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System estimation method, program, recording medium, system estimation device meetings achieved

Foreign code F110004200
File No. Y0412WO
Posted date Jul 12, 2011
Country EPO
Application number 04771550
Gazette No. 1657818
Gazette No. 1657818
Date of filing Aug 5, 2004
Gazette Date May 17, 2006
Gazette Date Apr 15, 2015
International application number JP2004011568
International publication number WO2005015737
Date of international filing Aug 5, 2004
Date of international publication Feb 17, 2005
Priority data
  • 2004JP011568 (Aug 5, 2004) WO
  • P2003-291614 (Aug 11, 2003) JP
Title System estimation method, program, recording medium, system estimation device meetings achieved
Abstract It is possible to establish an estimation method capable of logically and optimally deciding a forgetting coefficient and develop an estimation algorithm and a high-speed algorithm which are numerically stable.
Firstly, a processing section reads out or receives an upper limit value gamma f from a storage section or an input section (S101).
The processing section decides a forgetting coefficient rho by equation (15) (S103).
After this, according to the forgetting coefficient p, the processing section executes a hyper H infin filter of equations (10-13) (S105).
The processing section (101) calculates the existence condition of equation (17) (or equation (18) which will be given later) (S107).
When the existence condition is satisfied at all the times (S109), gamma f is decreased by DELTA gamma and the same processing is repeated (S111).
On the other hand, when the existence condition is not satisfied by a certain gamma f (S109), the DELTA gamma is added to the gamma f and the sum is output to an output section and/or stored in the storage section as an optimal value gamma f **op of the gamma f (S113).
Scope of claims [claim1]
1. A system estimation method, applicable to a system in the form of a communication system or a sound system or used for sound field reproduction or noise control, for making state estimation robust and optimizing a forgetting factor rho simultaneously in an estimation algorithm, said system being defined by
a state space model expressed by following expressions: (Equation image 85 not included in text) (Equation image 86 not included in text) (Equation image 87 not included in text)
where, x k is defined as a state vector, w k is defined as a system noise, v k is defined as an observation noise, y k is defined as an observation signal, z k is defined as an output signal, F k is defined as dynamics of said system, and G k is defined as a drive matrix, H k is defined as an observation matrix, wherein 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 w k and the observation noise v k and is weighted with the forgetting factor rho , is suppressed to be smaller than a term corresponding to a predetermined upper limit value gamma f, said filter error being associated with a filter used in said system estimation method, said filter receiving as an input signal said observation signal of said system, and
the system estimation method comprises: a step at which a processing section used in said system estimation method inputs the upper limit value gamma f, the observation signal y k as an input of said filter and a value including the observation matrix H k from a storage section or an input section; a step at which the processing section determines the forgetting factor rho relevant to said system defined by the state space model in accordance with the upper limit value gamma f; a step of executing a hyper H infin filtering in said filter at which the processing section reads out an initial value or a value including the observation matrix H k at a time from the storage section and obtains a filter gain K s,k by using the forgetting factor rho and a gain matrix K **- k and by following expressions: (Equation image 88 not included in text) (Equation image 89 not included in text) (Equation image 90 not included in text) (Equation image 91 not included in text) (Equation image 92 not included in text) (Equation image 93 not included in text) where, (Equation image 94 not included in text)
where, y k is the observation signal, F k is the dynamics of the system, H k is the observation matrix, x^ k|k is defined as the estimated value of the state vector x k at the time k using the observation signals y 0 to y k, K s,k is defined as the filter gain, obtained from the gain matrix K **- k, and R e,k, L **~ k are defined as auxiliary variables; a step at which the processing section stores an estimated value of the state vector x k obtained by the hyper H infin filtering into the storage section; a step at which the processing section calculates an existence condition based on the upper limit value gamma f and the forgetting factor rho by the obtained observation matrix H i or the observation matrix H i and the filter gain K s,i, wherein the processing section calculates the existence condition in accordance with a following expression: (Equation image 95 not included in text) here, (Equation image 96 not included in text)
where the forgetting factor rho and the upper limit value gamma f have a following relation:
0 < rho = 1 - chi (gamma f) <= 1, where chi (gamma f) denotes a monotonically damping function of gamma f to satisfy chi (1) = 1 and chi (infin ) = 0,
and
a step at which the processing section sets the upper limit value to be small within a range where the existence condition is satisfied at each time and stores the value into the storage section, by decreasing the upper limit value gamma f and repeating the step of executing the hyper H infin filtering.
[claim2]
2. The system estimation method according to claim 1, wherein an estimated value z **v k|k of the output signal z k is obtained from the estimated value x^ k|k of the state vector x k at the time k by a following expression: (Equation image 97 not included in text)
[claim3]
3. The system estimation method according to claim 1, wherein the H infin filter equation is applied to obtain the estimated value x^ k|k = [h^ 1 [k] , ..., h^ N [k]] **T
a pseudo-echo is estimated by a following expression: (Equation image 98 not included in text)
and
an echo canceller is realized by canceling an actual echo by the obtained pseudo-echo.
[claim4]
4. A system estimation program for causing a computer to perform the method of any of claims 1 to 3.
[claim5]
5. A computer readable recording medium recording a system estimation program for causing a computer to perform the system estimation method of any of claims 1 to 3.
[claim6]
6. A system estimation device applicable to a system in the form of a communication system or a sound system or for sound field reproduction or noise control, for making state estimation robust and optimizing a forgetting factor rho simultaneously in an estimation algorithm, said system being defined by
a state space model expressed by following expressions: (Equation image 99 not included in text) (Equation image 100 not included in text) (Equation image 101 not included in text)
where, x k is defined as a state vector, w k is defined as a system noise, v k is defined as an observation noise, y k is defined as an observation signal, z k is defined as an output signal, F k is defined as dynamics of a system, G k is defined as a drive matrix, and H k is defined as an observation matrix, wherein, 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 w k and the observation noise v k and is weighted with the forgetting factor rho is suppressed to be smaller than a term corresponding to a predetermined upper limit value gamma f, said filter error being associated with a filter implemented in said system estimation device, said filter receiving as an input signal said observation signal of said system, and
the system estimation device comprises: a processing section configured to estimate said system by operating on said state space model; 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 said system defined by the state space model, wherein, a first means configured to enable the processing section to input the upper limit value gamma f, the observation signal y k as an input of said filter and a value including an observation matrix H k from the storage section or an input section; a second means configured to enable the processing section to determine the forgetting factor rho relevant to said system defined by the state space model in accordance with the upper limit value gamma f; a third means having implemented said filter so as to execute a hyper H infin filtering and being configured to enable the processing section to read out an initial value or a value including the observation matrix H k at a time from the storage section and to obtain a filter gain K s,k by using the forgetting factor rho and a gain matrix K k and by following expressions: (Equation image 102 not included in text) (Equation image 103 not included in text) (Equation image 104 not included in text) (Equation image 105 not included in text) (Equation image 106 not included in text) (Equation image 107 not included in text) Where, (Equation image 108 not included in text)
here, y k is the observation signal, F k is the dynamics of the system, H k is the observation matrix, x^ k|k is defined as the estimated value of the state vector x k at the time k using the observation signals y 0 to y k, K s,k is the filter gain, obtained from the gain matrix K **- k, and R e,k, L **~ k are defined as auxiliary variables; a fourth means configured to enable the processing section to store an estimated value of the state x k obtained by the hyper H infin filtering into the storage section; a fifth means configured to enable the processing section to calculate an existence condition based on the upper limit value gamma f and the forgetting factor rho by the obtained observation matrix H i or the observation matrix H i and the filter gain K s,i, wherein the processing section calculates the existence condition in accordance with a following expression: (Equation image 109 not included in text) here, (Equation image 110 not included in text)
where the forgetting factor rho and the upper limit value gamma f have a following relation:
0 < rho = 1 - chi (gamma f) <= 1, where chi (gamma f) denotes a monotonically damping function of gamma f to satisfy chi (1) = 1 and chi (infin ) = 0,
and
a sixth means configured to enable the processing section to set the upper limit value to be small within a range where the existence condition is satisfied at each time and to store the value into the storage section, by decreasing the upper limit value gamma f and re-applying said the third means for executing the hyper H infin filtering.
  • Applicant
  • JAPAN SCIENCE AND TECHNOLOGY AGENCY
  • Inventor
  • NISHIYAMA KIYOSHI
IPC(International Patent Classification)
Specified countries Contracting States: DE FR GB
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