For a fiber optic gyroscope, thermal deformation of the fiber coil can introduce additional thermal-induced phase errors, commonly referred to as thermal errors. Implementing effective thermal error compensation techniques is crucial to addressing this issue. These techniques operate based on the real-time sensing of thermal errors and subsequent correction within the output signal. Given the challenge of directly isolating thermal errors from the gyroscope’s output signal, predicting thermal errors based on temperature becomes necessary. To establish a mathematical model correlating the temperature and thermal errors, this study measured synchronized data of phase errors and angular velocity for the fiber coil under various temperature conditions, aiming to model it using data-driven methods. However, due to the difficulty of conducting tests and the limited number of data samples, direct engagement in data-driven modeling poses a risk of severe overfitting. To overcome this challenge, we propose a modeling algorithm that effectively integrates theoretical models with data, referred to as the TD-model in this paper. Initially, a theoretical analysis of the phase errors caused by thermal deformation of the fiber coil is performed. Subsequently, critical parameters, such as the thermal expansion coefficient, are determined, leading to the establishment of a theoretical model. Finally, the theoretical analysis model is incorporated as a regularization term and combined with the test data to jointly participate in the regression of model coefficients. Through experimental comparative analysis, it is shown that, relative to ordinary regression models, the TD-model effectively mitigates overfitting caused by the limited number of samples, resulting in a substantial 58% improvement in predictive accuracy.

To address the complexity and low detection accuracy issues in the intrinsic frequency detection process of fiber optic gyroscopes, a highly precise automatic measurement method based on optimal projection approximation is proposed. Building upon the digital closed-loop fiber optic gyroscope hardware circuit, this method generates a frequency-adjustable square wave with a 25% duty cycle through field-programmable gate array (FPGA) fractional division. Subsequently, it calculates the difference between the high and low levels of the sign bits of the modulated optical intensity signal sampled by the analog-to-digital converter (ADC). This yields an error signal related to the modulation frequency and intrinsic frequency. The modulation frequency is then approximated using the nearest projection of this error signal, thereby achieving automatic detection of the fiber optic gyroscope’s intrinsic frequency. The experimental results indicate that this method, requiring no external auxiliary equipment, enables rapid and highly accurate measurement of the intrinsic frequency of the fiber optic gyroscope. The measurement of intrinsic frequency takes approximately 300 milliseconds, achieving a measurement accuracy of up to 0.001 Hz.

For a fiber optic gyroscope, thermal deformation of the fiber coil can introduce additional ther-mal-induced phase errors, commonly referred to as thermal errors. Thermal error compensation techniques are effective means of addressing this issue. The principle behind these techniques involves real-time sensing of thermal errors and correcting them within the output signal. Since it is challenging to directly separate thermal errors from the output signal of the fiber optic gyro-scope, it is necessary to predict thermal errors based on temperature. To establish a mathematical model between temperature and thermal errors, this paper measured synchronized data of phase errors and angular velocity for the fiber coil under different temperature conditions and aimed to model it using data-driven methods. Due to the difficulty of conducting tests and the limited number of data samples, an algorithm called TD-model modeling is proposed to address the issue of overfitting, which can reduce the model's generalization ability. First, a theoretical analysis of the phase errors caused by thermal deformation of the fiber coil is performed. Subsequently, the critical parameters, such as the thermal expansion coefficient, are determined, and a theoretical model is established. Finally, the theoretical analysis model is incorporated as a regularization term and combined with the test data to jointly participate in the regression of model coefficients. Through experimental comparative analysis, it is shown that, relative to ordinary regression models, the TD-model effectively mitigates overfitting caused by the limited number of samples, leading to a 58% improvement in predictive accuracy.

For the output ripple phenomenon caused by sampling frequency jitter of digital closed-loop fiber optic gyroscope control system, based on the discrete control system theory, the theoretical model of digital closed-loop fiber optic gyroscope under four-state square wave modulation was established. The stability conditions, steady-state errors and frequency response characteristics of the control system were studied, and the ripple free minimum beat control scheme of digital closed-loop fiber optic gyroscope was proposed. Through comparison with the original control system by experiments, the results show that the ripple free minimum beat control effectively eliminates the output ripple caused by sampling frequency jitter in the digital closed-loop fiber optic gyroscope control system, effectively improves the accuracy of the digital closed-loop fiber optic gyroscope, and the bias stability is improved by about 30%.