## 1 Introduction
Aiming to improve the performance of the navigation system, our work analyzes the influence of sensor error-induced navigation degradation and find an approach to calibrate and eliminate measurement errors. Several typical error influences are simulated in this paper, and we found that gyro bias is the dominant part in terms of degrading the accuracy of the navigation system. In order to improve INS accuracy and navigation reliability, the rotational modulation method is adopted and the bias of individual gyro sensors in INS is calibrated, and the influence is eliminated in this paper. Inspired by the advantages of the rotational modulation method [29; 30], we built a single-axis rotational inertial navigation system (RINS) to eliminate the gyro bias in perpendicular directions to the rotational axis. The adoption of the rotational modulation method benefits two aspects. First, rotational modulation was proved to eliminate the influence of the noise of individual sensors on the direction perpendicular to the rotational direction. As the IMU rotates, the bias influence counteracts in a rotational circle and can be averaged to zero in one rotational cycle. Thus, the navigation error comes mainly from the gyro along the rotational direction, which is easy to calibrate gyro bias. Another benefit of a one-axis RINS is rotational turntables provides an independent observability of the rotational angle with high accuracy, which can be utilized to calibrate the gyro drifts in our algorithm. Thus, the compensation of gyro drift can be used in the navigation process method. In this article, we analyzed the navigation error model in a typical INS. Several error sources were analyzed, and our simulation shows that the dominant error comes from the gyro bias. In order to improve navigation accuracy, we propose a method to eliminate the influence of gyro bias. To test the effectiveness of our method, we constructed a one-axis RINS composed of an IMU on a rotational turntable. The rotational turntable could rotate with a controllable scheme, which serves to eliminate the gyro drift influence along axes perpendicular to the rotational direction. The rotational turntable was also used as an angle reference on the azimuth direction to calibrate gyro bias. After compensating the gyro bias in the navigation algorithm, the improvement of navigation accuracy was observed. In our experiments, the accuracy of our navigation system is improved from 7 km to less than 1 km in three individual tests. The work and contribution points of this paper are as follows:  
The error model of the navigation algorithm is conducted, and the influence of several error sources is analyzed and simulated. In our simulation, gyro bias is the primary error source in the navigation algorithm. A gyro drift calibration and compensation method was proposed through a comparison between turntable- and navigation-resolving results. With compensated gyro bias, the improvement of navigation accuracy was observed and analyzed. The proposed calibration and compensation method in this article can significantly improve the accuracy of the navigation. Several individual experiments were also carried out to verify the effectiveness of our compensation method, and the performance of our navigation accuracy was improved from 7 km to less than 1 km for 6 h navigation results. The remainder of this article is organized as follows. Section 2 describes the coordinates used in the navigation algorithm. Section 3 introduces the navigation algorithm, and the error models in a typical INS is established and analyzed. Section 4 proposes a gyro bias calibration method in a one-axis RINS. Section 5 discusses the results of several navigation experiments to verify the effectiveness of our method. Section 6 is the conclusion of this work.