Sins Algorithms Based On Dual Quaternions

Under highly-dynamic condition, SINS will cause noncommutativity error. Limited by the ability in information processing of the navigation computer, the computation needed to be strictly controlled when designing the SINS. Therefore, a high combination property SINS can not only compensate the noncommutativity error but also give consideration to the computation and ensure the timeliness of the algorithm.In view of the above mentioned problems, this paper does the following work:First of all, make a study of the optimization of the SINS designed for the noncommutativity error, including compensation optimization algorithms of coning error, sculling and scroll error compensation algorithm optimization of the two-sample. It deduces the three-sample and four-sample optimized compensation algorithm on the basis of the scroll error compensation algorithm optimization of the two-sample. The simulation results verify the effectiveness of various optimization algorithms.Secondly, it studies the SINS algorithms based on dual quaternions and deduces the formula of the screw compensation algorithm, which is concise and easy to be understood. Also, screw compensation algorithm is proved to include two parts, i.e. optimization of rotation vector and sculling compensation optimization algorithms. It verifies the sameness in the error propagation between the dual quaternion navigation algorithm and traditional SINS through the simulation under the condition of stationary base.Thirdly, SINS velocity update algorithm based on dual quaternion is compared with that based on traditional quaternion. Cause of accuracy difference between the two algorithms is theoretically analyzed. Difference in accuracy between the two algorithms is quantitatively characterized by defining the truncation error and approximation integral error. It is shown that under highly-dynamic and wide-maneuver condition, the new algorithm yields much better accuracy but little worse computation timeliness.Finally, simplified dual quaternion-based algorithm is designed for the problem of large computation of dual quaternion-based SINS algorithm, including the fourth-order algorithm and the first-order algorithm. The simplified algorithm maintains the accuracy of the traditional SINS, while greatly reducing the computation. It is shown that under highly-dynamic and wide-maneuver condition, the fourth-order approximation algorithm is of high performance and superior to traditional SINS in accuracy and computation. Comparing with the -first approximation algorithm and the traditional SINS, the -first approximation algorithm has better real time, and has same navigation accuracy.