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 pro- cessing 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 dis- crete parameters, namely the parameters associated with the noise distribution and the change-point locations. In this paper, we han- dle this by deriving a lower bound on the mean square error of these continuous and discrete parameters. Specifically, we propose a hybrid Crame ́r–Rao–Weiss-Weinstein bound and derive its as- sociated closed-form expressions. Numerical simulationsassess the tightness of the proposed bound in the case of Gaussian and Poisson observations.