In this article we propose a tractable nonlinear fault isolation filter along with explicit performance bounds for a class of linear dynamical systems in the presence of additive and multiplicative faults. The proposed filter architecture combines tools from model-based approaches in the control literature and regression techniques from machine learning. To this end, we view the regression operator through a system-theoretic perspective to develop operator bounds that are then utilized to derive performance bounds for the proposed diagnosis filter. In the special case of constant faults (both additive and multiplicative), the estimation (tracking) error of the faults signal provably converges to zero with an exponential rate. The performance of the proposed diagnosis filter is validated through an application on the lateral safety systems of SAE level 4 automated vehicles. The numerical results show that the theoretical bounds of this study are indeed close to optimal and potentially tight.