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

In this paper we present several algorithms related to the global total least squares (GTLS) modelling of multivariable time series observed over a finite time interval. A GTLS model is a linear, time-invariant finite-dimensional system with a behaviour that has minimal Frobenius distance to a given observation. The first algorithm determines this distance. We also give a recursive version of this, which is comparable to Kalman filtering. Necessary conditions for optimality are described in terms of state space representations. Further we present a Gauss-Newton algorithm for the construction of GTLS models. An example illustrates the results.