This thesis delivers a new framework for the robust parametric estimation of random fields and latent models through the use of the wavelet variance. By proposing a new M-estimation approach for the latter quantity and delivering results on the identifiability of a wide class of latent models, the thesis finally delivers a computationally efficient and statistically sound method to estimate complex models even when the data is contaminated. The results of this work are then implemented within a new statistical software which is also presented in this thesis, with a focus on its usefulness for inertial sensor calibration.