# Gyro Error Compensation in Optoelectronic Platform Based on a Hybrid ARIMA-Elman Model
## 4 Hybrid ARIMA-Elman Model
### The Final Compensation Results  
Through four-layer lift-wavelet decomposition and reconstruction, the drift component contained in the original gyro signal is obtained. Through steps 1 to 5 depicted in Section 4.1, the drift error can be approximated finally, as shown in Figure 9. Figure 10 shows the Allan variance after compensation, based on the hybrid ARIMA-Elman method. From Figure 9, it can be easily seen that the reconstructed drift error can be approximated by the proposed ARIMA-Elman model with high precision. The red and green lines are basically coincident. From Figure 10, we can conclude that the Allan variance value is much smaller after compensation, when compared with Figure 3. This phenomenon illustrates that the high frequency white noise and the non-stationarily distributed  
Figure 8: Flow chart of the hybrid ARIMA-Elman model.  
drift error have been compensated for fully. In addition, in order to explain the superiority of the proposed hybrid method, the compensation results with different methods have been listed in Table 1. From the table, it is very easy to see that all the coefficients of the main types of noise (quantization noise, angle random walk noise, zero offset instability noise, rate random walk noise, and rate ramp noise) have reduced, compared with the original signal. However, neither the single ARIMA model, nor the single Elman model, obtain better results than the hybrid ARIMA-Elman model. For example, in the original signal, the coefficient of quantization noise is \(-105.3339\), and with the single ARIMA method, the value changes to \(-12.0008\). With the single Elman method, the value changes to \(-4.8718\). Meanwhile, with the ARIMA-Elman method, it changes to \(-0.2821\). Especially for the rate ramp noise, the noise coefficient changes to zero after compensation using the proposed hybrid method. Furthermore, all of the other coefficient values have reduced sharply as well. All of these prove the effectiveness and superiority of the proposed method.  
The change of error coefficients, before and after compensation, with different methods are shown in Table 1.  
From the above comparison results, it can be easily seen that all of the error coefficients in the hybrid model are the smallest. After compensation, the coefficient of the rate random walk noise is zero. All of these illustrate that the proposed hybrid method can achieve satisfactory compensation results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Noise Type** & **QN** & **ARW** & **ZOI** & **RRW** & **RR** \\ \hline Original signal & \(-105.3339\) & \(151.0151\) & \(-3.9396\) & \(0.0399\) & \(0.0028\) \\ ARIMA & \(-12.0008\) & \(20.8510\) & \(-0.2162\) & \(-0.0102\) & \(0.0017\) \\ ELMAN & \(-4.8718\) & \(2.8510\) & \(-0.0162\) & \(-0.0079\) & \(0.0010\) \\ ARIMA + ELMAN & \(-0.2821\) & \(0.2115\) & \(-0.0273\) & \(0.0015\) & \(-0.0000\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison results of coefficients before and after compensation. Here, QN indicates Quantization Noise, ARW indicates Angle Random Walk, ZOI indicates Zero Offset Instability, RRW indicates Rate Random Walk, and RR indicates Rate Ramp.  
Figure 9: Approximation results based on the ARIMA-Elman method.