A promising line of research for radar systems attempts to optimize the detector thresholds so as to maximize the overall performance of a radar detector-tracker pair. In the present work, we attempt to move in a direction to fulfill this promise by considering a particular dynamic optimization scheme which relies on a non-simulation performance prediction (NSPP) methodology for the probabilistic data association filter (PDAF), namely, the modified Riccati equation (MRE). By using a suitable functional approximation, we propose a closed-form solution for the special case of a Neyman-Pearson (NP) detector. The proposed solution replaces previously proposed iterative solution formulations and results in dramatic improvement in computational complexity without sacrificed system performance. Moreover, it provides a theoretical lower bound on the detection signal-to-noise ratio (SNR) concerning when the whole tracking system should be switched to the track before detect (TBD) mode. (C) 2010 Elsevier Inc. All rights reserved.