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

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.