Asymptotic detection of incipient faults in the case of nonlinear heteroscedasticity and the calibration of measurement systems
Résumé
The sensor calibration is an important issue in the theory and practice of measurements. The calibration consists of comparing the output of the instrument or sensor under test against the output of an instrument of known accuracy when the same input is applied to both instruments. The goal of the sensor calibration is twofold: first, it is necessary to detect (and to remove) systematic biases in the sensor outputs; second it is necessary to adjust the model of random sensor error in order to get an optimal estimation of the measured parameters. This second task is especially important if the sensor outputs are processed by using the least-squares (LS) filter or the Kalman filter. The paper is devoted to the sensor calibration by using the sensor bias detection and the parameter estimation in the nonlinear model of the sensor heteroscedasticity. The heteroscedasticity occurs in regression when the measurement noise variance is non-constant. Both method, the bias detection test, and the sensor noise estimator, are based on a linear quasi-maximum likelihood estimator.