Abstract
The multi-output linear stochastic system identification problem is considered. By regarding the linear combination of the outputs, α'y, as a new output, the multi-output system can be transformed into a single output system. Consequently, the system parameters can be estimated while the difficult problem of structural identification being avoided. However, the value of α has a large effect on the estimation accuracy.
In this paper, the optimum value of α is obtained by minimizing the asymptotic generalized variance of the parameters estimate. It is shown that this optimum value, α*, is the eigen vector corresponding to the maximum eigen value of the covariance matrix of the normalized output. Since the covariance matrix of the innovation is required for calculating α*, the two stage least square method is adopted as the identification technique of this paper. In the first stage, a long AR-model is fitted to the data to calculate the residual sequence which is regarded as an approximation to the innovation sequence. In the second stage, the ordinary least square method is used to estimate the parameters of the transformed single output system. At the end of the paper, a computer simulation is carried out for different, randomly chosen, values of α, and the resulting estimates are compared. The results confirmed our finding that the optimum α yields the best estimates for most of the parameters.
