Tilted fiber Bragg gratings (TFBG) can be used as refractive index sensors, as their cladding modes, amplitude, and wavelength changes with the outer refractive index. However, as cladding modes have bandwidths that are narrower than the resolution of most infrared spectrometers, they can be detected only with an optical spectrum or vector analyzers. In this work, we demonstrate that through ad hoc implementation, the Karhunen-Loeve transform (KLT) algorithm can be used to demodulate a TFBG even using a coarse interrogator (156 pm), whereas cladding modes cannot be discriminated in the TFBG spectrum. We observe that the KLT output results are a reliable indicator to detect refractive index changes up to 1.85 ⋅ 10−3 refractive index units (RIU), down to a resolution of ~10−5 RIU. The KLT can be used to demodulate TFBG sensors and biosensors operating in small refractive index change conditions.