Estimation of parameters and model order in state space innovation forms

This paper presents procedures allowing us to estimate the parameters and model order of a state-space representation for a multivariable stationary stochastic process, from measured output data only. Three methods are presented to estimate the structure of the state-space model. The first method uses properties of a shifted block Hankel matrix, The second method uses the predictive efficiency criterion, The third method optimises mutual information in the past and future observations, A coefficient based statistical test for model order estimation is presented, by the use of the covariance matrix of the observability vector. It is shown that this test has a Chi-squared distribution and is performance in order determination is superior to the singular value decomposition of the block Hankel matrix. A numerical example based on random vibrations of a three degrees of freedom system is presented. An experimental mechanical system of three beams with coupled modes is treated.