首次给出单轨迹下线性切换系统参数估计的有限样本误差界。
A finite-sample bound for identifying partially observed linear switched systems from a single trajectory
- 从单条轨迹提取马尔可夫参数，用改进霍-卡尔曼算法恢复系统矩阵
- 在二次稳定假设下，保证参数估计误差有概率上界
- 适用于需要可靠系统辨识的控制与学习场景
我们为线性切换系统的系统辨识算法推导出一个有限样本的概率误差界。该算法从单条轨迹中估计马尔可夫参数，并应用霍-卡尔曼算法的变体来恢复系统矩阵。我们的误差界在真实系统满足二次稳定性假设的前提下，保证了统计一致性。证明基于弱相依过程理论。据我们所知，这是首个在单轨迹设定下针对该算法的有限样本误差界。
原文摘要 · Abstract (English)
We derive a finite-sample probabilistic bound on the parameter estimation error of a system identification algorithm for Linear Switched Systems. The algorithm estimates Markov parameters from a single trajectory and applies a variant of the Ho-Kalman algorithm to recover the system matrices. Our bound guarantees statistical consistency under the assumption that the true system exhibits quadratic stability. The proof leverages the theory of weakly dependent processes. To the best of our knowledge, this is the first finite-sample bound for this algorithm in the single-trajectory setting.
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