Maximization of the Fisher Information in PDA

In a cluttered environment, the probabilistic data association (PDA) model allows constructing efficient estimators. In this case, the Fisher information matrix (FIM) is equal to the FIM in the clean environment multiplied by the socalled information reduction factor. This factor depends implicitly on the detection and false alarms probabilities, hence on the threshold prior to the estimation step. The topic of this paper is to seek the optimal threshold, the one that maximizes the information reduction factor. Whereas the Poisson law is used as an approximation in PDA model, here we consider the binomial law for the large false alarms probabilities. An example, coming from signal processing, illustrates our analysis.