False Alarm Regulation for Off-Grid Target Detection With The Matched Filter

In the state-of-the-art, the Probability of False Alarm (P
FA
)- 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 article, an asymptotic P
FA
-threshold relationship for the popular Matched Filter is derived in the off-grid case under complex white Gaussian noise hypothesis using expected Euler characteristics. This asymptotic relationship fits very well with corresponding Monte-Carlo trials in the moderate to low P
FA
regime.