On the Detection of a Moving Noise Source in a Nonstationary Noise Background

This paper considers the detection of signal consisting of broad-band Gaussian noise whose level varies in some predictable manner with time—e.g., the signal received from a passing object. This study differs from previous ones concerned with this problem in that the background noise is explicitly assumed to be nonstationary. The assumed noise model consists, in fact, of a stationary Gaussian noise amplitude modulated by another random process having a relatively very long correlation time. It is shown that the detectability with this noise model is considerably below that obtained previously with a stationary noise model, and the exact dependence on correlation time, fluctuation of the noise level, etc., is obtained.