Multiple parameter estimation of composite signals in uncharacterized impulsive noise

The problem of estimating amplitudes and arrival times of composite signals in non-Gaussian noise is addressed. The maximum likelihood estimator (MLE) in Gaussian mixture noise with statistical independent noise samples is presented, and it is shown that the MLE is related to a nonlinear form of the orthogonality principle. Some important properties of the multiple parameter estimation problem are extracted from Fisher's information matrix. The problem of the MLE is that the noise density is seldom known in practice. A nonlinear nonparametric iterative method which does not require the knowledge of the noisy density is presented and compared to the MLE. The basic difference between the nonparametric method and the MLE is that the nonlinear manipulations are based on the actual input samples, and therefore the nonparametric method is applicable in nonstationary noise processes.