Lower bounds on the mean square error derived from mixture of linear and non-linear transformations of the unbiasness definition

Eric Chaumette (1) , Alexandre Renaux (2) , Pascal Larzabal (3)

1 ONERA - The French Aerospace Lab [Palaiseau]
2 L2S - Laboratoire des signaux et systèmes
3 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie

It is well known that in non-linear estimation problems the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR or number of snapshots. This effect is caused by outliers and is not captured by standard tools such as the Cram´er-Rao bound (CRB). The search of the SNR threshold value can be achieved with the help of approximations of the Barankin bound (BB) proposed by many authors. These approximations result from a linear transformation (discrete or integral) of the uniform unbiasness constraint introduced by Barankin. Nevertheless, non-linear transformations can be used as well for some class of p.d.f. including the Gaussian case. The benefit is their combination with existing linear transformation to get tighter lower bounds improving the SNR threshold prediction.

Mots clés: Parameter estimation; mean-square-error bounds; SNR threshold

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

Eric Chaumette, Alexandre Renaux, Pascal Larzabal. Lower bounds on the mean square error derived from mixture of linear and non-linear transformations of the unbiasness definition. ICASSP 2009 - 34th IEEE International Conference on Acoustics, Speech and Signal Processing, 2009, Taipei, Taiwan. ⟨10.1109/icassp.2009.4960266⟩. ⟨inria-00444810⟩