To increase system robustness and autonomy, in this article, we propose a nonlinear fault estimation filter for a class of linear dynamical systems, subject to structured uncertainty, measurement noise, and system delays, in the presence of additive and multiplicative faults. The proposed filter architecture combines tools from model-based control approaches, regression techniques, and convex optimization. The proposed method estimates the additive and multiplicative faults using a linear residual generator combined with nonlinear regression. An offline simulator allows us to numerically characterize the mismatch between an assumed linear model and a range of alternative linear models that exhibit different levels of structured uncertainty. Moreover, we show how the performance bounds of the estimator, valid in the absence of uncertainty, can be used to determine appropriate countermeasures for measurement noise. In the scope of this work, we focus particularly on a fault estimation problem for Society of Automotive Engineers (SAEs) level 4 automated vehicles, which must remain operational in various cases and cannot rely on the driver. The proposed approach is demonstrated in simulations and in an experimental setting, where it is shown that additive and multiplicative faults can be estimated in a real vehicle under the influence of model uncertainty, measurement noise, and delay.