Sagnac effect can be enhanced with squeezed vacuum light input and Quantum Balanced Homodyne Detection (QBHD), which can result in the improvement of the gyroscope precision. By considering the phase sensitivity obtained by QBHD is related to the phase itself, the best sensitivity is achieved only at some certain value of phase. A scheme based photon counting was designed to extract the Sagnac output phase with Bayesian theory. The theoretical analysis results show that, the proposed scheme can break through the Shot Noise Limit(SNL), and the phase accuracy can reach Heisenberg Limit(HL) theoretically when the power of squeezed vacuum light and coherent light are equal. Meanwhile, the best phase sensitivity can be achieved at any value of phase, which is advantageous for gyro to reach the best sensitivity at any output phase.