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System estimation method and program, recording medium, and system estimation device 新技術説明会 実績あり

外国特許コード F110005755
整理番号 Y0412WO
掲載日 2011年9月14日
出願国 アメリカ合衆国
出願番号 56751404
公報番号 20070185693
公報番号 7480595
出願日 平成16年5月8日(2004.5.8)
公報発行日 平成19年8月9日(2007.8.9)
公報発行日 平成21年1月20日(2009.1.20)
国際出願番号 JP2004011568
国際公開番号 WO2005015737
国際出願日 平成16年5月8日(2004.5.8)
国際公開日 平成17年2月17日(2005.2.17)
優先権データ
  • 特願2003-291614 (2003.8.11) JP
  • 2004JP011568 (2004.8.5) WO
発明の名称 (英語) System estimation method and program, recording medium, and system estimation device 新技術説明会 実績あり
発明の概要(英語) 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 gammaf 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 rho, the processing section executes a hyper H∞ 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), gammaf is decreased by Deltagamma and the same processing is repeated (S111).
On the other hand, when the existence condition is not satisfied by a certain gammaf (S109), the Deltagamma is added to the gammaf and the sum is output to an output section and/or stored in the storage section as an optimal value gammafOP of the gammaf (S113).
従来技術、競合技術の概要(英語) BACKGROUND OF THE INVENTION
1.
Technical Field
The present invention relates to a system estimation method and program, a recording medium, and a system estimation device, and particularly to a system estimation method and program, a recording medium, and a system estimation device, in which the generation of robustness in state estimation and the optimization of a forgetting factor are simultaneously realized by using a fast Hinfin filtering algorithm of a hyper Hinfin filter developed on the basis of an Hinfin evaluation criterion.
2. Background Art
In general, system estimation means estimating a parameter of a mathematical model (transfer function, impulse response, etc.) of an input/output relation of a system based on input/output data.
Typical application examples include an echo canceller in international communication, an automatic equalizer in data communication, an echo canceller and sound field reproduction in a sound system, active noise control in a vehicle etc. and the like.
For more information, see non-patent document 1: "DIGITAL SIGNAL PROCESSING HANDBOOK" 1993, The Institute of Electronics, Information and Communication Engineers, and the like.
(Basic Principle)
FIG. 8 shows an example of a structural view for system estimation (unknown system may be expressed by an IIR (Infinite Impulse Response) filter).
This system includes an unknown system 1 and an adaptive filter 2.
The adaptive filter 2 includes an FIR digital filter 3 and an adaptive algorithm 4.
Hereinafter, an example of an output error method to identify the unknown system 1 will be described.
Here, uk denotes an input of the unknown system 1, dk denotes an output of the system, which is a desired signal, and d^k denotes an output of the filter. (Incidentally, "^" means an estimated value and should be placed directly above a character, however, it is placed at the upper right of the character for input convenience.
The same applies hereinafter.).
Since an impulse response is generally used as a parameter of an unknown system, the adaptive filter adjusts a coefficient of the FIR digital filter 3 by the adaptive algorithm so as to minimize an evaluation error ek=dk-d^k of the figure.
Besides, conventionally, a Kalman filter based on an update expression (Riccati equation) of an error covariance matrix has been widely used for the estimation of a parameter (state) of a system.
The details are disclosed in non-patent document 2: S. Haykin: Adaptive filter theory, Prentice-Hall (1996) and the like.
Hereinafter, the basic principle of the Kalman filter will be described.
A minimum variance estimate x^k|k of a state xk of a linear system expressed in a state space model as indicated by the following expression:
xk+1=rho -1/2xk, yk=Hkxk+vk (1)
is obtained by using an error covariance matrix SIGMA ^k|k-1 of the state as follows.
(Equation image 1 not included in text)
xk: State vector or simply a state; unknown and this is an object of estimation.
yk: Observation signal; input of a filter and known.
Hk: Observation matrix; known.
Vk: Observation noise; unknown.
rho : Forgetting factor; generally determined by trial and error.
Kk: Filter gain; obtained from matrix SIGMA ^k|k-1.
SIGMA ^k|k: Corresponds to the covariance matrix of an error of x^k|k; obtained by a Riccati equation.
SIGMA ^k+1|k: Corresponds to the covariance matrix of an error of
x^k+1|k; obtained by the Riccati equation.
SIGMA ^1|0: Corresponds to the covariance matrix in an initial state; although originally unknown, epsilon 0I is used for convenience.
The present inventor has already proposed a system identification algorithm by a fast Hinfin filter (see patent document 1).
This is such that an Hinfin evaluation criterion is newly determined for system identification, and a fast algorithm for the hyper Hinfin filter based thereon is developed, while a fast time-varying system identification method based on this fast Hinfin filtering algorithm is proposed.
The fast Hinfin filtering algorithm can track a time-varying system which changes rapidly with a computational complexity of O (N) per unit-time step.
It matches perfectly with a fast Kalman filtering algorithm at the limit of the upper limit value.
By the system identification as stated above, it is possible to realize the fast real-time identification and estimation of the time-invariant and time-varying systems.
Incidentally, with respect to methods normally known in the field of the system estimation, see, for example, non-patent documents 2 and 3.
(Applied Example to Echo Canceller)
In a long distance telephone circuit such as an international telephone, a four-wire circuit is used from the reason of signal amplification and the like.
On the other hand, since a subscriber's circuit has a relatively short distance, a two-wire circuit is used.
FIG. 9 is an explanatory view concerning a communication system and an echo.
A hybrid transformer as shown in the figure is introduced at a connection part between the two-wire circuit and the four-wire circuit, and impedance matching is performed.
When the impedance matching is complete, a signal (sound) from a speaker B reaches only a speaker A. However, in general, it is difficult to realize the complete matching, and there occurs a phenomenon in which part of the received signal leaks to the four-wire circuit, and returns to the receiver (speaker A) after being amplified.
This is an echo (echo).
As a transmission distance becomes long (as a delay time becomes long), the influence of the echo becomes large, and the quality of a telephone call is remarkably deteriorated (in the pulse transmission, even in the case of short distance, the echo has a large influence on the deterioration of a telephone call).
FIG. 10 is a principle view of an echo canceller.
Then, as shown in the figure, the echo canceller (echo canceller) is introduced, an impulse response of an echo path is successively estimated by using a received signal which can be directly observed and an echo, and a pseudo-echo obtained by using it is subtracted from the actual echo to cancel the echo and to remove it.
The estimation of the impulse response of the echo path is performed so that the mean square error of a residual echo ek becomes minimum.
At this time, elements to interfere with the estimation of the echo path are circuit noise and a signal (sound) from the speaker A. In general, when two speakers simultaneously start to speak (double talk), the estimation of the impulse response is suspended.
Besides, since the impulse response length of the hybrid transformer is about 50 [ms], when the sampling period is made 125 [mu s], the order of the impulse response of the echo path becomes actually about 400.
Non-patent document 1
"DIGITAL SIGNAL PROCESSING HANDBOOK" 1993 The Institute of Electronics, Information and Communication Engineers
Non-patent document 2
S.
Haykin: Adaptive filter theory, Prentice-Hall (1996)
Non-patent document 3
B.
Hassibi, A. H. Sayed, and T. Kailath: "Indefinite-Quadratic Estimation and Control", SIAM (1996)
Patent document 1
JP-A-2002-135171

BRIEF
特許請求の範囲(英語) [claim1]
1. 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 rho 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, andGk: 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 rho is suppressed to be smaller than a term corresponding to a previously given upper limit value gamma f, andthe system estimation method comprises:a step at which a processing section inputs the upper limit value gamma f, 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 rho ;
as a following function of gamma f;

rho =1-chi (gamma f)
where chi (gamma f) denotes a monotonicaly damping function of gamma f to satisfy chi (1)=1 and chi (infin )=0,;
a step of executing a hyper Hinfin 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 rho and a gain matrix Kk and by following expressions (20) to (22):
(Equation image 34 not included in text) THETA (k) denotes a J-unitary matrix, that is, satisfiesTHETA (k) JTHETA H(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
(Equation image 35 not included in text)
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,SIGMA ^k|k: corresponding to a covariance matrix of an error of x^k|k,THETA (k): the J-unitary matrix, andRe,k: an auxiliary variable,a step at which the processing section stores an estimated value of the state xk by the hyper Hinfin , filter 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 Hi or the observation matrix Hi and the filter gain Ks,i, anda step at which the processing section decreases the upper limit value gamma f by a factor of DELTA gamma and stores the resultant value into the storage section while the existence condition is satisfied in the step of executing the hyper Hinfin , filter,wherein the Hinfin 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:
(Equation image 36 not included in text)
and an actual echo is cancelled by the obtained pseudo-echo.
[claim2]
2. The system estimation method according to claim 1, wherein the processing section calculates the existence condition in accordance with a following expression:
(Equation image 37 not included in text)
[claim3]
3.
The system estimation method according to claim 1, wherein the processing section calculates the existence condition in accordance with a following expression:
(Equation image 38 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.
[claim4]
4. The system estimation method according to claim 1, wherein the step of executing the hyper Hinfin filter includes: a step at which the processing section calculates SIGMA ^k+1|k1/2 by using the expression (22);a step at which the processing section calculates the filter gain Ks,k based on an initial condition of SIGMA ^k|k-1 and an initial condition of Ck, by using the expression (21);a step at which the processing section updates a filter equation of the Hinfin filter of the expression (20);
and
a step at which the processing section repeatedly executes the step of calculating by using the expression (20), the step of calculating by using the expression (21) and, the step of updating while advancing the time k.
[claim5]
5. 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 rho 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, andGk: 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 rho is suppressed to be smaller than a term corresponding to a previously given upper limit value gamma f, andthe system estimation method comprises:a step at which a processing section inputs the upper limit value gamma f, 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 rho relevant to the state space model in accordance with the upper limit value gamma f;
as a following function of gamma f,
rho =1-chi (gamma f)
where chi (gamma f) denotes a monotonicaly damping function of gamma f to satisfy chi (1)=1 and chi (infin )=0, a step of executing a hyper Hinfin 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 rho and a gain matrix Kk and by following expressions:
(Equation image 39 not included in text)
here, THETA (k) denotes an arbitrary J-unitary matrix, and {hacek over (C)}k={hacek over (C)}k+1PSI is established, where
(Equation image 40 not included in text)
(Equation image 41 not included in text)
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,THETA (k): the J-unitary matrix, andRe,k: an auxiliary variable,a step at which the processing section stores an estimated value of the state xk by the hyper Hinfin filter 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 Hi or the observation matrix Hi and the filter gain Ks,i, anda step at which the processing section decreases the upper limit value gamma f by a factor of DELTA gamma and stores the resultant value into the storage section while the existence condition is satisfied in the step of executing the hyper Hinfin filter,wherein the Hinfin 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:
(Equation image 42 not included in text)
and an actual echo is cancelled by the obtained pseudo-echo.
[claim6]
6. The system estimation method according to claim 5, wherein the step of executing the hyper Hinfin filter includes: a step at which the processing section calculates K-k based on an initial condition of Re,k+1, Rr,k+1 and L{tilde over ( )}k+1 by using the expression (63);a step at which the processing section calculates the filter gain Ks,k based on the initial condition and by using the expression (62);a step at which the processing section updates a filter equation of the Hinfin filter of the expression (61);
and
a step at which the processing section repeatedly executes the step of calculating by using the expression (63), the step of calculating by using the expression (62), and, the step of updating while advancing the time k.
[claim7]
7. 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 rho 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, andGk: 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 rho is suppressed to be smaller than a term corresponding to a previously given upper limit value gamma f, andthe system estimation method comprises:a step at which a processing section inputs the upper limit value gamma f, 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 rho as a following function gamma f,
rho =1-chi (gamma f)
where chi (gamma f) denotes a monotonicaly damping function of gamma f to satisfy chi (1)=1 and chi (infin )=0, a step of executing a hyper Hinfin , 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 rho and a gain matrix K-k and by following expressions:
(Equation image 43 not included in text)
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, andRe,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 Hinfin filter 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 Hi or the observation matrix Hi and the filter gain Ks,i, anda step at which the processing section decreases the upper limit value gamma f by a factor of DELTA gamma and stores the resultant value into the storage section while the existence condition is satisfied in the step of executing the hyper Hinfin filter,wherein the Hinfin 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:
(Equation image 44 not included in text)
and an actual echo is cancelled by the obtained pseudo-echo.
[claim8]
8. The system estimation method according to claim 1, wherein an estimated value zvk|k of the output signal is obtained from the state estimated value x^k|k at the time k by a following expression:
zvk|k=Hkx^k|k.
[claim9]
9. 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 rho 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, andGk: 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 rho is suppressed to be smaller than a term corresponding to a previously given upper limit value gamma f, andthe system estimation program causes the computer to execute:a step at which a processing section inputs the upper limit value gamma f, 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 rho as a following function gamma f,
rho =1-chi (gamma f)
where rho (gamma f) denotes a monotonicaly damping function of gamma f to satisfy chi (1)=1 and chi (infin )=0, a step of executing a hyper Hinfin 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 rho and a gain matrix K-k and by following expressions:
(Equation image 45 not included in text)
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, andRe,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 Hinfin filter 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 Hi or the observation matrix Hi and the filter gain Ks,i, anda step at which the processing section decreases the upper limit value gamma f by a factor of DELTA gamma and stores the resultant value into the storage section while the existence condition is satisfied in the step of executing the hyper Hinfin filter;wherein the Hinfin 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:
(Equation image 46 not included in text)
and an actual echo is cancelled by the obtained pseudo-echo.
[claim10]
10. 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 rho 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, andGk: 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 rho is suppressed to be smaller than a term corresponding to a previously given upper limit value gamma f, andthe 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 gamma f, 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 rho relevant to the state space model in accordance as a following function gamma f,
rho =1-chi (gamma f)
where chi (gamma f) denotes a monotonicaly damping function of gamma f to satisfy chi (1)=1 and chi (infin )=0, a step of executing a hyper Hinfin 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 rho and a gain matrix K-k and by following expressions:
(Equation image 47 not included in text)
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, andRe,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 Hinfin filter 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 Hi or the observation matrix Hi and the filter gain Ks,i, anda step at which the processing section decreases the upper limit value gamma f by a factor of DELTA gamma and stores the resultant value into the storage section while the existence condition is satisfied in the step of executing the hyper Hinfin filter,wherein the Hinfin 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:
(Equation image 48 not included in text)
and an actual echo is cancelled by the obtained pseudo-echo.
[claim11]
11. 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 rho 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, andGk: 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 rho is suppressed to be smaller than a term corresponding to a previously given upper limit value gamma f, andthe 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 gamma f, 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 rho as a following function gamma f,
rho =1-chi (gamma f)
where chi (gamma f) denotes a monotonicaly damping function of gamma f to satisfy chi (1)=1 and chi (infin )=0, a means of executing a hyper Hinfin 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 rho and a gain matrix K-k and by following expressions:
(Equation image 49 not included in text)
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, andRe,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 Hinfin filter into the storage section;a means 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 Hi or the observation matrix Hi and the filter gain Ks,i anda means at which the processing section decreases the upper limit value gamma f by a factor of DELTA gamma and stores the resultant value into the storage section while the existence condition is satisfied in the means of executing the hyper Hinfin filter,wherein the Hinfin 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:
(Equation image 50 not included in text)
and an actual echo is cancelled by the obtained pseudo-echo.
[claim12]
12. The system estimation method according to claim 5, wherein the processing section calculates the existence condition in accordance with a following expression:
(Equation image 51 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.
[claim13]
13. The system estimation method according to claim 5, wherein an estimated value zvk|k of the output signal is obtained from the state estimated value x^k|k at the time k by a following expression:
zvk|k=Hkx^k|K.
[claim14]
14. The system estimation method according to claim 7, wherein the processing section calculates the existence condition in accordance with a following expression:
(Equation image 52 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.
[claim15]
15. The system estimation method according to claim 7, wherein an estimated value zvk|k of the output signal is obtained from the state estimated value x^k|k at the time k by a following expression:
zvk|k=Hkx^k|k.
  • 発明者/出願人(英語)
  • NISHIYAMA KIYOSHI
  • JAPAN SCIENCE AND TECHNOLOGY AGENCY
国際特許分類(IPC)
米国特許分類/主・副
  • 703/1
  • 367/901
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