Novel Estimation Problems in Non-Gaussian Noise Models: Maximum Likelihood Approach

Scalar estimation in the presence of noise is a basic problem in the estimation theory, an important branch of statistical signal processing. Estimation in Gaussian noise is well-studied and important in communication theory. However, one can find gaps in maximum likelihood (ML) estimation problems in non-Gaussian noise (NGN). NGN, such as exponential noise and Gamma noise, exist in laser imaging systems. In this short work, I consider novel ML estimation problems in exponential noise and Gamma noise, which are non-trivial and interesting. I present an analysis of the ML estimates and obtain interesting insights. It includes analytical expressions for insightful lower bounds on the variance of the estimated parameter for both the noise models. For a finite number of observations, I present numerical examples and determine the estimated value of the scalar. The problems and analysis I present are useful in applications such as optical imaging, where NGN is present.