Detection and estimation of abrupt changes contaminated by multiplicative Gaussian noise

The problem of abrupt change detection has received much attention in the literature. The Neyman—Pearson detector can be derived and yields the well-known CUSUM algorithm, when the abrupt change is contaminated by an additive noise. However, a multiplicative noise has been observed in many signal processing applications. These applications include radar, sonar, communication and image processing. This paper addresses the problem of abrupt change detection in presence of multiplicative noise. The optimal Neyman—Pearson detector is studied when the abrupt change and noise parameters are known. The parameters are unknown in most practical applications and have to be estimated. The maximum likelihood estimator is then derived for these parameters. The Neyman—Pearson detector combined with the maximum likelihood estimator yields the generalized likelihood ratio detector.