Numerical Methods for Stochastic Differential Equations in Matrix Lie Groups Made Simple
- 26 January 2018
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 63 (12) , 4035-4050
Abstract
A large number of significant applications involve numerical solution of stochastic differential equations (SDE's) evolving in Lie Groups such as SO(3). In the engineering literature the proper formulation of numerical schemes has largely been ignored so that many schemes are flawed i.e. do not guarantee the solution stays in the Lie Group. There is a small mathematics literature but it is not easily accessible. With this in mind we give a directly accessible derivation of numerical schemes for solving SDE's that do not rely on differential geometry or advanced random process theory. In so doing we develop some new results. We illustrate the numerical schemes with simulations.Keywords
Funding Information
- Australian Research Council
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