We propose a high resolution ranging algorithm for unsynchronized impulse radio Ultra-wideband (UWB) communication systems in gaussian noise. We pose the ranging problem as a Maximum Likelihood (ML) estimation problem for the channel delays and attenuations and phase offset at receiver. Then we translate the obtained delay estimates into an estimate of the distance. 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 show that our algorithm performs significantly better than previously published heuristics. We tested the approach on a real non-line of sight system and obtained good accuracy.