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A fiber-optic gyroscope (FOG) with lower precision but higher cost advantage is typically selected according to working conditions and engineering budget. Thermal drift is the main factor affecting FOG precision. External thermal calibration methods by algorithms can effectively weaken the influence of thermal drift. This paper presents a thermal calibration method of a two-dimensional N-order polynomial (TDNP) and compares it with artificial neural network (ANN) methods to determine a software FOG thermal calibration method for landslide displacement monitoring. The TDNP thermal calibration coefficient matrix was established, and the thermal calibration capability of the TDNP method with different orders N was evaluated on the basis of error analysis. The ANN model with 1 to 18 hidden neural layers was established on the basis of LM, BR, and SCG algorithms to choose a suitable ANN. Finally, the mean absolute errors of FOG thermal calibration through the TDNP with different orders and the LM were compared. This method was applied in the Huangtupo landslide area, China. The results highlight that the TDNP method with order 5 had better performance and satisfied the requirements of landslide displacement monitoring. The research results can compensate for the lack of adaptability of the FOG thermal calibration method in landslide displacement monitoring. [ABSTRACT FROM AUTHOR]