An Error-Minimizing Approach to Regularization in Indirect Measurements

Indirect measurements often amount to the estimation of the parameters of a mathematical model that describes the object under investigation, and this process may numerically be ill conditioned. Various regularization techniques are used to solve the problem. This paper shows that popular regularization methods can be depicted as special cases of a generalized approach based on a penalty term in the minimized criterion function and how different kinds of a priori knowledge can be engaged into each of them. A new function, which depends on the estimate bias and variance, is proposed to find a regularization parameter that minimizes the error of estimation, as well as a novel approach for nonlinear estimation that results in the iterative minimization (IM) method. The superiority of IM with respect to the conventional Marquardt procedure is demonstrated. Based on analysis, it also follows that the regularization technique can be used even in the case of numerically well-conditioned indirect measurements, decreasing the total error of estimation.