<p>Simultaneous measurements of multiple physical quantities under variable conditions are essential from fundamental research to application. However, multiparametric sensors often need intricate calibration procedures which can be compromised by changing environmental conditions. Here, we present a robust sensing concept based on the Fourier components of a nonlinear response of an excitation. By extracting amplitude ratios and phase differences between different harmonics, a set of characteristic shape parameters are extracted ensuring independence from external factors such as amplifier gain or instrumental delays. This principle is demonstrated using magneto-optical readout of magnetization loops in a perpendicular bismuth-substituted yttrium iron garnet indicator film. Two-dimensional parameter maps spanning both temperature and magnetic field are measured, providing a sensor-specific fingerprint for parallel detection. Using lookup-table interpolation and a random forest regressor, robust and accurate simultaneous extraction of temperature and magnetic field is demonstrated. The presented magneto-optical method offers a universal, gain and delay invariant framework for multiparametric sensing in nonlinear materials.</p>