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A nonlinear observer on the Special Euclidean group $\mathrm{SE(3)}$ for fullpose estimation, that takes the system outputs on the real projective spacedirectly as inputs, is proposed. The observer derivation is based on a recentadvanced theory on nonlinear observer design. A key advantage with respect toexisting pose observers on $\mathrm{SE(3)}$ is that we can now incorporate in aunique observer different types of measurements such as vectorial measurementsof known inertial vectors and position measurements of known feature points.The proposed observer is extended allowing for the compensation of unknownconstant bias present in the velocity measurements. Rigorous stability analysesare equally provided. Excellent performance of the proposed observers are shownby means of simulations.

Gradient-like observer design on the Special Euclidean group SE(3) with system outputs on the real projective space