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In this paper, a machine learning based observer for systems evolving onmanifolds is designed such that the state of the observer is restricted to theLie group on which the system evolves. Conventional techniques involvingmachine learning based observers on systems evolving on Lie groups involvedesigning charts for the Lie group, training a machine learning based observerfor each chart, and switching between the trained models based on the state ofthe system. We propose a novel deep learning based technique whose predictionsare restricted to a measure 0 subset of Euclidean space without using charts.Using this network, we design an observer ensuring that the state of theobserver is restricted to the Lie group, and predicting the state using onlyone trained algorithm. The deep learning network predicts an ``error term'' onthe Lie algebra of the Lie group, uses the map from the Lie algebra to thegroup, and uses the group action and the present state to estimate the state atthe next epoch. This model being purely data driven does not require the modelof the system. The proposed algorithm provides a novel framework forconstraining the output of machine learning networks to a measure 0 subset of aEuclidean space without chart specific training and without requiringswitching. We show the validity of this method using Monte Carlo simulationsperformed of the rigid body rotation and translation system.

Machine learning based state observer for discrete time systems evolving on Lie groups