Stability analysis and near optimal gain tuning of an attitude estimator on the special orthogonal group

In this paper, we investigate the effect of non-ideal sensor measurements on the performance of a nonlinear attitude estimator. Bounded deterministic disturbances are considered in both vector measurements and angular velocity reading. We derive conditions under which the practical stability of estimator is guaranteed and present an upper-bound for the steady state attitude estimation error. We also consider the problem of minimizing the ultimate bound of estimation error by proper choice of constant observer gains according to the properties of vector measurements. A key contribution of the paper is to propose a set of Linear Matrix Inequalities which result in the near optimal observer gains in a sense that they minimize the ultimate bound of estimation error. Meanwhile a case study, some interesting results of the optimization procedure are also discussed which provide a greater insight into the problem.