A Hybrid Lower Bound for Parameter Estimation of Signals With Multiple Change-Points

Lucien Bacharach (1) , Mohammed Nabil El Korso (2) , Alexandre Renaux (1) , Jean-Yves Tourneret (3, 4)

1 L2S - Laboratoire des signaux et systèmes
2 LEME - Laboratoire Energétique Mécanique Electromagnétisme
3 IRIT-MINDS - CoMputational imagINg anD viSion
4 Toulouse INP - Institut National Polytechnique (Toulouse)

Change-point estimation has received much attention in the literature as it plays a significant role in several signal processing applications. However, the study of the optimal estimation performance in such context is a difficult task since the unknown parameter vector of interest may contain both continuous and discrete parameters, namely the parameters associated with the noise distribution and the change-point locations. In this paper, we handle this by deriving a lower bound on the mean square error of these continuous and discrete parameters. Specifically, we propose a Hybrid Cramér-Rao-Weiss-Weinstein bound and derive its associated closed-form expressions. Numerical simulations assess the tightness of the proposed bound in the case of Gaussian and Poisson observations.

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

Lucien Bacharach, Mohammed Nabil El Korso, Alexandre Renaux, Jean-Yves Tourneret. A Hybrid Lower Bound for Parameter Estimation of Signals With Multiple Change-Points. IEEE Transactions on Signal Processing, 2019, 67 (5), pp.1267-1279. ⟨10.1109/TSP.2018.2890029⟩. ⟨hal-02078353⟩