Efficient numerical algorithms and software for subspace-based system identification

Advances in the numerical algorithms and software for subspace-based linear multivariable system identification are described. Techniques for data compression of the input-output data, needed for the preliminary processing are investigated. They include standard QR factorization of a block-Hankel-block matrix, and the Cholesky factorization of the associated (inter)-correlation matrix built exploiting the block-Hankel structure. Structure exploiting algorithms and dedicated linear algebra tools, performing all the processing stages of two commonly used subspace identification algorithms, MOESP and N4SID, are presented. These techniques have been implemented in the new system identification toolbox for the SLICOT Library. Numerical results, showing the performance of the new algorithms and associated software, in comparison with the available tools, are given, and illustrate the advantages of the proposed numerical approaches.