Hybrid methods for parameter estimation comparison and numerical applications

The genetic algorithm can be used directly on a model in order to estimate its parameters. However, the time of calculus can be not reasonable and its results can be conditioned by the sensitivity of the measured signal to some parameters. In this paper, a novel procedure combining the classical input-output-parameter approach and the genetic algorithm allows to overcome this problem. The classical input-output-parameter approach requires the estimation of derivatives from a noisy signal. Several methods have already been used but in this paper a new one based on the distribution theory is proposed. It allows to obtain very satisfactory results for a first parameter estimation. Afterwards, instead of improving the results with a local algorithm like Levenberg-Marquardt which does not converge in all the cases or which converges towards a local minimum and not the global one according to the quality of the first initial value, the genetic algorithm is used in taking into account the first previous estimate. Indeed, the advantage of this algorithm is to explore a larger domain and thus, is less likely to give a local minimum. The results are compared to the ones obtained using directly the genetic algorithm on the initial system. Our theoretical result is supported by an application in the pharmacokinetic domain.