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We propose globally exponentially convergent continuous observers forinvariant kinematic systems on finite-dimensional matrix Lie groups. Such anobserver estimates, from measurements of landmarks, vectors and biasedvelocity, both the system state and the unknown constant bias in velocitymeasurement, where the state belongs to the state-space Lie group and thevelocity to the Lie algebra of the Lie group. The main technique is to embed agiven system defined on a matrix Lie group into Euclidean space and buildobservers in the Euclidean space. The theory is illustrated with the specialEuclidean group in three dimensions.

Design of Globally Exponentially Convergent Continuous Observers for Velocity Bias and State for Systems on Real Matrix Groups