Indirect measurements: combining parameter selection with ridge regression

Indirect measurements often require the solution of inverse problems, which can be ill-posed or ill-conditioned. There are several methods for dealing with ill-conditioned problems. Two of them, parameter selection and ridge regression, are described in the paper. The idea of parameter selection consists of estimation of the subset of model parameters selected on the ground of sensitivity analysis and ascribing `typical' values to the others. Ridge regression is a regularization technique reducing collinearities in the matrix being inverted. The methods have been combined to maximize their advantages and improve the accuracy of measurement. Statistical analysis of parameter estimators, including their bias, variance and total uncertainty, is presented together with a simple artificial as well as a complex realistic example. The regularized estimation of selected parameters proposed in the paper is characterized by an improvement in the numerical conditioning of model identification and error reduction in indirect measurement.