Estimation of Variance and Skewness of non-Gaussian zero mean white noise from measurements of the atomic transition probabilities

Estimation of noise parameters is always an important and tedious task when the system under consideration is of the order of atomic level. The majority of estimation algorithms available in the literature assume that the additive noise has a Gaussian distribution. Though it is good model for thermal noise, but in the real world, noise experienced is due to a variety of man-made sources, which deviates from the Gaussian way and is non-Gaussian in nature. Though there are other methods to estimate the parameters of a random non-Gaussian process, for e.g. - Maximum Likelihood Estimator (MLE). In order to construct the MLE of σ² and γ based on quantum measurement would involve constructing the joint pdf of the samples of complex wave function at discrete times. This would be a highly nonlinear function of σ² and γ. The optimization would involve computationally heavy search algorithms. Moments matching is simpler though sub optimal and hence, we have chosen this. In this paper, we proposed a new method to estimate the parameters of non-Gaussian random process based on the higher order statistics (spectra) analysis and quantum measurement which involve the measurement of atomic transition probabilities. Simulated results and comparison between the theoretical values of Variance (finite) and Skewness (non-zero triple moment) have been presented here.