Nanoelectromechanical resonators (NEMS) have recently emerged as mass measurement devices with interesting potential, and with mass ranges hardly covered by conventional techniques, they offer the possibility of studying intact nanoparticles, whether artificial or biological. However, different physical phenomena perturb the NEMS signals, lowering the mass accuracy and resolution of our devices. In a previous report, we thus proposed a model to remove colored noise affecting NEMS signals: Through a total variation formulation, noisy NEMS signals are "projected" onto the space of piecewise constant functions, to which non-noisy NEMS signals should theoretically belong. For the simulated NEMS signals, we obtained better mass accuracy and resolution than a commonly used reference method. However, this first model is not adapted to handle true experimental NEMS signals because, in the latter, we observe piecewise linear structures in addition to noise effects. As these unexpected structures, which we refer to as "drifts", perturb NEMS signals and consequently mass measurements, we propose a new denoising model that takes into account both noise and drift effects under any experimental conditions. This model shows increased mass accuracy and resolution, improved signal-to-noise ratio compared to a commonly used reference method, and is robust enough to handle data from experimental measurements. Moreover, as the quantification of drift features becomes accessible, we develop a scenario about the origin of the drifts and compare it with our experimental results.