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

Abstract : 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.
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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, Institute of Electrical and Electronics Engineers, 2019, 67 (5), pp.1267-1279. ⟨10.1109/TSP.2018.2890029⟩. ⟨hal-02078353⟩

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