Algorithms for global total least squares modelling of finite multivariable time series

Abstract

We consider the optimal approximation of an observed multivariable time series by one that satisfies a set of linear, time-invariant diflerence equations, under a constraint on the number of independent equations and their total lag.

Nonlinear System Identification through Local Model Approaches: Partitioning Strategies and Parameter Estimation

“…In this section weighted TLS and GTLS algorithms for the estimation of the local model parameters are presented. The application of Total Least Squares for parameter estimation from noisy inputs and outputs has been suggested repeatedly in recent years, Heij C. (1999); Markovsky et al (2005);Roorda (1995). Demonstrative introductions and derivations of TLS are given in e. g. De Groen (1996); Golub & Loan (1980); Markovsky & Huffel (2007).…”

An optimal model approximation scheme for linear time-invariant behaviors

“…These numbers are well defined [7][8][9], m is called the rank and n the degree of 8. The rank and degree of a system have simple system theoretic interpretations: the rank m corresponds to the number of inputs and the degree n to the dimension of the state space in any (minimal) input-state-output representation of the system B.…”

A behavioral approach to optimal model reduction

“…Z+ and Z_ denote the nonnegative and negative elements of Z, respectively. For for all N ~ n. Then m and n are well defined [6,7], m is called the rank of the system, n its degree, and the pair (m, n) will be refered to as the complexity of the system 18.…”

“…Similarly, if U is taken as output and Y as input then the transfer function associated with (7.1) is given by 2 G2(Z) = Gil = _Z_~-:-A numerical algorithm for the computation of the optimal approximant of degree n' = 1 of $ makes use of isometric state space representations [7] of the system /13, but is not detailed in this paper for reasons of space. The optimal approximation is given by the solution set of the equation …”