Statistical Modeling of Rate Gyros

Abstract

Gyroscopes are integral components of inertial measurement units, which are used for guidance and stabilization of many platforms. This paper presents an algorithm for estimating the statistical parameters that govern the performance of rate gyros, i.e., the spectral densities <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> of the angle random walk and rate random walk components, respectively. Previous work on gyro modeling is based on computing the Allan variance of a gyro signal and using a well-known formula for its mean. The algorithm in this paper uses these as well as the following quantities, which are derived in this paper: the theoretical variance of the Allan variance and the covariance between different Allan variance points. The algorithm is developed using the formulation of the best linear unbiased estimator from statistical estimation theory. The performance of the algorithm is demonstrated using simulated and experimental data. A bound on the error in the integral of the gyro output, as a function of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> , is also derived.