Three-sample rotation vector algorithm with angular rate input

In order to research the attitude algorithm with angular rate input under the conical motion, a optimal three sample rotation vector algorithm based on single-step Newton backward interpolation is proposed. Using the principle of limited rigid body rotation and the characteristic of angular rate input, three-sample rotation vector algorithm is derivated. To minimum attitude errors, three-sample rotation vector algorithm is optimized. Three angular rate extraction methods of single step entire sample recursion, multi-step entire sample and single step Newton backward interpolation are proposed. Under the condition of conical motion with semi-cone angle 3° and angular frequency 2πrad/s , simulation is done. The simulation results show that single-step Newton backward interpolation is superior to the other two methods, and its maximum error peak is 0.01°, error drift rate is 0.0367h. Experiments in three-axis flying turntable with the same parameters are carried out, and the results show that error drift rates of three-channels are less than those of traditional quaternion, which are 13.53%,12.08% and 23.68 % lower respectively. It also verified that the new algorithm can perform a high accuracy under the conical motion.