Identification of System Order and Parameter from Input-Output Data Corrupted by Noise

A procedure is presented for identification of a multiple-input multiple-output linear discrete-time system whose input signals and output signals are corrupted by additive noise from the view point of canonical form. The approah is based on the correlation technique between input-output data from which the Markov parameter matrices are estimated when the system is driven by white input sequence. The system order is decided from the observability subindices (Kronecker invariants) which are identified by considering the rank conditions of the matrices composed of the estimates of the Markov parameters. Obtaining the observability subindices yields the identification of the system matrix and the input matrix with a pure algebraic method. The sequential calculating algorithm of the correlation of input-output data is presented for the purpose of saving computer memory and speeding up of calculation. Simulation results are shown to illustrate this overall identification method.