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Estimation of rigid body attitude motion is a long-standing problem ofinterest in several applications. This problem is challenging primarily becauserigid body motion is described by nonlinear dynamics and the state space isnonlinear. The extended Kalman filter and its several variants have remainedthe standard and most commonly used schemes for attitude estimation over thelast several decades. These schemes are obtained as approximate solutions tothe nonlinear optimal filtering problem. However, these approximate or nearoptimal solutions may not give stable estimation schemes in general. Thevariational attitude estimator was introduced recently to fill this gap instable estimation of arbitrary rigid body attitude motion in the presence ofuncertainties in initial state and unknown measurement noise. This estimator isobtained by applying the Lagrange-d'Alembert principle of variational mechanicsto a Lagrangian constructed from residuals between measurements and stateestimates with a dissipation term that is linear in the angular velocitymeasurement residual. In this work, the variational attitude estimator isgeneralized to include angular velocity measurements that have a constant biasin addition to measurement noise. The state estimates converge to true statesalmost globally over the state space. Further, the bias estimates converge tothe true bias once the state estimates converge to the true states.

The Variational Attitude Estimator in the Presence of Bias in Angular Velocity Measurements