## 3 Modeling and Error Analysis of the Navigation Process in RINS
### Simulation of Measurement Error Influence  
In order to evaluate the influence of measurement error on navigation accuracy, a numerical simulation was conducted in a typical RINS situation. In this section, experimental navigation results were used, and several simulated error sources were added into the navigation-resolving process. The influences of various error sources include the following:  
Gyro bias influence: The gyro bias is a significant parameter that influences the navigation algorithm's accuracy. In order to analyze the influence of gyro bias and other error sources, we used a six-hour navigation experiment result, and various gyro bias errors are added to the navigation algorithm. We consider a situation where a strapdown INS is rotating along the azimuth direction. The influence of gyro bias on azimuth is simulated. Azimuth gyro bias-induced latitude, longitude and position inaccuracies are shown in Figure 1. From the simulation results, it can be seen that the larger the azimuth bias, the more divergent the navigation accuracy. In addition, it can also be concluded that the original navigation gyro data would also have a bias. Roll Gyro bias-induced navigation inaccuracy: According to the rotational modulation theory, the rotational modulation of the IMU could eliminate the gyro bias in an axis along the direction perpendicular to the rotational axis. In order to evaluate the effectiveness of the rotational modulation method, we constructed a comparison simulation to analyze the influence of gyro bias on roll direction. The navigation algorithm method is used to simulate the influence of gyro bias along the roll direction, and the results are shown in Figure 2. Compared with Figure 1, we observe that the gyro bias on roll direction almost has less influence on navigation accuracy. These two results prove that the rotational modulation method is an effective method to eliminate the influence of gyro bias. Figure 1: Different gyro bias (along azimuth direction)-induced navigation errors in a typical RINS. Gyro scale factor induced navigation error: The scale factor stability of gyro is another parameter that influences the navigation accuracy. In order to analyze the influence of scale factor error, several simulations were conducted with various scale factor errors. The influence of the gyro scale factor error induced latitude, longitude and position inaccuracies, as shown in Figure 3. From the simulation results, it can be seen that the scale factor error has an influence on navigation accuracy. In our simulation, a scale factor error of 200 ppm would cause a navigation error of less than one kilometer. Thus, the scale factor error is not a dominant error source compared with gyro bias. Acceleration bias induced navigation error: The influence of acceleration bias is also simulated. In Figure 4, the acceleration bias error ranging from \(-1\) mg to 1 mg is simulated to observe the influence of navigation position accuracy. We could see that the acceleration bias could cause an error of several kilometers with a bias of 1 mg. In a typical IMU, the accelerometer bias is smaller than 0.1 mg, so the acceleration bias is not the dominant factor in degrading the navigation performance. Inaccurate initial alignments induced navigation error: In the navigation algorithm, the initial alignment process could estimate the initial attitude of the carrier. However,  
Figure 4: Simulation of the acceleration bias’s influence on the navigation algorithm. Figure 3: Simulation of the scale factor error’s influence on the navigation algorithm. Figure 2: Simulation of gyro bias’s (along roll direction) influence on the navigation algorithm. navigation is a consecutive process, so the initial misalignment of the carrier's attitude would result in navigation-resolving inaccuracy and degrades the reliability and accuracy of a navigation system.