We pose the estimation of the parameters of multiple superimposed exponential signals in additive Gaussian noise problem as a Maximum Likelihood (ML) estimation problem. The ML problem is very non linear and hard to solve. Some previous works focused on finding alternative estimation procedures, for example by denoising. In contrast, we tackle the ML estimation problem directly. First, we use the same transformation as the first step of Iterative Quadratic Maximum Likelihood (IQML) and transform the ML problem into another optimization problem that gets rid of the amplitude coefficients. Second, we solve the remaining optimization problem with a gradient descent approach (“pseudo-quadratic maximum likelihood”). We also use this algorithm for Ultra-Wideband channel estimation and estimate ranging in non-line of sight environment.