Parameter estimation and GLRT detection in colored non-Gaussian autoregressive processes

The problem of estimating signal and noise parameters from a mixture of nonGaussian autoregressive noise with partially known deterministic signal is discussed. Two models are considered in order to examine different kinds of additive mixing. The Cramer-Rao bounds to the joint estimation of the signal amplitude and the noise parameters are presented. A computationally simple estimator, which was previously proposed for estimation in the absence of signal, is extended for the two models under consideration. The proposed method essentially consists of two stages of least squares estimation which is motivated by the maximum likelihood estimation. The technique is applied to the problem of detecting a signal known except for amplitude in colored nonGaussian noise Two slightly different mixing models are used, and a generalized likelihood ratio test (GLRT), coupled with the proposed estimation scheme, is used to solve the problems. The results of computer simulations are presented as evidence of the validity of the theoretical productions of performance.>