• Corpus ID: 237562903

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… 

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