Kalman filter for estimation of a linear regression model with account of the regression vector error and its application to calibration of measuring instruments

In this paper a Kalman filter algorithm for estimating a linear regression model with account of the regression vector error is presented. That approach has been applied to calibrating measuring instruments and gives a rigorous derivation of a recurrent algorithm for estimating the parameters of the calibration curve with the incorporation of the errors in reproducing the inputs. Calibration of the differential pressure gauge by the standard pressure setting devices (piston gauges) is demonstrated in the paper as an example.