Detection and estimation of multiplicative jumps

Multiplicative jumps have been considered in many applications. These applications include speckle signal in radar images, mechanical vibrations, non-linear time series and random communication models. The problem addressed here is the detection of multiplicative jumps using the Neyman-Pearson test. This test constitutes a reference to which suboptimal detectors can be compared. In practical applications, the parameters of the noise and of the jump have to be estimated. The maximum likelihood estimator and the Cramer Rao bound for these parameters are then studied.