Finite Sample Analysis of Subspace Identification for Stochastic Systems

Shuai Sun; Weikang Hu; Xu Wang

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arXiv · 2501.18853

Finite Sample Analysis of Subspace Identification for Stochastic Systems

Shuai Sun·Weikang Hu·Xu Wang

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Abstract

The subspace identification method (SIM) has become a widely adopted approach for the identification of discrete-time linear time-invariant (LTI) systems. In this paper, we derive finite sample high-probability error bounds for the system matrices $A,C$, the Kalman filter gain $K$ and the estimation of system poles. Specifically, we demonstrate that, ignoring the logarithmic factors, for an $n$-dimensional LTI system with no external inputs, the estimation error of these matrices decreases at a rate of at least $ \mathcal{O}(\sqrt{1/N}) $, while the estimation error of the system poles decays at a rate of at least $ \mathcal{O}(N^{-1/2n}) $, where $ N $ represents the number of sample trajectories. Furthermore, we reveal that achieving a constant estimation error requires a super-polynomial sample size in $n/m $, where $n/m$ denotes the state-to-output dimension ratio. Finally, numerical experiments are conducted to validate the non-asymptotic results.

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BibTeX RIS

Shuai Sun, Weikang Hu, Xu Wang. 2025-07-02. Finite Sample Analysis of Subspace Identification for Stochastic Systems. https://arxiv.org/abs/2501.18853

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