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The problem of estimating the parameters of a one- dimensional signal comprising of a time varying deterministic signal plus zero mean non-stationary non-Gaussian noise (NSNGN) is addressed. An algorithm has been developed to estimate the deterministic signal as well as the parameters of NSNGN of the signal. NSNGN has been modelled by Gaussian mixture probability density functions (pdf). The parameters of NSNGN was estimated using maximization of log likelihood function. Simulation results are included to validate this algorithm.