# Non asymptotic estimation lower bounds for LTI state space models with Cram\'er-Rao and van Trees

@inproceedings{Djehiche2021NonAE, title={Non asymptotic estimation lower bounds for LTI state space models with Cram\'er-Rao and van Trees}, author={Boualem Djehiche and Othmane Mazhar}, year={2021} }

We study the estimation problem for linear time-invariant (LTI) state-space models with Gaussian excitation of an unknown covariance. We provide non asymptotic lower bounds for the expected estimation error and the mean square estimation risk of the least square estimator, and the minimax mean square estimation risk. These bounds are sharp with explicit constants when the matrix of the dynamics has no eigenvalues on the unit circle and are rate-optimal when they do. Our results extend and…

## One Citation

Finite-sample analysis of identification of switched linear systems with arbitrary or restricted switching

- Mathematics, Computer ScienceIEEE Control Systems Letters
- 2022

To capture the effect of the parameters of the switching strategies on the LS estimation error, finite-sample error bounds are developed in this letter and show that in the presence of unstable modes, the switching strategy should be properly designed to avoid the significant increase of the estimation error.

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