In this paper, we analyze the finite sample complexity of stochastic system
identification using modern tools from machine learning and statistics. An
unknown discrete-time linear system evolves over time under Gaussian noise
without external inputs. The objective is to recover the system parameters as
well as the Kalman filter gain, given a single trajectory of output
measurements over a finite horizon of length $N$. Based on a subspace
identification algorithm and a finite number of $N$ output samples, we provide
non-asymptotic high-probability upper bounds for the system parameter
estimation errors. Our analysis uses recent results from random matrix theory,
self-normalized martingales and SVD robustness, in order to show that with high
probability the estimation errors decrease with a rate of $1/\sqrt{N}$. Our
non-asymptotic bounds not only agree with classical asymptotic results, but are
also valid even when the system is marginally stable.

本文探讨了使用现代机器学习和统计学工具分析随机系统识别的有限样本复杂性，使用子空间识别算法和 N 个输出样本提供了系统参数估计误差的非渐近高概率上界。