System estimation method and program, recording medium, and system estimation device
Foreign code  F110005755 

File No.  Y0412WO 
Posted date  Sep 14, 2011 
Country  United States of America 
Application number  56751404 
Gazette No.  20070185693 
Gazette No.  7480595 
Date of filing  Aug 5, 2004 
Gazette Date  Aug 9, 2007 
Gazette Date  Jan 20, 2009 
International application number  JP2004011568 
International publication number  WO2005015737 
Date of international filing  Aug 5, 2004 
Date of international publication  Feb 17, 2005 
Priority data 

Title  System estimation method and program, recording medium, and system estimation device 
Abstract 
(US7480595) It is possible to establish an estimation method capable of logically and optimally deciding a forgetting coefficient and develop an estimation algorithm and a highspeed 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 (1013) (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). 
Scope of claims 
[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 =1chi (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 Junitary 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^kk: 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 ^kk: corresponding to a covariance matrix of an error of x^kk,THETA (k): the Junitary 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^kK=[h^1[k],. . . , h^N[k]]T, where h^[k] is the estimated value of impulse response,a pseudoecho is estimated by a following expression: (Equation image 36 not included in text) and an actual echo is cancelled by the obtained pseudoecho. [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 =1chi (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+1k1/2 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 ^kk1 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 =1chi (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 Junitary 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^kk: 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 Junitary 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^kK=[h^1[k],. . . , h^N[k]]T, where h^[k] is the estimated value of impulse response,a pseudoecho is estimated by a following expression: (Equation image 42 not included in text) and an actual echo is cancelled by the obtained pseudoecho. [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 Kk 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 =1chi (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 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^kk: 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 Kk, 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^kK=[h^1[k],. . . , h^N[k]]T, where h^[k] is the estimated value of impulse response,a pseudoecho is estimated by a following expression: (Equation image 44 not included in text) and an actual echo is cancelled by the obtained pseudoecho. [claim8] 8. The system estimation method according to claim 1, wherein an estimated value zvkk of the output signal is obtained from the state estimated value x^kk at the time k by a following expression: zvkk=Hkx^kk. [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 computerreadable 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 =1chi (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 Kk 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^kk: 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 Kk, 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^kK=[h^1[k],. . . , h^N[k]]T, where h^[k] is the estimated value of impulse response,a pseudoecho is estimated by a following expression: (Equation image 46 not included in text) and an actual echo is cancelled by the obtained pseudoecho. [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 computerreadable 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 =1chi (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 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^kk: 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 Kk, 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^kK=[h^1[k],. . . , h^N[k]]T, where h^[k] is the estimated value of impulse response,a pseudoecho is estimated by a following expression: (Equation image 48 not included in text) and an actual echo is cancelled by the obtained pseudoecho. [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 =1chi (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 Kk 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^kk: 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 Kk, 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^kK=[h^1[k],. . . , h^N[k]]T, where h^[k] is the estimated value of impulse response,a pseudoecho is estimated by a following expression: (Equation image 50 not included in text) and an actual echo is cancelled by the obtained pseudoecho. [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 =1chi (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 zvkk of the output signal is obtained from the state estimated value x^kk at the time k by a following expression: zvkk=Hkx^kK. [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 =1chi (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 zvkk of the output signal is obtained from the state estimated value x^kk at the time k by a following expression: zvkk=Hkx^kk. 


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