An H/sub /spl infin// optimization and its fast algorithm for time-variant system identification

In some estimation or identification techniques, a forgetting factor /spl rho/ has been used to improve the tracking performance for time-varying systems. However, the value of /spl rho/ has been typically determined empirically, without any evidence of optimality. In our previous work, this open problem is solved using the framework of H/sub /spl infin// optimization. The resultant H/sub /spl infin// filter enables the forgetting factor /spl rho/ to be optimized through a process noise that is determined by the filter Riccati equation. This paper seeks to further explain the previously derived H/sub /spl infin// filter, giving an H/sub /spl infin// interpretation of its tracking capability. Additionally, a fast algorithm of the H/sub /spl infin// filter, called the fast H/sub /spl infin// filter, is presented when the observation matrix has a shifting property. Finally, the effectiveness of the derived fast algorithm is illustrated for time-variant system identification using several computer simulations. Here, the fast H/sub /spl infin// filter is shown to outperform the well known least-mean-square algorithm and the fast Kalman filter in convergence rate.

[1]  D. Lin.  On digital implementation of the fast kalman algorithms , 1984 .

[2]  Babak Hassibiy,et al.  Linear Estimation in Krein Spaces -part Ii: Applications , 1996 .

[3]  Ali H. Sayed,et al.  Linear Estimation in Krein Spaces - Part I: Theory , 1996 .

[4]  U. Shaked,et al.  H,-OPTIMAL ESTIMATION: A TUTORIAL , 1992 .

[5]  T. Kailath,et al.  Linear estimation in Krein spaces. I. Theory , 1996, IEEE Trans. Autom. Control..

[6]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[7]  L. Ljung,et al.  Fast calculation of gain matrices for recursive estimation schemes , 1978 .

[8]  Thomas Kailath,et al.  Fast reliable algorithms for matrices with structure , 1999 .

[9]  P. Khargonekar,et al.  Filtering and smoothing in an H/sup infinity / setting , 1991 .

[10]  T. Kailath,et al.  A state-space approach to adaptive RLS filtering , 1994, IEEE Signal Processing Magazine.

[11]  Uri Shaked,et al.  Nondefinite least squares and its relation to H/sub infinity /-minimum error state estimation , 1991 .

[12]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[13]  Babak Hassibi,et al.  Indefinite-Quadratic Estimation And Control , 1987 .

[14]  U. Shaked,et al.  Game theory approach to optimal linear state estimation and its relation to the minimum H/sub infinity /-norm estimation , 1992 .

[15]  T. Kailath,et al.  Linear estimation in Krein spaces. II. Applications , 1996, IEEE Trans. Autom. Control..

[16]  Pramod P. Khargonekar,et al.  FILTERING AND SMOOTHING IN AN H" SETTING , 1991 .

[17]  Ali H. Sayed,et al.  Extended Chandrasekhar recursions , 1994, IEEE Trans. Autom. Control..

[18]  T. Kailath,et al.  Indefinite-quadratic estimation and control: a unified approach to H 2 and H ∞ theories , 1999 .

[19]  S. Thomas Alexander,et al.  Adaptive Signal Processing , 1986, Texts and Monographs in Computer Science.

[20]  Roo Filters.  Derivation of A Fast Algorithm of Modified , 2000 .

[21]  M. Morf,et al.  Some new algorithms for recursive estimation in constant, linear, discrete-time systems , 1974 .

[22]  Ali H. Sayed,et al.  H∞ optimality of the LMS algorithm , 1996, IEEE Trans. Signal Process..

[23]  U. Shaked,et al.  H/sub infinity /-optimal estimation: a tutorial , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[24]  K. Nishiyama.  Derivation of a fast algorithm of modified H/sub /spl infin// filters , 2000, 2000 26th Annual Conference of the IEEE Industrial Electronics Society. IECON 2000. 2000 IEEE International Conference on Industrial Electronics, Control and Instrumentation. 21st Century Technologies.

[25]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .