Some Closed-Form Expressions for Absorptive Plume Detection

For additive signals on Gaussian clutter, the optimal detector is a linear matched filter that is adapted to the known signal and the covariance of the background. This adaptive matched filter (AMF) is widely used for gas-phase plume detection, even though the effect of the plume on the background is not strictly additive. Here, a derivation of the matched filter for a strictly absorptive plume produces, even in the weak plume limit, a quadratic filter. Assuming a Gaussian background, we derive two expressions, one based on the locally most powerful (LMP) detector which corresponds to the weak plume limit, and one based on the generalized likelihood ratio test (GLRT). Numerical experiments indicate that, as long as the plume is strong enough to be detected at all, both the GLRT and the linear matched filter outperform the LMP detector.