Current Research

• Non-linear observers and vehicle localisation
• Information geometry, geometrical methods in learning
• Control of mechanical systems

Observers and symmetries

There are symmetries in the basic laws which govern the physical world. But how can a law be "symmetrical"? We should maybe adopt the definition of Hermann Weyl who says a thing is symmetrical if one can subject it to a certain operation and it appears exactly the same after the operation. So the question is what operation we can do to a an experiment, and leave the result the same. For instance the conservation laws involved in the dynamic models of chemical reactors are independent of the choice of physical units (mol, kg, ...).
What about the estimation algorithms? If an algorithm is meant to estimate a physical quantity why should a certain operation affect the algorithm, and not the physical model? For chemical reactors it seems logical that the estimation algorithms do not depend on the units either. More generally for systems possessing symmetries, the extended Kalman filter (one of the most commonly used nonlinear filter), can change under some operations whereas the system under consideration remains unchanged ! The theory of symmetry-preserving obsevers is a geometrical framework allowing to build estimators (observers) possessing the same symmetries as the system under consideration. The usual inputs "u" are re-interpreted as all the features of the environment having to be moved over such that the model looks the same after the operation.