Abstract
The identification of the ARMAX model and the state space model of the multivariable system is investigated in the presence of coloured noise. Firstly. the optimal input vector design is introduced to identify the Markov parameter matrices. Secondly. in the description of the multi-dimensional ARMAX model. an order recursive algorithm is presented for estimating the order and the parameter matrices of the ARMAX model using the estimated Markov matrices. The aymptotic biases are compensated to achieve higher identification precision. Furthermore. the autocorrelation function matrices of the observation noise are estimated. Finally. the recursive algorithm of the identification of the Kronecker structure invariants and the parameters of the state space model of the multivariable system is suggested.
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