On the efficiency of blind and non-blind estimation for coupled LL1 tensor models using the randomly-constrained Cramér-Rao bound
Résumé
In this paper, we study the performance of two algorithms for tensor reconstruction in the presence of random uncertainties: the first one is the non-blind state-of-the-art, and the second one, new, is blind and is designed to deal with such uncertainties. Using coupled tensor LL1 models, we show that the proposed algorithm performs better than the stateof-the-art, which naturally raises the question of its efficiency. In that perspective, the standard approach is to resort to the usual constrained Cramér-Rao bound (CCRB), which appears to be only partially informative when addressing the asymptotic achievable performance of the considered model. Indeed, the usual CCRB is not able to account for randomness in the set of constraints. To fill this gap, we also introduce a new randomlyconstrained Cramér-Rao bound and we illustrate its relevance to analyze the relative efficiency of the proposed algorithm. As a by-product, we provide closed-form expressions for the Fisher information matrices based on the LL1 model.
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