On the influence of detection tests on deterministic parameters estimation

In non-linear estimation problems three distinct regions of operation can be observed [1][2]. In the asymptotic region, the Mean Square Error (MSE) of Maximum Likelihood Estimators (MLE) is small and, in many cases, close to the Cramer-Rao bound (CRB) [3]. In the a priory performance region where the number of independent snapshots and/or the SNR are very low, the MSE is close to that obtained from the prior knowledge about the problem. Between these two extremes, there is an additional transition region where MSE of estimators deteriorates with respect to CRB. The present paper provides exemples of improvement of MSE prediction by CRB, not only in the transition region but also in the a priori region, resulting from introduction of a detection step, which proves that this refinement in MSE lower bounds derivation is worth investigating.