Identical synchronization, with translation invariance, implies parameter estimation

If a real system and its perfect model (with identical parameters) can be made to synchronize identically, then for an imperfect model of a real system with some unknown parameters, one can design a parameter estimation law, so that all parameters of the real system can be estimated from the model. While the information needed to implement the law is not available in all cases, sufficient information is generally available for a PDE system that possesses translational symmetry if some of the relevant state variables are known at the discrete set of points (or for the finite set of Fourier components) that are coupled to the model. Parameter estimation is illustrated for a geophysical fluid dynamics model.