US 10,863,272 B2Granted

System identification device, system identification method, system identification program, and recording medium recording system identification program

AssigneesNational University Corporation, Iwate University, Rion Co., Ltd.

InventorsKiyoshi Nishiyama, Masahiro Sunohara, Nobuhiko Hiruma, Chiho Haruta, Makoto Tateno

Life of this patent

Estimating the term…

Abstract

A system identification device for performing fast real-time identification for a system from input/output data includes a filter robust to disturbance, by setting the maximum energy gain from the disturbance to a filter error, as an evaluation criterion, smaller than a given upper limit. The filter estimates a state estimation value of a state of the system.

Claims18

Dependent claims

A system identification method for performing fast real-time identification for a system from input/output data, the method comprising:

estimating a state estimation value x{circumflex over ( )}k|k of a state xk of the system from a received signal uk of an interface in an acoustic system or a communication system and from an observation signal yk of an echo or a feedback by using a filter robust to disturbance in such a manner that a maximum energy gain from the disturbance to a filter error is, as an evaluation criterion, set smaller than a given upper limit γf2;
and
canceling out the echo or the feedback using a result of the state estimation value x{circumflex over ( )}k|k, wherein
the filter is, by Expressions (49) to (62) below, provided to a state space model represented by Expressions (11) to (13) below to estimate the state estimation value x{circumflex over ( )}k|k of the state xk of the system:
x
k
+
1
=
⁢
x
k
+
G
k
⁢
w
k
,
w
k
,
x
k
∈
ℛ
N
⁢
(
11
)
y
k
=
⁢
H
k
⁢
x
k
+
υ
k
,
y
k
,
υ
k
∈
ℛ
⁢
(
12
)
z
k
=
⁢
H
k
⁢
x
k
,
z
k
∈
ℛ
,
H
k
∈
ℛ
1
×
N
⁢
(
13
)
x
^
k
❘
k
=
⁢
x
^
k
-
1
❘
k
-
1
+
K
s
,
k
⁡
(
y
k
-
H
k
⁢
x
^
k
-
1
❘
k
-
1
)
⁢
(
49
)
K
s
,
k
=
⁢
K
~
k
⁡
(
:
,
1
)
R
e
,
k
⁡
(
1
,
1
)
⁢
(
50
)
b
k
=
⁢
b
k
-
1
-
ρ
-
1
⁢
K
~
k
⁢
W
⁢
⁢
e
_
k
⁢
(
51
)
S
_
k
=
⁢
ρ
⁢
S
_
k
-
1
+
e
_
k
T
⁢
W
⁢
⁢
e
~
_
k
⁢
(
52
)
e
_
k
=
⁢
χ
k
-
1
⁢
e
~
_
k
⁢
(
53
)
χ
k
=
⁢
ρ
-
1
⁢
R
e
,
k
⁢
W
⁢
(
54
)
R
e
,
k
=
⁢
R
e
,
k
-
1
+
e
~
k
⁢
e
~
k
T
S
k
-
1
-
e
~
_
k
⁢
μ
~
k
⁢
(
55
)
e
~
_
k
=
⁢
S
_
k
-
1
⁢
μ
~
k
T
⁢
(
56
)
K
~
k
=
⁢
m
~
k
-
b
k
-
1
⁢
μ
~
k
⁢
(
57
)
[
m
~
k
μ
~
k
]
=
⁢
[
0
K
~
k
-
1
]
+
[
1
a
k
-
1
]
⁢
e
~
k
T
S
k
-
1
⁢
(
58
)
a
k
=
⁢
a
k
-
1
-
ρ
-
1
⁢
K
~
k
-
1
⁢
W
⁢
⁢
e
k
⁢
(
59
)
S
k
=
⁢
ρ
⁢
⁢
S
k
-
1
+
e
k
T
⁢
W
⁢
⁢
e
~
k
⁢
(
60
)
e
k
=
⁢
χ
k
-
1
-
1
⁢
e
~
k
⁢
(
61
)
e
~
k
=
⁢
c
k
+
C
k
-
1
⁢
a
k
-
1
⁢
(
62
)
where Ck and W are defined by the following expressions:
C
k
=
[
H
k
H
k
]
,
W
=
[
1
0
0
-
γ
f
-
2
]
,
ck∈R2×1 is a first column vector of C
C
⋓
k
=
[
u
k
…
u
k
-
N
u
k
…
u
k
-
N
]
(
63
)
C
⋓
k
⁡
(
:
,
1
)
=
c
k
=
[
u
k
u
k
]
T
,
C
⋓
k
⁡
(
:
,
i
)
=
C
⋓
k
-
1
⁡
(
:
,
i
-
1
)
,
⁢
i
=
2
,
…
⁢
,
N
+
1
⁢
⁢
H
k
=
[
u
k
,
…
⁢
,
u
k
-
N
+
1
]
T
,
(
64
)
xk:
a state vector or merely a state;
unknown, and this is a target for estimation,
x0:
an initial state;
unknown,
wk:
system noise;
unknown,
vk:
observation noise;
unknown,
yk:
an observation signal;
taken as filter input, and known,
zk:
an output signal;
unknown,
Gk:
a drive matrix;
known upon execution,
Hk:
an observation matrix, known,
x{circumflex over ( )}k|k:
an estimation value, using observation signals y0 to yk, of the state xk (an impulse response of an unknown system) at time k;
provided by a filter equation,
x{circumflex over ( )}k+1|k:
a single-step prediction value, using the observation signals y0 to yk, of a state xk+1 at the time k;
provided by the filter equation,
x{circumflex over ( )}−1|−1:
an initial estimation value of the state;
unknown in a normal situation, but zero is used for convenience,
Ks,k:
a filter gain;
obtained from a matrix Σ{circumflex over ( )}k|k−1,
Re,k:
an auxiliary variable;
a 2×2 matrix,
χk:
a conversion factor;
a 2×2 matrix,
N:
a dimension (a tap number) of the state vector;
provided in advance,
μ{tilde over ( )}k:
an N+1-th 1×2 row vector of KUk;
obtained by KUk,
mk:
an N×2 matrix including first to N-th rows of KUk;
obtained by KUk,
W:
a weighting matrix;
determined by γf,
ak:
a forward linear prediction factor;
an N-dimensional column vector,
bk:
a backward linear prediction factor;
an N-dimensional column vector,
ek:
an ex-post forward prediction error;
a two-dimensional column vector,
ek:
an ex-post backward prediction error;
a two-dimensional column vector, and
γf:
an attenuation level;
provided upon designing.

649 more elements

A system identification method for performing fast real-time identification for a system from input/output data, the method comprising:

estimating a state estimation value x{circumflex over ( )}k|k of a state xk of the system from a received signal uk of an interface in an acoustic system or a communication system and from an observation signal yk of an echo or a feedback by using a filter robust to disturbance in such a manner that a maximum energy gain from the disturbance to a filter error is, as an evaluation criterion, set smaller than a given upper limit γf2;
and
canceling out the echo or the feedback using a result of the state estimation value x{circumflex over ( )}k|k, wherein
the filter is, by Expressions (49), (50), (55), (58), (60) to (62) below, provided to a state space model represented by Expressions (11) to (13) below to estimate the state estimation value x{circumflex over ( )}k|k of the state xk of the system:
x
k
+
1
=
⁢
x
k
+
G
k
⁢
w
k
,
w
k
,
x
k
∈
ℛ
N
⁢
(
11
)
y
k
=
⁢
H
k
⁢
x
k
+
υ
k
,
y
k
,
υ
k
∈
ℛ
⁢
(
12
)
z
k
=
⁢
H
k
⁢
x
k
,
z
k
∈
ℛ
,
H
k
∈
ℛ
1
×
N
⁢
(
13
)
x
^
k
❘
k
=
⁢
x
^
k
-
1
❘
k
-
1
+
μ
⁢
K
~
k
⁡
(
:
,
1
)
R
e
,
k
⁡
(
1
,
1
)
⁢
(
y
k
-
H
k
⁢
x
^
k
-
1
❘
k
-
1
)
⁢
(
49
)
,
(
50
)
R
e
,
k
=
⁢
R
e
,
k
-
1
+
c
k
⁢
c
k
T
S
k
-
1
-
c
k
-
N
⁢
μ
~
k
⁢
(
55
)
[
K
~
k
μ
~
k
]
=
⁢
[
c
k
/
S
k
-
1
K
~
k
-
1
]
⁢
(
58
)
S
k
=
⁢
ρ
⁢
⁢
S
k
-
1
+
c
k
T
⁢
W
⁢
⁢
c
~
k
=
ρ
⁢
⁢
S
k
-
1
+
(
1
-
γ
f
-
2
)
⁢
u
k
2
⁢
(
60
)
e
~
k
=
⁢
c
k
,
e
k
=
c
k
,
c
k
=
[
u
k
u
k
]
T
⁢
(
61
)
,
(
62
)
where Ck and W are defined by the following expressions:
C
k
=
[
H
k
H
k
]
,
W
=
[
1
0
0
-
γ
f
-
2
]
,
ck∈R2×1 is a first column vector of Ck=[ck, . . . , ck−N+1],
C
˘
k
=
[
u
k
…
u
k
-
N
u
k
…
u
k
-
N
]
(
63
)
C
˘
k
⁡
(
:
,
1
)
=
c
k
=
[
u
k
u
k
]
T
,
C
˘
k
⁡
(
:
,
i
)
=
C
˘
k
-
1
⁡
(
:
,
i
-
1
)
,
⁢
i
=
2
,
…
⁢
,
N
+
1
H
k
=
[
u
k
,
…
⁢
,
u
k
-
N
+
1
]
T
,
(
64
)
xk:
a state vector or merely a state;
unknown, and this is a target for estimation,
x0:
an initial state;
unknown,
wk:
system noise;
unknown,
vk:
observation noise;
unknown,
yk:
an observation signal;
taken as filter input, and known,
zk:
an output signal;
unknown,
Gk:
a drive matrix;
known upon execution,
Hk:
an observation matrix, known,
x{circumflex over ( )}k|k:
an estimation value, using observation signals y0 to yk, of the state xk (an impulse response of an unknown system) at time k;
provided by a filter equation,
x{circumflex over ( )}k+1|k:
a single-step prediction value, using the observation signals y0 to yk, of a state xk+1 at the time k;
provided by the filter equation,
x{circumflex over ( )}−1|−1:
an initial estimation value of the state;
unknown in a normal situation, but zero is used for convenience,
Ks,k:
a filter gain;
obtained from a matrix Σ{circumflex over ( )}k|k−1,
Re,k:
an auxiliary variable;
a 2×2 matrix,
N:
a dimension (a tap number) of the state vector;
provided in advance,
μ{tilde over ( )}k:
an N+1-th 1×2 row vector of KUk;
obtained by KUk,
W:
a weighting matrix;
determined by γf,
ek:
an ex-post forward prediction error;
a two-dimensional column vector,
ek:
an ex-post backward prediction error;
a two-dimensional column vector,
γf:
an attenuation level;
provided upon designing, and
μ:
a step size (a relaxation factor);
a real number of μ>0, and provided in advance.

470 more elements

A system identification method for performing fast real-time identification for a system from input/output data, the method comprising:

estimating a state estimation value x{circumflex over ( )}k|k of a state xk of the system from a received signal uk of an interface in an acoustic system or a communication system and from an observation signal yk of an echo or a feedback by using a filter robust to disturbance in such a manner that a maximum energy gain from the disturbance to a filter error is, as an evaluation criterion, set smaller than a given upper limit γf2;
and
canceling out the echo or the feedback using a result of the state estimation value x{circumflex over ( )}k|k, wherein
the filter is, by Expressions (49), (50), (55), (58) below, provided to a state space model represented by Expressions (11) to (13) below to estimate the state estimation value x{circumflex over ( )}k|k of the state xk of the system:
x
k
+
1
=
x
k
+
G
k
⁢
w
k
,
w
k
,
x
k
∈
N
(
11
)
y
k
=
H
k
⁢
x
k
+
v
k
,
y
k
,
v
k
∈
(
12
)
z
k
=
H
k
⁢
x
k
,
z
k
∈
,
H
k
∈
1
×
N
(
13
)
x
^
k
|
k
=
x
^
k
-
1
|
k
-
1
+
μ
⁢
K
~
k
⁡
(
:
,
1
)
R
e
,
k
⁡
(
1
,
1
)
⁢
(
y
k
-
H
k
⁢
x
^
k
-
1
|
k
-
1
)
(
49
)
,
(
50
)
R
e
,
k
=
R
e
,
k
-
1
+
ϵ
0
⁢
c
k
⁢
c
k
T
-
c
k
-
N
⁢
μ
~
k
(
55
)
[
K
~
k
μ
~
k
]
=
[
ϵ
0
⁢
c
k
K
~
k
-
1
]
(
58
)
where Ck and W are defined by the following expressions:
C
k
=
[
H
k
H
k
]
,
W
=
[
1
0
0
-
γ
f
-
2
]
,
ck∈R2×1 is a first column vector of Ck=[ck, . . . , ck−N+1],
C
˘
k
=
[
u
k
…
u
k
-
N
u
k
…
u
k
-
N
]
(
63
)
C
˘
k
⁡
(
:
,
1
)
=
c
k
=
[
u
k
u
k
]
T
,
C
˘
k
⁡
(
:
,
i
)
=
C
˘
k
-
1
⁡
(
:
,
i
-
1
)
,
⁢
i
=
2
,
…
⁢
,
N
+
1
H
k
=
[
u
k
,
…
⁢
,
u
k
-
N
+
1
]
T
,
(
64
)
xk:
a state vector or merely a state;
unknown, and this is a target for estimation,
x0:
an initial state;
unknown,
wk:
system noise;
unknown,
vk:
observation noise;
unknown,
yk:
an observation signal;
taken as filter input, and known,
zk:
an output signal;
unknown,
Gk:
a drive matrix;
known upon execution,
Hk:
an observation matrix, known,
x{circumflex over ( )}k|k:
an estimation value, using observation signals y0 to yk, of the state xk (an impulse response of an unknown system) at time k;
provided by a filter equation,
x{circumflex over ( )}k+1|k:
a single-step prediction value, using the observation signals y0 to yk, of a state xk+1 at the time k;
provided by the filter equation,
x{circumflex over ( )}−1|−1:
an initial estimation value of the state;
unknown in a normal situation, but zero is used for convenience,
Ks,k:
a filter gain;
obtained from a matrix Σ{circumflex over ( )}k|k−1,
Re,k:
an auxiliary variable;
a 2×2 matrix,
N:
a dimension (a tap number) of the state vector;
provided in advance,
μ{tilde over ( )}k:
an N+1-th 1×2 row vector of KUk;
obtained by KUk,
W:
a weighting matrix;
determined by γf,
ek:
an ex-post forward prediction error;
a two-dimensional column vector,
ek:
an ex-post backward prediction error;
a two-dimensional column vector,
ε0:
an optional positive constant;
ε0>0, and provided in advance,
γf:
an attenuation level;
provided upon designing, and
μ:
a step size (a relaxation factor);
a real number of μ>0, and provided in advance.

375 more elements

Dependencies are inferred from the claim text.

Facts

Application: 16/418,579Filed 21 May 2019
Priority: JP 2018-09850323 May 2018
Published: US 2019/0364361 A128 Nov 2019
Granted: 8 Dec 2020
Term ends: Not estimatedThe source records don’t support an estimate.

Classification12 codes

H03H 21/0043
Digital adaptive filters: adaptive algorithms
H04R 3/04
Circuits for transducers: for correcting frequency response
G05B 13/048
Involving the use of models or simulators: using a predictor
G10L 21/0232
Characterised by the method used for estimating noise: processing in the frequency domain

Family

US 2019/0364361 A1Pre-grant publication · published 28 Nov 2019
US 10,863,272 B2This patent

From the US filing history. Foreign family members aren’t listed.

Timeline

Citations

Open elsewhere

patentgrep

Loading patent…

Abstract

A system identification method for performing fast real-time identification for a system from input/output data, the method comprising:

estimating a state estimation value x{circumflex over ( )}k|k of a state xk of the system from a received signal uk of an interface in an acoustic system or a communication system and from an observation signal yk of an echo or a feedback by using a filter robust to disturbance in such a manner that a maximum energy gain from the disturbance to a filter error is, as an evaluation criterion, set smaller than a given upper limit γf2;
and
canceling out the echo or the feedback using a result of the state estimation value x{circumflex over ( )}k|k, wherein
the filter is, by Expressions (49) to (62) below, provided to a state space model represented by Expressions (11) to (13) below to estimate the state estimation value x{circumflex over ( )}k|k of the state xk of the system:
x
k
+
1
=
⁢
x
k
+
G
k
⁢
w
k
,
w
k
,
x
k
∈
ℛ
N
⁢
(
11
)
y
k
=
⁢
H
k
⁢
x
k
+
υ
k
,
y
k
,
υ
k
∈
ℛ
⁢
(
12
)
z
k
=
⁢
H
k
⁢
x
k
,
z
k
∈
ℛ
,
H
k
∈
ℛ
1
×
N
⁢
(
13
)
x
^
k
❘
k
=
⁢
x
^
k
-
1
❘
k
-
1
+
K
s
,
k
⁡
(
y
k
-
H
k
⁢
x
^
k
-
1
❘
k
-
1
)
⁢
(
49
)
K
s
,
k
=
⁢
K
~
k
⁡
(
:
,
1
)
R
e
,
k
⁡
(
1
,
1
)
⁢
(
50
)
b
k
=
⁢
b
k
-
1
-
ρ
-
1
⁢
K
~
k
⁢
W
⁢
⁢
e
_
k
⁢
(
51
)
S
_
k
=
⁢
ρ
⁢
S
_
k
-
1
+
e
_
k
T
⁢
W
⁢
⁢
e
~
_
k
⁢
(
52
)
e
_
k
=
⁢
χ
k
-
1
⁢
e
~
_
k
⁢
(
53
)
χ
k
=
⁢
ρ
-
1
⁢
R
e
,
k
⁢
W
⁢
(
54
)
R
e
,
k
=
⁢
R
e
,
k
-
1
+
e
~
k
⁢
e
~
k
T
S
k
-
1
-
e
~
_
k
⁢
μ
~
k
⁢
(
55
)
e
~
_
k
=
⁢
S
_
k
-
1
⁢
μ
~
k
T
⁢
(
56
)
K
~
k
=
⁢
m
~
k
-
b
k
-
1
⁢
μ
~
k
⁢
(
57
)
[
m
~
k
μ
~
k
]
=
⁢
[
0
K
~
k
-
1
]
+
[
1
a
k
-
1
]
⁢
e
~
k
T
S
k
-
1
⁢
(
58
)
a
k
=
⁢
a
k
-
1
-
ρ
-
1
⁢
K
~
k
-
1
⁢
W
⁢
⁢
e
k
⁢
(
59
)
S
k
=
⁢
ρ
⁢
⁢
S
k
-
1
+
e
k
T
⁢
W
⁢
⁢
e
~
k
⁢
(
60
)
e
k
=
⁢
χ
k
-
1
-
1
⁢
e
~
k
⁢
(
61
)
e
~
k
=
⁢
c
k
+
C
k
-
1
⁢
a
k
-
1
⁢
(
62
)
where Ck and W are defined by the following expressions:
C
k
=
[
H
k
H
k
]
,
W
=
[
1
0
0
-
γ
f
-
2
]
,
ck∈R2×1 is a first column vector of C
C
⋓
k
=
[
u
k
…
u
k
-
N
u
k
…
u
k
-
N
]
(
63
)
C
⋓
k
⁡
(
:
,
1
)
=
c
k
=
[
u
k
u
k
]
T
,
C
⋓
k
⁡
(
:
,
i
)
=
C
⋓
k
-
1
⁡
(
:
,
i
-
1
)
,
⁢
i
=
2
,
…
⁢
,
N
+
1
⁢
⁢
H
k
=
[
u
k
,
…
⁢
,
u
k
-
N
+
1
]
T
,
(
64
)
xk:
a state vector or merely a state;
unknown, and this is a target for estimation,
x0:
an initial state;
unknown,
wk:
system noise;
unknown,
vk:
observation noise;
unknown,
yk:
an observation signal;
taken as filter input, and known,
zk:
an output signal;
unknown,
Gk:
a drive matrix;
known upon execution,
Hk:
an observation matrix, known,
x{circumflex over ( )}k|k:
an estimation value, using observation signals y0 to yk, of the state xk (an impulse response of an unknown system) at time k;
provided by a filter equation,
x{circumflex over ( )}k+1|k:
a single-step prediction value, using the observation signals y0 to yk, of a state xk+1 at the time k;
provided by the filter equation,
x{circumflex over ( )}−1|−1:
an initial estimation value of the state;
unknown in a normal situation, but zero is used for convenience,
Ks,k:
a filter gain;
obtained from a matrix Σ{circumflex over ( )}k|k−1,
Re,k:
an auxiliary variable;
a 2×2 matrix,
χk:
a conversion factor;
a 2×2 matrix,
N:
a dimension (a tap number) of the state vector;
provided in advance,
μ{tilde over ( )}k:
an N+1-th 1×2 row vector of KUk;
obtained by KUk,
mk:
an N×2 matrix including first to N-th rows of KUk;
obtained by KUk,
W:
a weighting matrix;
determined by γf,
ak:
a forward linear prediction factor;
an N-dimensional column vector,
bk:
a backward linear prediction factor;
an N-dimensional column vector,
ek:
an ex-post forward prediction error;
a two-dimensional column vector,
ek:
an ex-post backward prediction error;
a two-dimensional column vector, and
γf:
an attenuation level;
provided upon designing.

649 more elements

Facts

Application

16/418,579Filed 21 May 2019

Priority

JP 2018-09850323 May 2018

Published

US 2019/0364361 A128 Nov 2019

Granted

8 Dec 2020

Term ends

Not estimatedThe source records don’t support an estimate.

Classification12 codes

H03H 21/0043
Digital adaptive filters: adaptive algorithms
H04R 3/04
Circuits for transducers: for correcting frequency response
G05B 13/048
Involving the use of models or simulators: using a predictor
G10L 21/0232
Characterised by the method used for estimating noise: processing in the frequency domain