Analysis and Modeling of Inertial Sensors Using Allan Variance

It is well known that inertial navigation systems can provide high-accuracy position, velocity, and attitude information over short time periods. However, their accuracy rapidly degrades with time. The requirements for an accurate estimation of navigation information necessitate the modeling of the sensors´ error components. Several variance techniques have been devised for stochastic modeling of the error of inertial sensors. They are basically very similar and primarily differ in that various signal processings, by way of weighting functions, window functions, etc., are incorporated into the analysis algorithms in order to achieve a particular desired result for improving the model characterizations. The simplest is the Allan variance. The Allan variance is a method of representing the root means square (RMS) random-drift error as a function of averaging time. It is simple to compute and relatively simple to interpret and understand. The Allan variance method can be used to determine the characteristics of the underlying random processes that give rise to the data noise. This technique can be used to characterize various types of error terms in the inertial-sensor data by performing certain operations on the entire length of data. In this paper, the Allan variance technique will be used in analyzing and modeling the error of the inertial sensors used in different grades of the inertial measurement units. By performing a simple operation on the entire length of data, a characteristic curve is obtained whose inspection provides a systematic characterization of various random errors contained in the inertial-sensor output data. Being a directly measurable quantity, the Allan variance can provide information on the types and magnitude of the various error terms. This paper covers both the theoretical basis for the Allan variance for modeling the inertial sensors´ error terms and its implementation in modeling different grades of inertial sensors.