Valley-positioning-assisted discrete cross-correlation algorithm for fast cavity length interrogation of fiber-optic Fabry–Perot sensors

•Valley-positioning-assisted discrete cross-correlation algorithm proposed.•Interrogated fiber-optic FP sensors with high resolution in 20–130 μm cavity length.•Maximum error of 3.97 nm and resolution of 2.62 nm achieved.•Number of template cavity lengths that required to be cross-correlated decreased.•Reduction in computation amount without sacrificing the interrogating resolution.