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There has been a remarkable effort in the last years in the robotics community to formulate estimation problems properly (Eade, 2013)(Barfoot, 2017). This is motivated by an increasing demand for precision, consistency, and stability of the solutions. Indeed, proper modeling of the states and measurements, the functions relating them, and their uncertainties, is crucial to achieve these goals. This has led to problem formulations involving what has been known as ‘manifolds’, which in this context are no less than the smooth topologic surfaces of the Lie groups where the state representations evolve (Chirikjian, 2011).

Manif: A micro Lie theory library for state estimation in robotics applications