US 7,480,595 B2 · System estimation method and program, recording medium, and system estimation device

A system estimation method, for a communication system or a sound system or sound field reproduction or noise control, for making state estimation robust and optimizing a forgetting factor ρ simultaneously in an estimation algorithm, in which

for a state space model expressed by following expressions:
xk+1=Fkxk+Gkwk
yk=Hkxk+vk
zk=Hkxk
here,
xk:
a state vector or simply a state,
wk:
a system noise,
vk:
an observation noise,
yk:
an observation signal,
zk:
an output signal,
Fk:
dynamics of a system, and
Gk:
a drive matrix,
as an evaluation criterion, a maximum value of an energy gain which indicates a ratio of a filter error to a disturbance including the system noise wk and the observation noise vk and is weighted with the forgetting factor ρ is suppressed to be smaller than a term corresponding to a previously given upper limit value γf, and
the system estimation method comprises:
a step at which a processing section inputs the upper limit value γf, the observation signal yk as an input of a filter and a value including an observation matrix Hk from a storage section or an input section;
a step at which the processing section determines the forgetting factor ρ;
as a following function of γf;
ρ=1−χ(γf)
where χ(γf) denotes a monotonicaly damping function of γf to satisfy χ(1)=1 and χ(∞)=0,;
a step of executing a hyper H∞ filter at which the processing section reads out an initial value or a value including the observation matrix Hk at a time from the storage section and obtains a filter gain Ks,k by using the forgetting factor ρ and a gain matrix Kk and by following expressions (20) to (22):
x
^
k
⁢
|
k
⁢
=
⁢
x
^
k
-
1
|
k
-
1
+
K
s
,
k
⁡
(
y
k
-
H
k
⁢
⁢
x
^
k
-
1
⁢
|
k
-
1
)
(
20
)
K
s
,
k
=
K
k
⁡
(
:
,
1
)
/
R
e
,
k
⁡
(
1
,
1
)
,
K
k
=
ρ
1
2
⁡
(
ρ
-
1
2
⁢
K
k
⁢
R
e
,
k
-
1
2
⁢
J
1
-
1
)
⁢
J
1
⁢
R
e
,
k
1
2
(
21
)
[
R
k
1
2
C
k
⁢
⁢
Σ
^
k
|
k
-
1
1
2
⁢
0
ρ
-
1
2
⁢
Σ
^
k
|
k
-
1
1
2
]
⁢
Θ
⁡
(
k
)
=
[
R
e
,
k
1
2
0
ρ
-
1
2
⁢
K
k
⁢
R
e
,
k
-
1
2
⁢
J
1
-
1
Σ
^
k
+
1
|
k
1
2
]
⁢
⁢
Where
,
(
22
)
R
k
=
R
k
1
2
⁢
J
1
⁢
R
k
T
2
,
⁢
R
k
1
2
=
[
ρ
1
2
0
0
ρ
1
2
⁢
γ
f
]
,
⁢
J
1
=
[
1
0
0
-
1
]
,
⁢
Σ
^
k
|
k
-
1
=
Σ
^
k
|
k
-
1
1
2
⁢
Σ
^
k
|
k
-
1
T
2
⁢
⁢
R
e
,
k
=
R
k
+
C
k
⁢
Σ
^
k
|
k
-
1
⁢
C
k
T
,
⁢
C
k
=
[
H
k
H
k
]
,
⁢
R
e
,
k
=
R
e
,
k
1
2
⁢
J
1
⁢
R
e
,
k
T
2
,
⁢
x
^
0
|
0
=
x
⋓
0
(
23
)
Θ(k) denotes a J-unitary matrix, that is, satisfies
Θ(k) JΘH(k)T=J, J=(J1⊕I), I denotes a unit matrix, Kk(:, 1) denotes a column vector of a first column of the matrix Kk
R
k
=
[
ρ
0
0
-
ργ
f
2
]
here,
x^k|k:
the estimated value of the state xk at the time k using the observation signals y0 to yk,
yk:
the observation signal,
Fk:
the dynamics of the system, Fk=I for simplification,
Ks,k:
the filter gain,
Hk:
the observation matrix,
Σ^k|k:
corresponding to a covariance matrix of an error of x^k|k,
Θ(k):
the J-unitary matrix, and
Re,k:
an auxiliary variable,
a step at which the processing section stores an estimated value of the state xk by the hyper H∞, filter into the storage section;
a step at which the processing section calculates an existence condition based on the upper limit value γf and the forgetting factor ρ by the obtained observation matrix Hi or the observation matrix Hi and the filter gain Ks,i, and
a step at which the processing section decreases the upper limit value γf by a factor of Δγ and stores the resultant value into the storage section while the existence condition is satisfied in the step of executing the hyper H∞, filter,
wherein the H∞ filter equation is applied to obtain the state estimated value x^k|K=[h^1[k],. . . , h^N[k]]T, where h^[k] is the estimated value of impulse response,
a pseudo-echo is estimated by a following expression:
d
^
k
=
∑
i
=
0
N
-
1
⁢
h
^
i
⁡
[
k
]
⁢
u
(
k
-
i
)
,
⁢
k
=
0
,
1
,
2
,
…
(
34
)
and an actual echo is cancelled by the obtained pseudo-echo.

449 more elements

A system estimation method, for a communication system or a sound system or sound field reproduction or noise control, for making state estimation robust and optimizing a forgetting factor ρ simultaneously in an estimation algorithm, in which

for a state space model expressed by following expressions:
xk+1=Fkxk+Gkwk
yk=Hkxk+vk
zk=Hkxk
here,
xk:
a state vector or simply a state,
wk:
a system noise,
vk:
an observation noise,
yk:
an observation signal,
zk:
an output signal,
Fk:
dynamics of a system, and
Gk:
a drive matrix,
as an evaluation criterion, a maximum value of an energy gain which indicates a ratio of a filter error to a disturbance including the system noise wk and the observation noise vk and is weighted with the forgetting factor ρ is suppressed to be smaller than a term corresponding to a previously given upper limit value γf, and
the system estimation method comprises:
a step at which a processing section inputs the upper limit value γf, the observation signal yk as an input of a filter and a value including an observation matrix Hk from a storage section or an input section;
a step at which the processing section determines the forgetting factor ρ relevant to the state space model in accordance with the upper limit value γf;
as a following function of γf,
ρ=1−χ(γf)
where χ(γf) denotes a monotonicaly damping function of γf to satisfy χ(1)=1 and χ(∞)=0,
a step of executing a hyper H∞ filter at which the processing section reads out an initial value or a value including the observation matrix Hk at a time from the storage section and obtains a filter gain Ks,k by using the forgetting factor ρ and a gain matrix Kk and by following expressions:
x
^
k
|
k
=
x
^
k
-
1
|
k
-
1
+
K
s
,
k
⁡
(
y
k
-
H
k
⁢
x
^
k
-
1
|
k
-
1
)
(
61
)
K
s
,
k
=
K
k
⁡
(
:
,
1
)
/
R
e
,
k
⁡
(
1
,
1
)
,
⁢
K
k
=
ρ
1
2
⁡
(
K
_
k
⁢
R
e
,
k
-
1
2
)
⁢
R
e
,
k
1
2
(
62
)
[
R
e
,
k
+
1
1
2
0
[
K
_
k
+
1
0
]
⁢
R
e
,
k
+
1
-
T
2
⁢
J
1
L
~
k
+
1
⁢
R
r
,
k
+
1
-
T
2
]
=
[
R
e
,
k
1
2
C
⋓
k
+
1
⁢
L
~
k
⁢
R
r
,
k
-
1
2
[
0
⁢
K
⁢
_
⁢
k
]
⁢
R
e
,
k
-
1
2
⁢
J
1
ρ
-
1
2
⁢
L
~
k
⁢
R
r
,
k
-
1
2
]
⁢
Θ
⁡
(
k
)
(
63
)
here, Θ(k) denotes an arbitrary J-unitary matrix, and {hacek over (C)}k={hacek over (C)}k+1Ψ is established, where
R
k
=
R
k
1
2
⁢
J
1
⁢
R
k
T
2
,
⁢
R
k
1
2
=
[
ρ
1
2
0
0
ρ
1
2
⁢
γ
f
]
,
⁢
J
1
=
[
1
0
0
-
1
]
,
⁢
Σ
^
k
|
k
-
1
=
Σ
^
k
|
k
-
1
1
2
⁢
Σ
^
k
|
k
-
1
T
2
⁢
⁢
R
e
,
k
=
R
k
+
C
k
⁢
Σ
^
k
|
k
-
1
⁢
C
k
T
,
⁢
C
k
=
[
H
k
H
k
]
,
⁢
R
e
,
k
=
R
e
,
k
1
2
⁢
J
1
⁢
R
e
,
k
T
2
,
⁢
x
^
0
|
0
=
x
⋓
0
(
23
)
R
k
=
[
ρ
0
0
-
ργ
f
2
]
here,
x^k|k:
the estimated value of the state xk at the time k using the observation signals y0 to yk,
yk:
the observation signal,
Ks,k:
the filter gain,
Hk:
the observation matrix,
Θ(k):
the J-unitary matrix, and
Re,k:
an auxiliary variable,
a step at which the processing section stores an estimated value of the state xk by the hyper H∞ filter into the storage section;
a step at which the processing section calculates an existence condition based on the upper limit value γf and the forgetting factor ρ by the obtained observation matrix Hi or the observation matrix Hi and the filter gain Ks,i, and
a step at which the processing section decreases the upper limit value γf by a factor of Δγ and stores the resultant value into the storage section while the existence condition is satisfied in the step of executing the hyper H∞ filter,
wherein the H∞ filter equation is applied to obtain the state estimated value x^k|K=[h^1[k],. . . , h^N[k]]T, where h^[k] is the estimated value of impulse response,
a pseudo-echo is estimated by a following expression:
d
^
k
=
∑
i
=
0
N
-
1
⁢
h
^
i
⁡
[
k
]
⁢
u
(
k
-
i
)
,
⁢
k
=
0
,
1
,
2
,
…
(
34
)
and an actual echo is cancelled by the obtained pseudo-echo.

459 more elements

A system estimation method, for a communication system or a sound system or sound field reproduction or noise control, for making state estimation robust and optimizing a forgetting factor ρ simultaneously in an estimation algorithm, in which

for a state space model expressed by following expressions:
xk+1=Fkxk+Gkwk
yk=Hkxk+vk
zk=Hkxk
here,
xk:
a state vector or simply a state,
wk:
a system noise,
vk:
an observation noise,
yk:
an observation signal,
zk:
an output signal,
Fk:
dynamics of a system, and
Gk:
a drive matrix,
as an evaluation criterion, a maximum value of an energy gain which indicates a ratio of a filter error to a disturbance including the system noise wk and the observation noise vk and is weighted with the forgetting factor ρ is suppressed to be smaller than a term corresponding to a previously given upper limit value γf, and
the system estimation method comprises:
a step at which a processing section inputs the upper limit value γf, the observation signal yk as an input of a filter and a value including an observation matrix Hk from a storage section or an input section;
a step at which the processing section determines the forgetting factor ρ as a following function γf,
ρ=1−χ(γf)
where χ(γf) denotes a monotonicaly damping function of γf to satisfy χ(1)=1 and χ(∞)=0,
a step of executing a hyper H∞, filter at which the processing section reads out an initial value or a value including the observation matrix Hk at a time from the storage section and obtains a filter gain Ks,k by using the forgetting factor ρ and a gain matrix K−k and by following expressions:
⁢
x
^
k
⁢
|
k
⁢
=
⁢
x
^
k
-
1
|
k
-
1
+
K
s
,
k
⁡
(
y
k
-
H
k
⁢
⁢
x
^
k
-
⁢
1
|
k
-
1
)
(
25
)
⁢
K
s
,
k
=
ρ
1
2
⁢
K
_
k
⁡
(
:
,
1
)
/
R
e
,
k
⁡
(
1
,
1
)
(
26
)
⁢
[
K
_
k
+
1
0
]
=
[
0
K
_
k
]
-
ρ
-
1
2
⁢
L
~
k
⁢
R
r
,
k
-
1
⁢
L
~
k
T
⁢
C
⋓
k
+
1
T
(
27
)
⁢
L
~
k
+
1
=
ρ
-
1
2
⁢
L
~
k
-
[
0
K
_
k
]
⁢
R
e
,
k
-
1
⁢
C
⋓
k
+
1
⁢
L
~
k
(
28
)
⁢
R
e
,
k
+
1
=
R
e
,
k
-
C
⋓
k
+
1
⁢
L
~
k
⁢
R
r
,
k
-
1
⁢
L
~
k
T
⁢
C
⋓
k
+
1
T
(
29
)
⁢
R
r
,
k
+
1
=
R
r
,
k
-
L
~
k
T
⁢
C
⋓
k
+
1
T
⁢
R
e
,
k
-
1
⁢
C
⋓
k
+
1
⁢
L
~
k
⁢
⁢
Where
,
(
30
)
⁢
C
⋓
k
+
1
=
[
H
k
+
1
H
⋓
k
+
1
]
,
⁢
H
⋓
k
+
1
=
[
u
k
+
1
⁢
u
⁡
(
k
+
1
-
N
)
]
=
[
u
⁡
(
k
+
1
)
⁢
u
k
]
,
⁢
H
⋓
1
=
[
u
⁡
(
1
)
,
0
,
…
⁢
,
0
]
⁢
⁢
R
e
,
1
=
R
1
+
C
⋓
1
⁢
Σ
⋓
1
|
0
⁢
C
⋓
1
T
,
⁢
R
1
=
[
ρ
0
0
-
ρ
⁢
⁢
γ
f
2
]
,
⁢
Σ
⋓
1
|
0
=
diag
⁢
⁢
{
ρ
2
,
ρ
3
,
…
⁢
,
ρ
N
+
2
}
,
⁢
ρ
=
1
-
χ
⁢
(
γ
f
)
⁢
⁢
L
~
0
=
[
1
0
0
0
0
1
]
∈
ℛ
(
N
+
1
)
×
2
,
⁢
R
r
,
0
=
[
-
1
0
0
ρ
-
N
]
,
⁢
K
_
0
=
0
,
⁢
x
^
0
|
0
=
x
^
0
,
⁢
K
_
k
=
ρ
-
1
2
⁢
K
k
(
31
)
⁢
here,
yk:
the observation signal,
Fk:
the dynamics of the system, Fk=I for simplification,
Hk:
the observation matrix,
x^k|k:
the estimated value of the state xk at the time k using the observation signals y0 to yk,
Ks,k:
the filter gain, obtained from the gain matrix K−k, and
Re,k,L{tilde over ( )}k:
an auxiliary variable,
a step at which the processing section stores an estimated value of the state xk by the hyper H∞ filter into the storage section;
a step at which the processing section calculates an existence condition based on the upper limit value γf and the forgetting factor ρ by the obtained observation matrix Hi or the observation matrix Hi and the filter gain Ks,i, and
a step at which the processing section decreases the upper limit value γf by a factor of Δγ and stores the resultant value into the storage section while the existence condition is satisfied in the step of executing the hyper H∞ filter,
wherein the H∞ filter equation is applied to obtain the state estimated value x^k|K=[h^1[k],. . . , h^N[k]]T, where h^[k] is the estimated value of impulse response,
a pseudo-echo is estimated by a following expression:
d
^
k
=
∑
i
=
0
N
-
1
⁢
h
^
i
⁡
[
k
]
⁢
u
(
k
-
i
)
,
⁢
k
=
0
,
1
,
2
,
…
(
34
)
and an actual echo is cancelled by the obtained pseudo-echo.

571 more elements

A system estimation program product, for a communication system or a sound system or sound field reproduction or noise control, embodied on a computer-readable medium and comprising code that, when executed, causes a computer to make state estimation robust and to optimize a forgetting factor ρ simultaneously in an estimation algorithm, in which

for a state space model expressed by following expressions:
xk+1=Fkxk+Gkwk
yk=Hkxk+vk
zk=Hkxk
here,
xk:
a state vector or simply a state,
wk:
a system noise,
vk:
an observation noise,
yk:
an observation signal,
zk:
an output signal,
Fk:
dynamics of a system, and
Gk:
a drive matrix,
as an evaluation criterion, a maximum value of an energy gain which indicates a ratio of a filter error to a disturbance including the system noise wk and the observation noise vk and is weighted with the forgetting factor ρ is suppressed to be smaller than a term corresponding to a previously given upper limit value γf, and
the system estimation program causes the computer to execute:
a step at which a processing section inputs the upper limit value γf, the observation signal yk as an input of a filter and a value including an observation matrix Hk from a storage section or an input section;
a step at which the processing section determines the forgetting factor ρ as a following function γf,
ρ=1−χ(γf)
where ρ(γf) denotes a monotonicaly damping function of γf to satisfy χ(1)=1 and χ(∞)=0,
a step of executing a hyper H∞ filter at which the processing section reads out an initial value or a value including the observation matrix Hk at a time from the storage section and obtains a filter gain Ks,k by using the forgetting factor ρ and a gain matrix K−k and by following expressions:
x
^
k
⁢
|
k
⁢
=
⁢
x
^
k
-
1
|
k
-
1
+
K
s
,
k
⁡
(
y
k
-
H
k
⁢
⁢
x
^
k
-
1
⁢
|
k
-
1
)
(
25
)
⁢
K
s
,
k
=
ρ
1
2
⁢
K
_
k
⁡
(
:
,
1
)
/
R
e
,
k
⁡
(
1
,
1
)
(
26
)
⁢
[
K
_
k
+
1
0
]
=
[
0
K
_
k
]
-
ρ
-
1
2
⁢
L
~
k
⁢
R
r
,
k
-
1
⁢
L
~
k
T
⁢
C
⋓
k
+
1
T
(
27
)
⁢
L
~
k
+
1
=
ρ
-
1
2
⁢
L
~
k
-
[
0
K
_
k
]
⁢
R
e
,
k
-
1
⁢
C
⋓
k
+
1
⁢
L
~
k
(
28
)
⁢
R
e
,
k
+
1
=
R
e
,
k
-
C
⋓
k
+
1
⁢
L
~
k
⁢
R
r
,
k
-
1
⁢
L
~
k
T
⁢
C
⋓
k
+
1
T
(
29
)
⁢
R
r
,
k
+
1
=
R
r
,
k
-
L
~
k
T
⁢
C
⋓
k
+
1
T
⁢
R
e
,
k
-
1
⁢
C
⋓
k
+
1
⁢
L
~
k
⁢
⁢
Where
,
(
30
)
⁢
C
⋓
k
+
1
=
[
H
⋁
k
+
1
H
⋓
k
+
1
]
,
⁢
H
⋓
k
+
1
=
[
u
k
+
1
⁢
u
⁡
(
k
+
1
-
N
)
]
=
[
u
⁡
(
k
+
1
)
⁢
u
k
]
,
⁢
H
⋓
1
=
[
u
⁡
(
1
)
,
0
,
…
⁢
,
0
]
⁢
⁢
R
e
,
1
=
R
1
+
C
⋓
1
⁢
Σ
⋓
1
|
0
⁢
C
⋓
1
T
,
⁢
R
1
=
[
ρ
0
0
-
ρ
⁢
⁢
γ
f
2
]
,
⁢
Σ
⋓
1
|
0
=
diag
⁢
⁢
{
ρ
2
,
ρ
3
,
…
⁢
,
ρ
N
+
2
}
,
⁢
ρ
=
1
-
χ
⁢
(
γ
f
)
⁢
⁢
L
~
0
=
[
1
0
0
0
0
1
]
∈
ℛ
(
N
+
1
)
×
2
,
⁢
R
r
,
0
=
[
-
1
0
0
-
ρ
N
]
,
⁢
K
_
0
=
0
,
⁢
x
^
0
|
0
=
x
^
0
,
⁢
K
_
k
=
ρ
-
1
2
⁢
K
k
(
31
)
⁢
here,
yk:
the observation signal,
Fk:
the dynamics of the system, Fk=I for simplification,
Hk:
the observation matrix,
x^k|k:
the estimated value of the state xk at the time k using the observation signals y0 to yk,
Ks,k:
the filter gain, obtained from the gain matrix K−k, and
Re,k, L{tilde over ( )}k:
an auxiliary variable,
a step at which the processing section stores an estimated value of the state xk by the hyper H∞ filter into the storage section;
a step at which the processing section calculates an existence condition based on the upper limit value γf and the forgetting factor ρ by the obtained observation matrix Hi or the observation matrix Hi and the filter gain Ks,i, and
a step at which the processing section decreases the upper limit value γf by a factor of Δγ and stores the resultant value into the storage section while the existence condition is satisfied in the step of executing the hyper H∞ filter;
wherein the H∞ filter equation is applied to obtain the state estimated value x^k|K=[h^1[k],. . . , h^N[k]]T, where h^[k] is the estimated value of impulse response,
a pseudo-echo is estimated by a following expression:
d
^
k
=
∑
i
=
0
N
-
1
⁢
h
^
i
⁡
[
k
]
⁢
u
(
k
-
i
)
,
⁢
k
=
0
,
1
,
2
,
…
(
34
)
and an actual echo is cancelled by the obtained pseudo-echo.

571 more elements

A computer readable recording medium recording a system estimation program product, for a communication system or a sound system or sound field reproduction or noise control, embodied on a computer-readable medium and comprising code that, when executed, causes a computer to make state estimation robust and to optimize a forgetting factor ρ simultaneously in an estimation algorithm, in which

for a state space model expressed by following expressions:
xk+1=Fkxk+Gkwk
yk=Hkxk+vk
zk=Hkxk
here,
xk:
a state vector or simply a state,
wk:
a system noise,
vk:
an observation noise,
yk:
an observation signal,
zk:
an output signal,
Fk:
dynamics of a system, and
Gk:
a drive matrix,
as an evaluation criterion, a maximum value of an energy gain which indicates a ratio of a filter error to a disturbance including the system noise wk and the observation noise vk and is weighted with the forgetting factor ρ is suppressed to be smaller than a term corresponding to a previously given upper limit value γf, and
the computer readable recording medium recording the system estimation program causes the computer to execute:
a step at which a processing section inputs the upper limit value γf, the observation signal yk as an input of a filter and a value including an observation matrix Hk from a storage section or an input section;
a step at which the processing section determines the forgetting factor ρ relevant to the state space model in accordance as a following function γf,
ρ=1−χ(γf)
where χ(γf) denotes a monotonicaly damping function of γf to satisfy χ(1)=1 and χ(∞)=0,
a step of executing a hyper H∞ filter at which the processing section reads out an initial value or a value including the observation matrix Hk at a time from the storage section and obtains a filter gain Ks,k by using the forgetting factor ρ and a gain matrix K−k and by following expressions:
x
^
k
|
k
=
x
^
k
-
1
|
k
-
1
+
K
s
,
k
⁡
(
y
k
-
H
k
⁢
x
^
k
-
1
|
k
-
1
)
(
25
)
K
s
,
k
=
ρ
1
2
⁢
K
_
k
⁡
(
:
,
1
)
/
R
e
,
k
⁡
(
1
,
1
)
(
26
)
[
K
_
k
+
1
0
]
=
[
0
K
_
k
]
-
ρ
-
1
2
⁢
L
~
k
⁢
R
r
,
k
-
1
⁢
L
~
k
T
⁢
C
⋓
k
+
1
T
(
27
)
L
~
k
+
1
=
ρ
-
1
2
⁢
L
~
k
-
[
0
K
_
k
]
⁢
R
e
,
k
-
1
⁢
C
⋓
k
+
1
⁢
L
~
k
(
28
)
R
e
,
k
+
1
=
R
e
,
k
-
C
⋓
k
+
1
⁢
L
~
k
⁢
R
r
,
k
-
1
⁢
L
~
k
T
⁢
C
⋓
k
+
1
T
(
29
)
R
r
,
k
+
1
=
R
r
,
k
-
L
~
k
T
⁢
C
⋓
k
+
1
T
⁢
R
e
,
k
-
1
⁢
C
⋓
k
+
1
⁢
L
~
k
⁢
⁢
Where
,
(
30
)
C
⋓
k
+
1
=
[
H
⋓
k
+
1
H
⋓
k
+
1
]
,
⁢
H
⋓
k
+
1
=
[
u
k
+
1
⁢
u
⁡
(
k
+
1
-
N
)
]
=
[
u
⁡
(
k
+
1
)
⁢
⁢
u
k
]
,
⁢
H
⋓
1
=
[
u
⁡
(
1
)
,
0
,
…
⁢
,
0
]
⁢
⁢
R
e
,
1
=
R
1
+
C
⋓
1
⁢
Σ
⋓
1
|
0
⁢
C
⋓
1
T
,
⁢
R
1
=
[
ρ
0
0
-
ρ
⁢
⁢
γ
f
2
]
,
⁢
Σ
⋓
1
|
0
=
diag
⁢
{
ρ
2
,
ρ
3
,
…
⁢
,
ρ
N
+
2
}
,
⁢
ρ
=
1
-
χ
⁡
(
γ
f
)
⁢
⁢
L
~
0
=
[
1
0
0
0
0
1
]
∈
ℛ
(
N
+
1
)
×
2
,
⁢
R
r
,
0
=
[
-
1
0
0
ρ
-
N
]
,
⁢
K
_
0
=
0
,
⁢
x
^
0
|
0
=
x
⋓
0
,
⁢
K
_
k
=
ρ
-
1
2
⁢
K
k
(
31
)
here,
yk:
the observation signal,
Fk:
the dynamics of the system, Fk=I for simplification,
Hk:
the observation matrix,
x^k|k:
the estimated value of the state xk at the time k using the observation signals y0 to yk,
Ks,k:
the filter gain, obtained from the gain matrix K−k, and
Re,k, L{tilde over ( )}k:
an auxiliary variable,
a step at which the processing section stores an estimated value of the state xk by the hyper H∞ filter into the storage section;
a step at which the processing section calculates an existence condition based on the upper limit value γf and the forgetting factor ρ by the obtained observation matrix Hi or the observation matrix Hi and the filter gain Ks,i, and
a step at which the processing section decreases the upper limit value γf by a factor of Δγ and stores the resultant value into the storage section while the existence condition is satisfied in the step of executing the hyper H∞ filter,
wherein the H∞ filter equation is applied to obtain the state estimated value x^k|K=[h^1[k],. . . , h^N[k]]T, where h^[k] is the estimated value of impulse response,
a pseudo-echo is estimated by a following expression:
d
^
k
=
∑
i
=
0
N
-
1
⁢
h
^
i
⁡
[
k
]
⁢
u
(
k
-
i
)
,
⁢
k
=
0
,
1
,
2
,
…
(
34
)
and an actual echo is cancelled by the obtained pseudo-echo.

559 more elements

A system estimation device, for communication system or a sound system or sound field reproduction or noise control, for making state estimation robust and optimizing a forgetting factor ρ simultaneously in an estimation algorithm, in which

for a state space model expressed by following expressions:
xk+1=Fkxk+Gkwk
yk=Hkxk+vk
zk=Hkxk
here,
xk:
a state vector or simply a state,
wk:
a system noise,
vk:
an observation noise,
yk:
an observation signal,
zk:
an output signal,
Fk:
dynamics of a system, and
Gk:
a drive matrix,
as an evaluation criterion, a maximum value of an energy gain which indicates a ratio of a filter error to a disturbance including the system noise wk and the observation noise vk and is weighted with the forgetting factor ρ is suppressed to be smaller than a term corresponding to a previously given upper limit value γf, and
the system estimation device comprises:
a processing section to execute the estimation algorithm;
and
a storage section to which reading and/or writing is performed by the processing section and which stores respective observed values, set values, and estimated values relevant to the state space model,
further comprising:
a means at which the processing section inputs the upper limit value γf, the observation signal yk as an input of a filter and a value including an observation matrix Hk from the storage section or an input section;
a means at which the processing section determines the forgetting factor ρ as a following function γf,
ρ=1−χ(γf)
where χ(γf) denotes a monotonicaly damping function of γf to satisfy χ(1)=1 and χ(∞)=0,
a means of executing a hyper H∞ filter at which the processing section reads out an initial value or a value including the observation matrix Hk at a time from the storage section and obtains a filter gain Ks,k by using the forgetting factor ρ and a gain matrix K−k and by following expressions:
x
^
k
|
k
=
x
^
k
-
1
|
k
-
1
+
K
s
,
k
⁡
(
y
k
-
H
k
⁢
x
^
k
-
1
|
k
-
1
)
(
25
)
K
s
,
k
=
ρ
1
2
⁢
K
_
k
⁡
(
:
,
1
)
/
R
e
,
k
⁡
(
1
,
1
)
(
26
)
[
K
_
k
+
1
0
]
=
[
0
K
_
k
]
-
ρ
-
1
2
⁢
L
~
k
⁢
R
r
,
k
-
1
⁢
L
~
k
T
⁢
C
⋓
k
+
1
T
(
27
)
L
~
k
+
1
=
ρ
-
1
2
⁢
L
~
k
-
[
0
K
_
k
]
⁢
R
e
,
k
-
1
⁢
C
⋓
k
+
1
⁢
L
~
k
(
28
)
R
e
,
k
+
1
=
R
e
,
k
-
C
⋓
k
+
1
⁢
L
~
k
⁢
R
r
,
k
-
1
⁢
L
~
k
T
⁢
C
⋓
k
+
1
T
(
29
)
R
r
,
k
+
1
=
R
r
,
k
-
L
~
k
T
⁢
C
⋓
k
+
1
T
⁢
R
e
,
k
-
1
⁢
C
⋓
k
+
1
⁢
L
~
k
⁢
⁢
Where
,
(
30
)
C
⋓
k
+
1
=
[
H
⋓
k
+
1
H
⋓
k
+
1
]
,
⁢
H
⋓
k
+
1
=
[
u
k
+
1
⁢
u
⁡
(
k
+
1
-
N
)
]
=
[
u
⁡
(
k
+
1
)
⁢
⁢
u
k
]
,
⁢
H
⋓
1
=
[
u
⁡
(
1
)
,
0
,
…
⁢
,
0
]
⁢
⁢
R
e
,
1
=
R
1
+
C
⋓
1
⁢
Σ
⋓
1
|
0
⁢
C
⋓
1
T
,
⁢
R
1
=
[
ρ
0
0
-
ρ
⁢
⁢
γ
f
2
]
,
⁢
Σ
⋓
1
|
0
=
diag
⁢
{
ρ
2
,
ρ
3
,
…
⁢
,
ρ
N
+
2
}
,
⁢
ρ
=
1
-
χ
⁡
(
γ
f
)
⁢
⁢
L
~
0
=
[
1
0
0
0
0
1
]
∈
ℛ
(
N
+
1
)
×
2
,
⁢
R
r
,
0
=
[
-
1
0
0
ρ
-
N
]
,
⁢
K
_
0
=
0
,
⁢
x
^
0
|
0
=
x
⋓
0
,
⁢
K
_
k
=
ρ
-
1
2
⁢
K
k
(
31
)
here,
yk:
the observation signal,
Fk:
the dynamics of the system, Fk=I for simplification,
Hk:
the observation matrix,
x^k|k:
the estimated value of the state xk at the time k using the observation signals y0 to yk,
Ks,k:
the filter gain, obtained from the gain matrix K−k, and
Re,k, L{tilde over ( )}k:
an auxiliary variable,
a means at which the processing section stores an estimated value of the state xk by the hyper H∞ filter into the storage section;
a means at which the processing section calculates an existence condition based on the upper limit value γf and the forgetting factor ρ by the obtained observation matrix Hi or the observation matrix Hi and the filter gain Ks,i and
a means at which the processing section decreases the upper limit value γf by a factor of Δγ and stores the resultant value into the storage section while the existence condition is satisfied in the means of executing the hyper H∞ filter,
wherein the H∞ filter equation is applied to obtain the state estimated value x^k|K=[h^1[k],. . . , h^N[k]]T, where h^[k] is the estimated value of impulse response,
a pseudo-echo is estimated by a following expression:
d
^
k
=
∑
i
=
0
N
-
1
⁢
h
^
i
⁡
[
k
]
⁢
u
(
k
-
i
)
,
⁢
k
=
0
,
1
,
2
,
…
(
34
)
and an actual echo is cancelled by the obtained pseudo-echo.

563 more elements

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

Life of this patent

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

Life of this patent

Abstract

Claims15