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We propose a high-resolution ranging algorithm for impulse radio (IR) ultra-WideBand (UWB) communication systems in additive white Gaussian noise. We formulate the ranging problem as a maximum- likelihood (ML) estimation problem for the channel delays and amplitudes at the receiver. Then we translate the obtained delay estimates into an estimate of the distance. The ML estimation problem is a non-linear problem and is hard to solve. Some previous works focus 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 we transform the ML problem into another optimization problem that avoids the estimation of the amplitude coefficients. Second, we solve the remaining optimization problem with a gradient descent approach (pseudo-quadratic maximum likelihood (PQML) algorithm). To demonstrate the good performance of the proposed estimator, we present the numerical evaluations under the IEEE 802.15.4a channel model. We show that our algorithm performs significantly better than previously published heuristics. We also derive a reduced complexity version of the algorithm algorithm, which will be implemented on the Xinlix field-programmable gate array (FPGA) board in the future. We test the approach in a real weak line of sight (LOS) propagation environment and obtained good accuracy for the ranging.