Abstract: We consider a unicycle vehicle model with unknown constant linear and angular speeds. Our objective is to estimate the heading and the linear and angular speeds of the vehicle using position measurements. We first employ nonlinear observability theory to prove that the system is indeed observable. We next extend the symmetry-preserving observer design in Bonnabel et al. (2008) to include two additional states that estimate the unknown speeds. We show stability and convergence properties of the resulting observer with appropriate observer gains. We also conduct simulations and demonstrate the superior performance of the designed observers over an extended Kalman filter.
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