Lower bounds for non-standard deterministic estimation

Jérôme Galy (1) , Eric Chaumette (2) , François Vincent (2) , Alexandre Renaux (3) , Pascal Larzabal (4)

1 LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace
3 L2S - Laboratoire des signaux et systèmes
4 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie

In this paper, non standard deterministic parameters estimation is considered, i.e. the situation 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 additional random variables. Unfortunately, in the general case, this marginalization is mathematically intractable, which prevents from using the known deterministic lower bounds on the mean-squared-error (MSE). However an embedding mechanism allows to transpose all the known lowers bounds into modified lower bounds fitted with non-standard deterministic estimation, encompassing the modified Cramér-Rao / Bhattacharyya bounds and hybrid lower bounds.

Domaines: Traitement du signal et de l'image [eess.SP]

Jérôme Galy, Eric Chaumette, François Vincent, Alexandre Renaux, Pascal Larzabal. Lower bounds for non-standard deterministic estimation. SAM: Sensor Array and Multichannel Signal Processing, Jul 2016, Rio de Janeiro, Brazil. ⟨10.1109/sam.2016.7569710⟩. ⟨hal-01346613⟩