Accurate Direct Strapdown Direction Cosine Algorithm

An assessment of the error inherent in a rotation vector algorithm utilized in a strapdown inertial navigation system is presented, which shows that the accuracy cannot be improved boundlessly only by increasing the number of the used samples. After reaching the upper limit for accuracy, increasing sample size would only enlarge the algorithm error rather than improve the performance of the rotation vector algorithm. After accuracy assessment, a new method to construct a strapdown attitude algorithm is originated. Unlike previous algorithms adopting a rotation vector, the new method utilizes the direction cosine matrix differential equation as its basis and discretizes this differential equation with Taylor time series, meanwhile extracting angular velocity and its derivatives by polynomial fitting. With this method, three direction cosine matrix attitude algorithms, taking 4, 5, and 6 samples, are deduced, and their performances are evaluated with coning motion and severe maneuver profile. The results show that the new algorithms based on a direction cosine matrix differential equation can effectively handle the coning error and severe maneuver error.