A fast, recursive MIMO state space model identification algorithm

The authors present a fast recursive implementation for the ordinary MIMO (multiple input, multiple output output-error state-space model identification, MOESP) algorithm. The core of the implementation is a partial update of an LQ factorization followed by a rank-one update of a SVD (singular value decomposition) step. The computational complexity of a single measurement update is O(L² ), where L is related to the dimension of the matrices to be processed. When one would straightforwardly apply existing rank-one update schemes as presented by J.R. Bunch et al. (1978), the order of complexity would be O(L³). The key point in obtaining this reduction in order of complexity is the rank-one update of a tridiagonal matrix instead of a diagonal matrix. The authors apply the proposed scheme to the identification of slowly time-variant systems and illustrate some of the potential of the MOESP scheme in estimating a nominal state-space model and error bounds when using error-affected measurements