Not Fully Overlapping Allan Variance and Total Variance for Inertial Sensor Stochastic Error Analysis

Stochastic errors characterize the performance of inertial sensors and indicate the potential improvements of the device. Accurate modeling of these errors can enhance the performance of inertial navigation system. The simplest and generally adopted method to model stochastic errors of inertial sensor is the normal nonoverlapped Allan variance, but its estimation accuracy decreases in long cluster time. The fully overlapping Allan variance improves the estimation accuracy in long cluster time very much, while the traditional total variance based on maximal-overlapping cluster samples further increases the estimation accuracy in long cluster time greatly. However, with these two methods, better estimation is achieved at the expense of much longer computation time. Besides, the computation burden for large dataset and many variance data points is extremely large, while the inertial sensors need large dataset with many variance data points to fully characterize their stochastic errors. This is because the correlation time for some stochastic error is very long (e.g., the correlation time is 3 h for rate random walk), and the Allan variance curve of some stochastic error is very complicated (e.g., sinusoidal noise). Consequently, the fully overlapping Allan variance and the traditional total variance are not suitable for inertial sensor stochastic error modeling. This paper proposes a not fully overlapping Allan variance which has similar estimation accuracy to fully overlapping Allan variance, and whose calculation time is greatly reduced relative to fully overlapping Allan variance. Then, the not fully overlapping concept is integrated to that of total variance to further improve the estimation accuracy in long cluster time with respect to Allan variance, and the calculation time of total variance is greatly reduced as well. This method enables high accuracy and high computational efficiency of Allan variance analysis at the same time, especially for large dataset and many variance data points analysis. Finally, the proposed methods are applied to 12-hour static data of gyroscopes and accelerometers from a position and orientation system, and their advantages are demonstrated.