Active optical metasurfaces provide a platform for dynamic and real-time manipulation of light at subwavelength scales. However, most active metasurfaces are unable to simultaneously possess a wide wavelength tuning range and narrow resonance peaks, thereby limiting further advancements in the field of high-precision sensing or detection. In the paper, we proposed a reprogrammable active metasurface that employs the non-volatile phase change material Ge2Sb2Te5 and demonstrated its excellent performance in on-chip spectrometer. The active metasurfaces support magnetic modes and feature Friedrich-Wintgen quasi bound states in the continuum, capable of achieving multi-resonant near-perfect absorption, a multilevel tuning range, and narrowband performance in the infrared band. Meanwhile, we numerically investigated the coupling phenomenon and the intrinsic relationship between different resonance modes under various structural parameters. Furthermore, using the active metasurfaces as tunable filters and combined with compressive sensing algorithms, we successfully reconstructed various types of spectral signals with an average fidelity rate exceeding 0.99, utilizing only 51 measurements with a single nanostructure. A spectral resolution of 0.5 nm at a center wavelength 2.538 µm is predicted when the crystallization fractions of GST change from 0 to 20%. This work has promising potential in on-site matter inspection and point-of-care (POC) testing.