Abstract
In the strapdown inertial navigation system, the accuracy of the solving attitude and position is closely related to the quaternion update algorithm. For this reason, what method is used to update the quaternion has become an important project. At present, the primary method is to update the quaternion by solving the equivalent rotation vector. A new quaternion update method is proposed in this paper. By using the third-order and fifth-order Taylor series to approximate the solution of the quaternion differential equation, two attitude quaternion update equations are derived. For single sample and two samples two cases, the derived formula is completely consistent with the common formula derived based on the equivalent rotation vector method. For the three samples in the coning motion environment, the fifth-order formula is derived in this paper, the error analysis method is applied to assess the accuracy of the formula, the two coefficients of the formula correction is optimized, and the drift rate error and drift rate are calculated, which are compared with the drift rate errors of the optimized three-sample equivalent rotation vector algorithm. The expressions for calculating the drift rate errors of the two are the same, and the calculation results are the same. In order to simplify the calculation, the established fifth-order formula is simplified to fourth-order one in this paper, but the drift rate error and drift rate remain unchanged. Finally, simulations and experiments demonstrate the correctness of the attitude quaternion update method proposed in this paper. The attitude quaternion update method proposed in this paper has certain theoretical research and application value for the attitude and position calculation of strapdown inertial navigation application, as well as the further studies of integrated navigation algorithm, and enriches the theoretical system of inertial navigation.
Highlights
The navigation algorithm of strapdown inertial navigation system is composed of attitude algorithm, speed algorithm and position algorithm, among of which, attitude algorithm is always the most important research content
SIMULATION AND EXPERIMENTAL VERIFICATION In order to prove the correctness of the attitude quaternion update method proposed in this paper, according to the derivation process of this paper, the attitude quaternion update equation derived from the method of approximating the solution of the quaternion differential equation with the third and fifth order Taylor series is used in this paper
This paper mainly focuses on the theoretical derivation, compares the results of the deduction and existing calculation methods, and verified its correctness
Summary
The navigation algorithm of strapdown inertial navigation system is composed of attitude algorithm, speed algorithm and position algorithm, among of which, attitude algorithm is always the most important research content. This paper attempts to use Taylor series to approximate the solution of the quaternion differential equation to derive the attitude quaternion update expression to deal with this non-commutativity error. For the two cases of the current collected gyro output θ(T ) plus the gyro output sample θ(T − h) in previous period and the two samples ( θ n1, θ n2), the third-order Taylor series expansion is adopted in this paper to derive a quaternion expression for attitude change. For the three samples under the cone motion environment, the fifth-order Taylor series expansion is adopted in this paper to derive a quaternion expression for attitude change. The attitude quaternion update method proposed in this paper has certain theoretical research and application value for the attitude and position calculation of strapdown inertial navigation application, as well as the further studies of integrated navigation algorithm, and enriches the theoretical system of inertial navigation. According to Equation (A-11) and (A-12), Equation (45) and (46) can be obtained
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