### Session A4: Integrated Inertial Navigation Systems

Accuracy Analysis of Attitude Non-commutativity Error Compensation Algorithm
Pan Jiang, Yanyan Wang, Jiachong Chang, Dingjie Xu, Harbin Institute of Technology, China
Location: Pavilion Ballroom East
Alternate Number 1

The accuracy of the strapdown inertial navigation system mainly depends on the accuracy of the inertial sensor components, the accuracy of the navigation algorithm, the processing power of the navigation computer, and the external environment in which the carrier is located. With the rapid development of computer technology, the processing power of navigation computers is no longer the main factor that restricts the accuracy of the strapdown inertial navigation system. With the improvement of the manufacturing level of the inertial sensor, the output data is getting closer to the actual motion of the carrier, and the error brought to the strapdown inertial navigation system is getting smaller and smaller. This puts higher requirements on the accuracy of the navigation algorithm. It is generally believed that the error of the navigation algorithm should be lower than 5% of the inertial device introduced error.
The key of the strapdown inertial navigation algorithm is the attitude update algorithm, which is the rigid body fixed axis rotation problem. Scholars have conducted extensive and in-depth research on them for many years. The mathematical tools describing the transformation of rigid body poses include Euler angles, direction cosine matrices, Rodrigue parameters, quaternions and equivalent rotation vectors. The methods for solving the attitude update are: first-order Euler method, fourth-order Runge-Kutta method, Picard series method and equivalent rotation vector algorithm. At present, the most popular method for solving pose update is to first calculate the equivalent rotation vector using the gyro angle incremental multi-sample sampling, compensate the rotation non-exchangeable error, and then calculate the attitude update quaternion using the equivalent rotation vector. However, in the traditional algorithm derivation, the influence of the third-order term at the right end of the Bortz equation is neglected, and the equivalent rotation vector in the second-order term is approximated as an angular increment. This makes the accuracy of traditional algorithms often fail to achieve the desired effect, especially in high dynamic environments, sometimes the accuracy of the high subsample algorithm is not as good as the low subsample.
Aiming at this problem, this paper makes a detailed error analysis of the attitude non-commutativity error compensation algorithm based on frequency Taylor series expansion. The reason for the above phenomenon in the traditional algorithm is pointed out, and compared with the recently proposed high-precision attitude non-commutativity error compensation algorithm. The simulation experiment results in pure cone motion and high dynamic environment are consistent with the theoretical analysis results. The correctness and reliability of the accuracy analysis method of the attitude non-commutativity error compensation algorithm proposed in this paper are proved.
With the improvement of the precision requirements of the strapdown attitude algorithm in inertial navigation applications, the accuracy of the algorithm that was neglected in the algorithm design needs to be re-examined. This paper presents the residual error expression of the attitude non-commutativity error compensation algorithm which explains the reason why the accuracy of the traditional high-sample algorithm is not as good as that of the low sub-sample under high dynamic environment. The accuracy analysis method of attitude non-commutativity error compensation algorithm proposed in this paper provides a good theoretical basis for subsequent algorithm design and accuracy evaluation.