For the problem of state observation the initial conditions are not known a priori and must be estimated, so the approach is of limited practical use. There are at least 4 ways to continue the study of the exterior differential system that results:
- Move up to the 2-jet.
- Use separation of variables.
- Define the cost geometrically as a Riemmanian geodesic energy integral.
- Forget about characteristics and compute symmetries.
- All of the above.