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Using geometric concepts from observability theory for nonlinear systems, we propose an approach for parameter estimation for linearly and nonlinearly parameterized systems that does not rely on persistence of excitation conditions. 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 give an observability check for parameters, and, in case the parameters are observable, we provide a constructive way to design a local parameter observer with established speed of convergence.