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In this article, a novel fast randomized subspace system identificationmethod for estimating combined deterministic-stochastic LTI state-space models,is proposed. The algorithm is especially well-suited to identify high-order andmulti-scale systems with both fast and slow dynamics, which typically require alarge number of input-output data samples for accurate identification usingtraditional subspace methods. Instead of working with such large matrices, thedataset is compressed using randomized methods, which preserve the range-spacesof these matrices almost surely. A novel identification algorithm using thiscompressed dataset, is proposed. This method enables the handling of extremelylarge datasets, which often make conventional algorithms like N4SID, MOESP,etc. run out of computer memory. Moreover the proposed method outperforms thesealgorithms in terms of memory-cost, data-movement, flop count and computationtime for cases where these algorithms still work in-spite of large data sizes.The effectiveness of the proposed algorithm is established by theoreticalanalysis and various real and simulated case studies.

Fast Randomized Subspace System Identification for Large I/O Data