On Cramér-Rao lower bounds with random equality constraints

Clémence Prévost (1) , Eric Chaumette (2) , Konstantin Usevich (1) , David Brie (1) , Pierre Comon (3)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace
3 GIPSA-GAIA - GIPSA Pôle Géométrie, Apprentissage, Information et Algorithmes

Numerous works have shown the versatility of deterministic constrained Cramér-Rao bound for estimation performance analysis and design of a system of measurements. Indeed, most of factors impacting the asymptotic estimation performance of the parameters of interest can be taken into account via equality constraints. In this communication, we introduce a new constrained Cramér-Rao-like bound for observations where the probability density function (p.d.f.) parameterized by unknown deterministic parameters results from the marginalization of a joint p.d.f. depending on random variables as well. In this setting, it is now possible to consider random equality constraints, i.e., equality constraints on the unknown deterministic parameters depending on the random parameters, which can not be addressed with the usual constrained Cramér-Rao bound. The usefulness of the proposed bound is illustrated by way of a coupled canonical polyadic model with linear constraints applied to the hyperspectral super-resolution problem.

Mots clés: Index Terms-Mean Squared Error; Deterministic parameters; Constrained Cramér-Rao bound; Random equality constraints

Domaines: Physique [physics]; Science non linéaire [physics]

Clémence Prévost, Eric Chaumette, Konstantin Usevich, David Brie, Pierre Comon. On Cramér-Rao lower bounds with random equality constraints. ICASSP 2020 - IEEE International Conference on Acoustics, Speech and Signal Processing, May 2020, Barcelone (virtual), Spain. ⟨10.1109/ICASSP40776.2020.9054031⟩. ⟨hal-02486600⟩