System identification method
Foreign code  F080001864 

File No.  Y0125US 
Posted date  Apr 25, 2008 
Country  United States of America 
Application number  41567401 
Gazette No.  20040059551 
Gazette No.  7039567 
Date of filing  Oct 16, 2001 
Gazette Date  Mar 25, 2004 
Gazette Date  May 2, 2006 
International application number  JP2001009082 
International publication number  WO2002035727 
Date of international filing  Oct 16, 2001 
Date of international publication  May 2, 2002 
Priority data 

Title  System identification method 
Abstract 
(US7039567) Quick realtime identification and estimation of a timenonvarying or timevarying system. A new H_{∞} evaluation criterion is determined, a fast algorithm for a modified H_{∞} filter based on the criterion is developed, and a quick timevarying system identifying method according to the fast H_{∞} filtering algorithm is provided. By the fast H_{∞} filtering algorithm, a timevarying system sharply varying can be traced with an amount of calculation O(N) per unit time step. The algorithm completely agrees with a fast Kalman filtering algorithm at the extreme of the upper limit value. If the estimate of impulse response is determined, a pseudoecho is sequentially determined from the estimate and subtracted from the real echo to cancel the echo. Thus an echo chancellor is realized. 
Scope of claims 
[claim1] 1. A system identification apparatus for performing a fast realtime identification of a timeinvariant or timevariant system, comprising a filter robust against disturbances, said filter is formed by setting, as an Hinfin evaluation criterion, a maximum energy gain from disturbances weighted by rho =1gamma f2 and SIGMA wi=gamma f2P^i+1i to a filter error to be smaller than a predetermined upper limit gamma f2,wherein said filter, for a statespace model as in the following equations (7) to (9),satisfies the evaluation criterion by expression (10) and is given by the following equations (11) to (15), {circumflex over (x)}k+1k+1={circumflex over (x)}kk+Ks,k+1(yk+1Hk+1{circumflex over (x)}kk)where, {circumflex over (x)}kk: The estimate of state xk at time k, obtained by using observation signals y0 to yk yk: Observation signalKs,k+1: Filter gainHk: Observation matrix xk+1=xk+wk, wk, xkepsilon RN (7) yk=Hkxk+vk, yk, vkepsilon R (8) zk=Hkxk, zkepsilon R, Hkepsilon R1 * N (9) (Equation image 37 not included in text) {hacek over (z)}kk=Hk{circumflex over (x)}kk (11) {circumflex over (x)}k+1k+1={circumflex over (x)}kk+Ks,k+1(yk+1Hk+1{circumflex over (x)}kk) Filter equation (12) Ks,k+1={circumflex over (P)}k+1kHk+1T(Hk+1{circumflex over (P)}k+1kHk+1T+rho )1 Filter gain (13) (Equation image 38 not included in text) where, (Equation image 39 not included in text) and the existence condition is given by the inequality P^kk11+HkTHk>0 which appears in (15), where, the notation is used as follows, xk: State vector or just state, unknown and to be estimated,x0: Initial state, unknown,wk: System noise, unknown,vk: Observation noise, unknown,yk: Observation signal, known and input to a filter,zk: Output signal, unknown,Hk: Observation matrix, known,x^kk: State value of the state xk at time k, estimated by using observation signals y0 to yk, given by the filter equation,x^00: Initial estimate of a state, essentially unknown but set to 0 for convenience,Ks,k+1: Filter gain, obtained by matrix P^k+1k, SIGMA wk: Corresponds to the covariance matrix of the system noise, known in theory but unknown in advance,P^kk1: Corresponds to the covariance matrix of the error of x^kk1, given by a Riccati equation,P^10: Corresponds to the covariance matrix of an error in the initial state, essentially unknown but set to epsilon 0I for convenience. [claim2] 2. A system identification apparatus according to claim 1, setting initial conditions of a recursive equation of the gain matrix Kk, the auxiliary variables Ak, Sk, Dk, and the state estimate x^kk, respectively, as follows, (Equation image 40 not included in text) recursively determining the auxiliary variables Ak and Sk at time k as follows, (Equation image 41 not included in text) obtaining a second gain matrix in which a row including the auxiliary variables is added to the gain matrix Kk as follows, (Equation image 42 not included in text) dividing the second gain matrix KUk and obtaining first and second divisional gain matrixes as follows, (Equation image 43 not included in text) determine Dk, and obtaining a gain matrix Kk+1 at time k+1, and obtaining a filter gain Ks,k+1 at time k+1 by the following equations including the first and second divisional gain matrixes, eta k=ckN+Ck+1Dk1 Dk=[Dk1mkWketa k][1mu kWketa k]1 Kk+1=mkDkmu k {tilde over (K)}k+1(i)=rho Kk+1(i, 1), i=1, . . . , N Ks,k+1=Gk+11{tilde over (K)}k+1, Gk+1=rho +gamma f2Hk+1{tilde over (K)}k+1 in which eta kepsilon R2 * 1, Dkepsilon RN * 1, Kk+1epsilon RN * 2, Ks,k+1epsilon RN * 1, 0<rho =1gamma f2 <= 1, gamma f>1,updating the filter equation (12) according to the obtained filter gain Ks,k+1 as follows, {circumflex over (x)}k+1k+1={circumflex over (x)}kk+Ks,k+1(yk+1Hk+1{circumflex over (x)}kk) and repeating each of the above means with the time being put forward,wherein the existence of the filter is checked by using the following equation as an existence condition suitable for fast processing, with the computational complexity of O(N), l{circumflex over (XI )}i+rho gamma f2>0, i=0, . . . , k where, (Equation image 44 not included in text) . [claim3] 3. A system identification apparatus according to claim 2, wherein an echo canceller is implemented by applying the filter to obtain the state estimate x^kk,producing a quasi echo as in the following equation, andcanceling an actual echo by the obtained quasi echo, (Equation image 45 not included in text) Hk=[uk, . . . , ukN+1]where, {circumflex over (d)}k Quasiechouk Received signalN Tap numberhi[k] Estimate of impulse response of echo path. [claim4] 4. A system identification apparatus according to claim 1, wherein an echo canceller is implemented by applying the filter to obtain the state estimate x^kk,producing a quasi echo as in the following equation, andcanceling an actual echo by the obtained quasi echo, (Equation image 46 not included in text) Hk=[uk, . . . , ukN+1]where, {circumflex over (d)}k Quasiechouk Received signalN Tap numberhi[k] Estimate of impulse response of echo path. 


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