Compensation of measurement noise and bias in geometric attitude estimation

Abstract

A geometry-based analytic attitude estimation using a rate measurement and measurement of a single reference vector has been recently proposed. Because rigid body attitude estimation is a fundamentally nonlinear problem, the geometry-based method does not contain errors consequent to linearization approximations. A critical source of residual error in the geometric solution is on account of the noise and bias in the vector and rate measurements. A methodical perturbation analysis of the attitude estimate is performed in this paper that reveals the effects of measurement noise and bias, and provides means to compensate for, or filter out, such errors. Application of the filter and compensation provides better attitude estimation than a standard Extended Kalman filter using an optimal Kalman gain. The geometric method is first verified in experiments and then simulation results are provided that validate the better performance of the geometric attitude and bias estimator.