Geodesic
Performance analysis of least squares algorithm for multivariable stochastic systems
Kybernetika, Tome 59 (2023) no. 1, pp. 28-44.

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In this paper, we consider the parameter estimation problem for the multivariable system. A recursive least squares algorithm is studied by minimizing the accumulative prediction error. By employing the stochastic Lyapunov function and the martingale estimate methods, we provide the weakest possible data conditions for convergence analysis. The upper bound of accumulative regret is also provided. Various simulation examples are given, and the results demonstrate that the convergence rate of the algorithm depends on the parameter dimension and output dimension.
DOI : 10.14736/kyb-2023-1-0028
Classification : 93A10, 93E12, 93E24
Keywords: least squares; martingale theory; non-persistent excitation 
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Wang, Ziming; Xing, Yiming; Zhu, Xinghua. Performance analysis of least squares algorithm for multivariable stochastic systems. Kybernetika, Tome 59 (2023) no. 1, pp. 28-44. doi : 10.14736/kyb-2023-1-0028. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2023-1-0028/

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