Sur la probabilité de fausse alarme du filtre adapté pour la détection distance-Doppler de cibles hors-grille

In most cases, the matched filter is evaluated for values of the non-linear target parameter values fixed on a discrete grid to have statistically independent tests. However, in practice, the target parameters lie in a continuous space, and will usually not fall exactly on the grid. When the matched filter is evaluated for all possible parameter values, the computation of the Probability of False Alarm (PFA) becomes more complex. In this paper, we compute the asymptotic PFA-threshold relation of this detector for distance-Doppler detection under complex white Gaussian noise using expected Euler characteristics. The obtained relation corresponds to the empirical results obtained via Monte Carlo simulations.