Kalman Filtering of 3-D Gyroscopic Measurements

This paper presents a new Kalman filtering method to estimate 3-D angular motion based on noisy gyroscopic measurements. The estimation problem is nonlinear since the dynamics of 3-D angular motion are described by Euler´s equations. Instead of using complex extended Kalman filtering techniques to solve this problem, a novel approach is developed where the nonlinear Euler´s model is decomposed into two pseudo-linear models, making it possible to run two interlaced discrete-linear Kalman filters. This technique, IKF, takes advantage of the linear form´s simplicity, computational efficiency and higher convergence speed, overcoming many drawbacks of conventional extended Kalman filtering techniques. The IKF effectiveness is evaluated through a computer simulation, which demonstrates that the new method yields excellent 3-D angular velocity estimates, very small mean-square-estimation errors, and about ten-to-one signal-to-noise ratio (SNR) improvement over angular velocity measurements obtained from 3 orthogonal gyroscopes, even under very low SNR conditions.