A novel method for estimation of model parameters for noise-corrupted signals

Often measured data are produced by an integration process over many layers, whereas the parameter values in every layer are of interest. The data are corrupted by noise. The estimation of the model parameters, if only the summed measured data and their relationships to the parameters (forward model) are known, is an inverse problem. The paper shows how coupled integrals near an a priori known situation can be summed up by an operator representation. A method is shown to calculate the probability density function for model parameter estimation. The obtained expectation value with the algebraic dependence of the parameters is related to the measured value and solves the inverse problem.