To address the issue of non-linear distortion in the Phase Generated Carrier-Antitangent demodulation (PGC-Atan) algorithm, we have developed an extrinsic Fabry-Perot Interferometer (EFPI) sensor demodulation system based on an improved PGC-Atan algorithm. The theoretical analysis focuses on the affect of nonlinear factors on sine and cosine signals used in arctangent operation of the PGC-Atan algorithm. Such factors include deviations from optimal values of the phase modulation depth (C), companion amplitude modulation, and carrier phase delay. As a solution, we propose an improved PGC-Atan algorithm based on a correction coefficient (PGC-CC-Atan) suitable for external modulation or the case of low companion amplitude modulation scenarios. The PGC-CC-Atan algorithm generates a coefficient relating to C and carrier phase delay while excluding nonlinear parameters in the arctangent operation. Furthermore, an improved PGC-Atan algorithm that utilizes an elliptic fitting algorithm (PGC-EF-Atan) is proposed for internal modulation. The ellipse fitting technique is employed to fit the eclipse using the least squares method based on a matrix block decomposition. The pair of signals that are influenced by nonlinear factors are corrected and transformed into orthogonal signals utilizing three parameters of the ellipse. Finally, the correctness of the two improved algorithms is verified through simulations and experiments. The PGC demodulation system comprises a high dv/di VCSEL laser and a conventional cavity length F-P sensor. By comparing the demodulation performance of the PGC-Atan algorithm with that of the two improved algorithms, their effectiveness in suppressing nonlinear distortion is verified. Experimental results indicate that the two improved algorithms exhibit effective demodulation in the presence of nonlinear factors within a specific range of C values. The signal-to-noise and distortion ratio (SINAD) of demodulation result obtained from PGC-EF-Atan algorithm surpasses that of the PGC-CC-Atan algorithm by 11.602 dB, while the Total Harmonic Distortion (THD) is reduced by 10.951%. Between the two improved algorithms, the PGC-EF-Atan algorithm possesses superior demodulation linearity, accuracy, and nonlinear distortion suppression performance.