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5G mmWave communication systems have the potential to jointly estimate the positions of user equipment (UE) and mapping their propagation environments using a single base station. But such potential depends on the characteristics of the reflecting surfaces, such as a deterministic specular nature, a stochastic diffuse/scattering nature, or a combination of both. In this letter, we proposed a 5G positioning and mapping algorithm with unknown orientation and clock bias for single-bounce diffuse multipath channel models. The method is able to accurately localize, calibrate and synchronize the UE, even in the absence of line-of-sight and specular components. This enables robust positioning and mapping using only diffuse multipath.