M. Coulon et al., Detection of multiplicative noise in stationary random processes using second- and higher order statistics, IEEE SIGNAL, 48(9), 2000, pp. 2566-2575
This paper addresses the problem of detecting the presence of colored multi
plicative noise, when the information process can he modeled as a parametri
c ARMA process. For the case of zero-mean multiplicative noise, a cumulant
based suboptimal detector is studied. This detector tests the nullity of a
specific cumulant slice, A second detector is developed when the multiplica
tive noise is nonzero mean. This detector consists of filtering the data by
an estimated AR filter. Cumulants of the residual data are then shown to b
e well suited to the detection problem. Theoretical expressions for the asy
mptotic probability of detection are given. Simulation-derived finite-sampl
e ROC curves are shown for different sets of model parameters.