False alarm regulation for off-grid target detection with the Matched Filter

In the state-of-the-art, the Probability of False Alarm (PFA)- threshold relationship for the popular Matched Filter (MF) is often derived assuming that unknown non-linear parameters lie on a grid. However, these parameters vary continuously in practice. This is known as the off-grid case. In this arti- cle, an asymptotic PFA-threshold relationship for the popular Matched Filter is derived in the off-grid case under complex white Gaussian noise hypothesis using expected Euler char- acteristics. This asymptotic relationship fits very well with corresponding Monte-Carlo trials in the moderate to low PFA regime.