Nonlinear Attitude and Bias Observer Design with a Gibbs-Inspired Cost Function Using Direct Vector Measurements

Abstract

This paper considers the problem of rigid-body attitude and rate-gyro bias estimation. Available measurements include a biased rate-gyro measurement and two or more linearly independent vector measurements. The gradient-based observer design methodology for Lie groups is employed to derive a provably convergent attitude observer. The observer propagates the state estimate along the gradient descent direction of a proposed attitude error function. The use of the proposed attitude error function, which is inspired by previous cost functions using the Gibbs parameterization, results in an innovation term that aggressively drives the attitude error to zero, leading to fast convergence of the observer. The innovation term can be constructed directly from the vector measurements. Numerical results are included that demonstrate the desirable convergence properties of the observer compared to previous results.