Department of Information Technology

General aspects


Torsten Söderström.

Some general aspects of system identification are studied.

In [1] we present a complete and comprehensive algorithm for computing the asymptotic accuracy of estimated state space models. The parameterization is assumed to be give a uniquely identifiable system, but is otherwise general. It is assumed that the system matrices and the noise characteristics are smooth functions of the unknown parameters. Expressions for the asymptotic covariance matrix of the parameter estimates are derived for some variants of the prediction error method. As a special case for Gaussian distributed data, the Cramér-Rao bound and the covariance matrix for maximum likelihood estimates are obtained.

In [2] state estimation of discrete-time nonlinear non-Gaussian stochastic systems by point-mass approach, which is based on discretization of state space by a regular grid and numerical solution of Bayesian recursive relations, is treated. The stress is laid to grid design which is crucial for estimator quality and significantly affects the computational demands of the estimator. Boundary based grid design, thrifty convolution, and multigrid design with grid splitting and merging are proposed. The main advantages of these techniques are nonnegligible support delimitation, time-saving computation of convolution, and effective processing of multimodal probability density functions, respectively. The techniques are involved into the basic point-mass approach and a new general-purpose, more sophisticated point-mass algorithm is designed. Computational demands and estimation quality of the designed algorithm are presented and compared with the particle filter in a numerical example.

A tutorial text on instrumental variables identification has been authored, [3]. The work [4] is a tutorial on linear stochastic models, using a polynomial framework. The paper [5] treats identification for data-driven controllers.


[1] T. Söderström: On computing the Cramér-Rao bound and covariance matrices for PEM estimates in linear state space models, 14th IFAC Symposium on System Identification, Newcastle, Australia, March, 29-31, 2006.

[2] M. Simandl, J. Královec and T. Söderström: Advanced point-mass method for nonlinear state estimation. Automatica, vol 42, no 7, pp 1133-1145, July 2006.

[3] T. Söderström: How accurate can instrumental variable models become? In L. Wang and H. Garnieer, eds: System Identification, Environmental Modelling and Control, Springer-Verlag, 2011. To appear (book to honor Peter Young).

[4] T. Söderström: Linear stochastic input-output models. Chapter 60 In W. Levine, ed.: The Control Handbook, Control System Advance Methods, 2nd edition, Taylor and Francis, UK, 2011.

[5] K. van Heusden, A. Karimi and T. Söderström: On identification methods for direct data-driven controller. International Journal of Adaptive Control and Signal Processing. To appear 2011. (available on-line, October 2010).

Updated  2011-02-05 19:11:35 by Torsten Söderström.