Bias and Optimal Linear Estimation in Comparison Calibrations

Comparison calibration designs are rank insufficient to permit a purely batch estimation of parameters, and require the input of some a priori knowledge. The estimator commonly used, which is based on Restrained Least Squares, is shown to be inappropriate because of its inability to take account of uncertainty in the a priori knowledge. A model in which the parameters represent the state of a dynamic stochastic system is proposed together with the appropriate recursive estimator, namely the Kalman filter-predictor. This estimator is less affected than Restrained Least Squares by errors in the a priori knowledge. Its application in mass comparisons in conjunction with a fully recursive approach, i.e. with use of all the available a priori knowledge, is discussed.