Estimation of measurement error variances from n-linear process data
Résumé
This paper deals with reconciling measurements characterized by an unknown variance from processes described by linear equations. We use the technique of maximum likelihood to give an estimate of the real values and of the measurement errors variance. To make this estimation we assume that the measurement errors follow a normal probability density function with a zero mean and a constant variance. We have developed a relaxation algorithm based on direct iteration to solve the problem of the optimisation of the likelihood function under linear constraints. In the first instance we apply this algorithm to systems operating near a single steady state regime, then we extend the results obtained to the case of several steady state regimes.