State-space model identification via exploitation of displacement structure: batch and recursive processing

Batch and recursive algorithms for identification of state space models are presented. They exploit the displacement and low-rank+shift structures of the matrices that arise in the identification procedure. The key idea is to manipulate (or update) the so-called generator vectors instead of matrices, which reduces the computational cost down to O(MN) FLOPS (O(M²+dM) when system parameters are updated at every d samples). Such reductions of computational burden may allow online identification of state space models in many potential applications. The results of computer simulation give some evidence of the viability of the fast identification technique