse response (FIR) filter, comprising a memory, a processor, and a computer program stored in the memory and executable by the processor, wherein the processor is configured to, when executing the computer program, perform the following steps:
obtaining an updated step-size diagonal matrix for a coefficient vector of the FIR filter; and
obtaining, based on the updated step-size diagonal matrix, an updated coefficient vector of the FIR filter;
wherein the processor is further configured to, when executing the computer program, perform the following steps: updating, based on an end moment of pre-learning and a pre-defined updating period, a step-size diagonal matrix used to update the coefficient vector of the FIR filter, to obtain the updated step-size diagonal matrix;
wherein the processor is further configured to, when executing the computer program, perform the following steps:
obtaining, a coefficient vector of the FIR filter at an updating moment of the step-size diagonal matrix;
obtaining, based on the coefficient vector of the FIR filter at the updating moment of the step-size diagonal matrix, an estimated value of an attenuation factor of a step-size diagonal matrix of an exponentially weighted step-size normalized least mean square (ES-NLMS) algorithm; and
obtaining, based on the estimated value of the attenuation factor, an updated step-size diagonal matrix of the ES-NLMS algorithm at the updating moment of the step-size diagonal matrix.
11. The device according to claim 10 , wherein in a case that the updating moment is the end moment of the pre-learning, the processor is further configured to, when executing the computer program, perform the following steps: obtaining, the coefficient vector of the FIR filter at the end moment of the pre-learning, according to the following formula
h
→
(
k
+
1
)
=
h
→
(
k
)
+
α
e
(
k
)
x
→
T
(
k
)
·
x
→
(
k
)
+
δ
(
k
)
x
→
(
k
)
;
wherein {right arrow over (h)}(k+1) is the coefficient vector of the FIR filter at a (k+1) th moment; {right arrow over (h)}(k) is a coefficient vector of the FIR filter at a k th moment; α is a learning rate constant, and 0<α<2; e(k) is an error signal at the k th moment; {right arrow over (x)}(k) is a far end received signal vector, {right arrow over (x)}(k)=[x(k), x(k−1), . . . , x(k−L+1)] T , x(k−n) is a far end received signal at a (k−n) th moment, n=0, 1, . . . , L−1, L is the quantity of coefficients of the filter, and T is a transpose operator; e(k)=y(k)−ŷ(k)+n(k); y(k) is an echo signal; ŷ(k) is an estimation of the echo signal; n(k) is an ambient noise signal received by a microphone; δ(k) is a time-varying regularization factor; (k+1) is a time index of a signal sample at the end moment of the pre-learning.
12. The device according to claim 10 , wherein in a case that the updating moment is a moment corresponding to the pre-defined updating period of the step-size diagonal matrix after the pre-learning is ended, the processor is further configured to, when executing the computer program, perform the following steps: obtaining, the coefficient vector of the FIR filter at the moment corresponding to the pre-defined updating period of the step-size diagonal matrix after the pre-learning is ended, according to the following formula
h
→
(
k
+
1
)
=
h
→
(
k
)
+
A
^
e
(
k
)
x
→
T
(
k
)
·
x
→
(
k
)
+
δ
(
k
)
x
→
(
k
)
;
wherein {right arrow over (h)}(k+1) is the coefficient vector of the FIR filter at a (k+1) th moment; {right arrow over (h)}(k) is a coefficient vector of the FIR filter at a k th moment; Â is the step-size diagonal matrix before updating; δ(k) is a time-varying regularization factor; {right arrow over (x)}(k) is a far end received signal vector, and {right arrow over (x)}(k)=[x(k), x(k−1), . . . , x(k−L+1)] T , x(k−n) is a far end received signal at a (k−n) th moment, n=0,1, . . . ,L−1, L is the quantity of coefficients of the filter, and T is a transpose operator; e(k) is an error signal at the k th moment, and e(k)=y(k)−ŷ(k)+n(k); y(k) is an echo signal; ŷ(k) is an estimation of the echo signal; n(k) is an ambient noise signal received by a microphone; (k+1) is a time index of a signal sample at the moment corresponding to the pre-defined updating period of the step-size diagonal matrix after the pre-learning is ended, and (k+1−T 0 ) is a positive integer multiple of T 1 ; T 0 is the end moment of the pre-learning, and T 1 is the pre-defined updating period for updating the step-size diagonal matrix.
13. The device according to claim 10 , wherein the processor is further configured to, when executing the computer program, perform the following steps: obtaining the estimated value of the attenuation factor according to the following formula
γ
^
=
∑
i
=
0
L
-
2
{
h
i
+
1
(
k
)
h
i
(
k
)
}
L
-
1
;
wherein {circumflex over (γ)} is the estimated value of the attenuation factor; h i (k) is an (i+1) th component of a coefficient vector of the FIR filter at a k th moment; h i+i (k) is an (i+2) th component of the coefficient vector of the FIR filter at the k th moment; i is an index variable of coefficients of the filter, i=0, 1, 2, . . . , L−2, and L is the quantity of the coefficients of the filter; k is the updating moment of the step-size diagonal matrix.
14. The device according to claim 10 , wherein the processor is further configured to, when executing the computer program, perform the following steps: obtaining, the updated step-size diagonal matrix of the ES-NLMS algorithm at the updating moment of the step-size diagonal matrix, according to the following formula
A
^
=
[
α
^
1
α
^
2
0
0
⋱
α
^
L
]
;
wherein  is the updated step-size diagonal matrix of the ES-NLMS algorithm; {circumflex over (α)} i is an i th element on a main diagonal of the step-size diagonal matrix, and {circumflex over (α)} i =α{circumflex over (γ)} i−1 ; α is a learning rate constant, and 0<α<2; {circumflex over (γ)} is the estimated value of the attenuation factor; i is an index variable of coefficients of the filter, i=1, 2, . . . L, and L is the quantity of the coefficients of the filter.
15. The device according to claim 10 , wherein the processor is further configured to, when executing the computer program, perform the following steps: obtaining the updated coefficient vector of the FIR filter according to the following formula
h
→
(
k
+
1
)
=
h
→
(
k
)
+
A
^
e
(
k
)
x
→
T
(
k
)
·
x
→
(
k
)
+
δ
(
k
)
x
→
(
k
)
;
wherein {right arrow over (h)}(k+1) is the coefficient vector of the FIR filter at a (k+1) th moment; {right arrow over (h)}(k) is a coefficient vector of the FIR filter at a k th moment; Â is a step-size diagonal matrix of the ES-NLMS algorithm; δ(k) is a time-varying regularization factor; {right arrow over (x)}(k) is a far end received signal vector, {right arrow over (x)}(k)=[x(k), x(k−1), . . . x(k−L+1)] T , x(k−n) is a far end received signal at a (k−n) th moment, n=0, 1, . . . , L−1, L is the quantity of coefficients of the filter, and T is a transpose operator; e(k) is an error signal at the k th moment, and e(k)=y(k)−ŷ(k)+n(k); y(k) is an echo signal; ŷ(k) is an estimation of the echo signal; n(k) is an ambient noise signal received by a microphone; k is a time index of a signal sample, k≥T 0 , and T 0 is an end moment of pre-learning.
16. A non-transitory computer-readable storage medium, having a computer program stored thereon, wherein the computer program, when being executed by a processor, performs the following steps:
obtaining an updated step-size diagonal matrix for a coefficient vector of the FIR filter; and
obtaining, based on the updated step-size diagonal matrix, an updated coefficient vector of the FIR filter;
wherein the obtaining the updated step-size diagonal matrix for the coefficient vector of the FIR filter comprises: updating, based on an end moment of pre-learning and a pre-defined updating period, a step-size diagonal matrix used to update the coefficient vector of the FIR filter, to obtain the updated step-size diagonal matrix;
wherein the updating, based on the end moment of the pre-learning and the pre-defined updating period, the step-size diagonal matrix used to update the coefficient vector of the FIR filter, to obtain the updated step-size diagonal matrix, comprises:
obtaining, a coefficient vector of the FIR filter at an updating moment of the step-size diagonal matrix;
obtaining, based on the coefficient vector of the FIR filter at the updating moment of the step-size diagonal matrix, an estimated value of an attenuation factor of a step-size diagonal matrix of an exponentially weighted step-size normalized least mean square (ES-NLMS) algorithm; and
obtaining, based on the estimated value of the attenuation factor, an updated step-size diagonal matrix of the ES-NLMS algorithm at the updating moment of the step-size diagonal matrix.
17. The non-transitory computer-readable storage medium according to claim 16 , wherein in a case that the updating moment is the end moment of the pre-learning, the obtaining the coefficient vector of the FIR filter at the updating moment of the step-size diagonal matrix comprises: obtaining, the coefficient vector of the FIR filter at the end moment of the pre-learning, according to the following formula
h
→
(
k
+
1
)
=
h
→
(
k
)
+
α
e
(
k
)
x
→
T
(
k
)
·
x
→
(
k
)
+
δ
(
k
)
x
→
(
k
)
;
wherein {right arrow over (h)}(k+1) is the coefficient vector of the FIR filter at a (k+1) th moment; {right arrow over (h)}(k) is a coefficient vector of the FIR filter at a k th moment; α is a learning rate constant, and 0<α<2; e(k) is an error signal at the k th moment; {right arrow over (x)}(k) is a far end received signal vector, {right arrow over (x)}(k)=[x(k), x(k−1), . . . , x(k−L+1)] T , x(k−n) is a far end received signal at a (k−n) th moment, n=0, 1, . . . , L−1, L is the quantity of coefficients of the filter, and T is a transpose operator; e(k)=y(k)−ŷ(k)+n(k); y(k) is an echo signal; ŷ(k) is an estimation of the echo signal; n(k) is an ambient noise signal received by a microphone; δ(k) is a time-varying regularization factor; (k+1) is a time index of a signal sample at the end moment of the pre-learning.
18. The non-transitory computer-readable storage medium according to claim 16 , wherein in a case that the updating moment is a moment corresponding to the pre-defined updating period of the step-size diagonal matrix after the pre-learning is ended, the obtaining the coefficient vector of the FIR filter at the updating moment of the step-size diagonal matrix comprises: obtaining, the coefficient vector of the FIR filter at the moment corresponding to the pre-defined updating period of the step-size diagonal matrix after the pre-learning is ended, according to the following formula
h
→
(
k
+
1
)
=
h
→
(
k
)
+
A
^
e
(
k
)
x
→
T
(
k
)
·
x
→
(
k
)
+
δ
(
k
)
x
→
(
k
)
;
wherein {right arrow over (h)}(k+1) is the coefficient vector of the FIR filter at a (k+1) th moment; {right arrow over (h)}(k) is a coefficient vector of the FIR filter at a k th moment; Â is the step-size diagonal matrix before updating; δ(k) is a time-varying regularization factor; {right arrow over (x)}(k) is a far end received signal vector, and {right arrow over (x)}(k)=[x(k), x(k−1), . . . , x(k−L+1)] T , x(k−n) is a far end received signal at a (k−n) th moment, n=0,1, . . . ,L−1, L is the quantity of coefficients of the filter, and T is a transpose operator; e(k) is an error signal at the k th moment, and e(k)=y(k)−ŷ(k)+n(k); y(k) is an echo signal; ŷ(k) is an estimation of the echo signal; n(k) is an ambient noise signal received by a microphone; (k+1) is a time index of a signal sample at the moment corresponding to the pre-defined updating period of the step-size diagonal matrix after the pre-learning is ended, and (k+1−T 0 ) is a positive integer multiple of T 1 ; T 0 is the end moment of the pre-learning, and T 1 is the pre-defined updating period for updating the step-size diagonal matrix.
19. The non-transitory computer-readable storage medium according to claim 16 , wherein the obtaining, based on the coefficient vector of the FIR filter at the updating moment of the step-size diagonal matrix, the estimated value of the attenuation factor of the step-size diagonal matrix of the ES-NLMS algorithm comprises: obtaining the estimated value of the attenuation factor according to the following formula
γ
^
=
∑
i
=
0
L
-
2
{
h
i
+
1
(
k
)
h
i
(
k
)
}
L
-
1
;
wherein {circumflex over (γ)} is the estimated value of the attenuation factor; h i (k) is an (i+1) th component of a coefficient vector of the FIR filter at a k th moment; h i+i (k) is an (i+2) th component of the coefficient vector of the FIR filter at the k th moment; i is an index variable of coefficients of the filter, i=0, 1, 2, . . . , L−2, and L is the quantity of the coefficients of the filter; k is the updating moment of the step-size diagonal matrix.
20. The non-transitory computer-readable storage medium according to claim 16 , wherein the obtaining, based on the estimated value of the attenuation factor, the updated step-size diagonal matrix of the ES-NLMS algorithm at the updating moment of the step-size diagonal matrix comprises: obtaining, the updated step-size diagonal matrix of the ES-NLMS algorithm at the updating moment of the step-size diagonal matrix, according to the following formula
A
^
=
[
α
^
1
α
^
2
0
0
⋱
α
^
L
]
;
wherein  is the updated step-size diagonal matrix of the ES-NLMS algorithm; {circumflex over (α)} i is an i th element on a main diagonal of the step-size diagonal matrix, and α i =α{circumflex over (γ)} i−1 ; α is a learning rate constant, and 0<α<2; {circumflex over (γ)} is the estimated value of the attenuation factor; i is an index variable of coefficients of the filter, i=1, 2, . . . L, and L is the quantity of the coefficients of the filter.