Observability and local observer construction for unknown parameters in linearly and nonlinearly parameterized systems

Using geometric concepts from observability theory for nonlinear systems, we propose an approach for parameter estimation for linearly and nonlinearly parameterized systems. The proposed approach relies on extending a parameter estimation problem to a state estimation problem by introducing the parameters as auxiliary state variables. Applying tools from geometric nonlinear control theory we establish an observability check for parameters, and we construct a local observer with established speed of convergence in the observable sets of the extended system.