Tilted fiber Bragg grating (TFBG) sensors have been employed in fiber-optic refractive index sensors and biosensors, thanks to their inherent sensitivity. However, low-cost coarse-sampling spectrometers are not able to discriminate TFBG cladding modes, which are used for refractive index sensing. In this work, we demonstrate that it is possible to detect small refractive index variations by analyzing the TFBG spectrum with the Karhunen-Loeve Transform (KLT), even if the cladding modes are not visible in the optical spectrum. The proposed work is a key asset towards the development of low-cost fast-response fiber-optic biosensors, as it shifts the complexity from the optical sensing structure to the signal-processing algorithm used for demodulation.