Fast error estimates for indirect measurements: Applications to pavement engineering (Q1921288)

Consider the following situation: The quantities \(y\) and \(x_1,\dots, x_n\) are functions of some unknown parameters of a physical model. The value of \(y\) which is not directly measurable must be determined from measurements of the \(x_i\). One can proceed in two steps: First the parameters are estimated from the measurements of the \(x_i\) by a least squares method. This can be very time consuming when the \(x_i\) depend in a highly nonlinear way on the parameters. Then \(y\) is calculated. Usual estimates for the error of \(y\) require that this procedure is repeated several times for different values of the \(x_i\). In this paper methods are proposed which calculate the error estimates from certain optimization problems. The estimate for \(y\) must be calculated only once. This gives a significant advantage whenever the parameter estimation needs much computer time. Interval estimates and estimates for random errors are considered. An application from pavement engineering is reported.