# Gyro Error Compensation in Optoelectronic Platform Based on a Hybrid ARIMA-Elman Model
## 1 Introduction  
Fiber-optic gyroscopes (gyros) [1; 2; 3] have been widely used due to their high precision, short starting time, strong impact resistance, and large dynamic range. For example, fiber optic gyro is usually installed in the azimuth and attitude measurement system to achieve high-precision measurement of the direction and attitude of the gun. Theoretically, as the core component of the measurement system, the characteristics of the all-solid structure and non-rotating components of the fiber-optic gyro give it strong anti-vibration capability and high stability. However, in the actual application process, the change of fiber ring stress caused by vibration, the vibration of the device pigtail, and the resonance of the structure will lead to gyro error, including constant drift and random drift. In turn, the error will affect the attitude calculation accuracy of the photoelectric stabilizationand track platform system. Therefore, eliminating the vibration error of the fiber-optic gyroscope has become a common concern of the fiber-optic gyroscope developers. At present, the commonly used method is focused on improving the structure and components of the fiber-optic gyroscope [4; 5]. For example, some authors proposed a new measurement to effectively suppress the thermo-induced non-reciprocal effect of the fiber optic gyroscope; that is, the single-mode solid fiber is replaced by a single-mode air-core photonic band gap photonic crystal fiber. The comparison result with the gyro using the traditional SMF28 fiber is that the thermal sensitivity of the hollow fiber optic gyroscope is reduced by 65 percent. However, at the current stage, it is usually difficult to apply the fiber optic gyroscope structure or hardware temperature control to the actual product, due to various constraints such as cost and technology. Fortunately, error modeling and compensation by software are easy to implement. The bias drift of the fiber-optic gyro error is non-stationary. It is essential to model its statistical correlation mathematically. A common method in engineering is to establish an AR or ARMA linear model (or a polynomial model) to compensate for gyro drift. However, due to the influence of many factors on the fiber optic gyroscope, its drift has very complex, nonlinear characteristics. Therefore, in some aspects, it is difficult to find a linear polynomial fitting method, or an accurate and stable AR model, to describe the gyroscope drift data's nonlinear characteristics fully and accurately. It is common that neural networks have a good ability to approximate complex nonlinear functions. Using a neural network to establish a fiber-optic gyroscope temperature drift model can achieve good approximation results. There is literature which uses a reverse transmission (BP) neural network and a mathematical statistics method to establish the drift error compensation model of the gyroscope. A three-layer feed-forward network is selected, and the hidden layer has six nodes. Experimental results show that the method can effectively improve the bias stability of the fiber-optic gyroscope under certain temperature conditions, and that the method is feasible. Some studies [6; 7] selected a radial basis (RBF) neural network to identify the temperature drift of the fiber-optic gyroscope. It has been verified that the RBF neural network and its learning algorithm can identify and compensate for zero drift quickly, effectively, and accurately. The Accumulated Generating Operation (AGO) and RBF neural networks are combined to propose a new network structure, namely the Gray Radial Basis Neural Network (GRBFN). The comparison of the simulation results verifies the superiority of GRBFN, which not only improves the convergence speed greatly, but also has a good modeling effect. However, whether it is a BP neural network or a RBF neural network, only three basic network layers are included and the modeling effect on time-varying signals is not very satisfactory.