Lie transformations for parameter estimation of continuous-time nonlinear systems

A method using Lie symmetry transformations is developed to change a given nonlinear continuous-time model to equivalent equations in which the parameters are affine in the parameters. Once affinity in the parameters are obtained, a direct estimation approach using the modulating functions methods is used to estimate these parameters. In choosing the symmetry generators, certain restrictions were observed to preserve the advantages of modulating functions method, such as avoiding the need to estimate initial conditions and the need to approximate derivatives of noisy data. Simulations show the effectiveness of the method, specifically on power-law kinetics. Speed-up over iterative nonlinear least-squares is significant; and the method does not suffer from the sensitivity to initial guesses.