In this paper, we investigate the problem of system identification for autonomous Markov jump linear systems (MJS) with complete state observations. We propose switched least squares method for identification of MJS, show that this method is strongly consistent, and derive data-dependent and data-independent rates of convergence. In particular, our data-independent rate of convergence shows that, almost surely, the system identification error is $\mathcal{O}\big(\sqrt{\log(T)/T} \big)$ where $T$ is the time horizon. These results show that switched least squares method for MJS has the same rate of convergence as least squares method for autonomous linear systems. We derive our results by imposing a general stability assumption on the model called stability in the average sense. We show that stability in the average sense is a weaker form of stability compared to the stability assumptions commonly imposed in the literature. We present numerical examples to illustrate the performance of the proposed method.

翻译：本文研究了具有完整状态观测的自治马尔可夫跳变线性系统（MJS）的系统辨识问题。我们提出了一种用于MJS辨识的切换最小二乘法，证明了该方法具有强一致性，并推导了数据相关与数据无关的收敛速率。特别地，数据无关收敛速率表明，几乎必然地，系统辨识误差为$\mathcal{O}\big(\sqrt{\log(T)/T} \big)$，其中$T$为时间范围。这些结果表明，MJS的切换最小二乘法与自治线性系统的最小二乘法具有相同的收敛速率。通过引入一个称为平均意义稳定性的模型一般稳定性假设，我们推导了上述结果。研究表明，与文献中常用的稳定性假设相比，平均意义稳定性是一种更弱的稳定性形式。最后，我们通过数值算例展示了所提出方法的性能。