On the influence of a detection step on lower bounds for deterministic parameter estimation

A wide variety of actual processing requires a detection step, whose main effect is to restrict the set of observations available for parameter estimation. Therefore, as a contribution to the theoretical formulation of the joint detection and estimation problem, we address the derivation of lower bounds for deterministic parameters conditioned by a binary hypothesis testing problem. The main result is the introduction of a general scheme-detailed in the particular case of CRB-enabling the derivation of conditional deterministic MSE lower bounds. To prove that it is meaningful, we also show, with the help of a fundamental application, that the problem of lower bound tightness at low SNR may arise from an incorrect lower bound formulation that does not take into account the true nature of the problem under investigation: a joint detection-estimation problem.