Continuous-time canonical state-space model identification via Poisson moment functionals

Abstract

In this paper, a method is presented for estimating continuous-time state-space models for linear timeinvariant multivariable systems. The proposed method does not require the observation of all state variables which is seldom the case in practice. The Poisson moment functional approach is used to handle the timederivative problem. It is shown that the simple leastsquares algorithm always gives asymptotically biased estimates in the presence of noise. An instrumental variable algorithm based on Poisson moment function& of system signals is then developed for reducing the bias of the parameter estimates. The least-squares and instrumental variable algorithms are evaluated by means of a numerical example through Monte Carlo simulations.

Optimal Iv Identification and Estimation of Continuous-Time Tf Models

“…RIVCID identification again suggests the correct [3,2,0] model order 6 and automatic initial prefilter selection was used in the RIVC algorithm. In contrast, the prefilter parameter α (see Garnier et al, 1995) in the IVGPMF has to be specified manually by the user.…”

“…In the present paper, however, its advantages in comparison with other algorithms are demonstrated on the simulation example used in the recent paper by Wang and Gawthrop (2001: WG from here on). The RIVC estimation results obtained in this manner are compared with those obtained by WG, as well as those obtained using another IV algorithm: the IVGPMF algorithm of Garnier et al (1995). This third algorithm uses the so-called Poisson Moment Functional (PMF) implementation of the State Variable Filter (SVF) concept and it also relates very closely to much earlier work by the present author (Young, 1970a and the prior references therein), who referred to the PMF filter chain as the 'Method of Multiple Filters' (MMF).…”

Identification and estimation of continuous-time, data-based mechanistic (DBM) models for environmental systems

“…More recently this MMF approach has been re-named the Generalized Poisson Moment Functionals (GPMF) approach (Saha and Rao 1983;Unbehauen and Rao 1987). Recent MMF/GPMF developments have been proposed by the second author and his co-workers (Garnier et al 1994(Garnier et al 1995(Garnier et al 1997Bastogne et al 2001).…”

Nuclear norm minimization in subspace based continuous-time Hammerstein system identification

“…The CSIM is based on different geometric projections and linear algebra approaches and includes two major computation steps, RQ factorization and singular value decomposition (SVD). Furthermore, the time-derivative for CSIM can be circumvented by the generalized Poisson moment functional (GPMF) [23][24][25], which is a linear filtering method [26]. However, the determination of model order depends on the SVD in CSIM, which will be error prone when the singular values are not separate clearly.…”