On the stability and biasedness of the cross-relation blind thermocouple characterisation method

The in situ characterisation of thermocouple sensors is a challenging problem. Recently the authors introduced a novel blind characterisation technique based on the cross-relation method of blind identification that allows in situ characterisation of temperature measurement probes consisting of twothermocouple sensors with differing time constants. While the technique has a number of advantages over competing methods, including low estimation variance and no need for a priori estimation of the time constant ratio, it was found to be positively biased and becomes unstable at high noise levels. In this paper the origin of the stability issues and bias are analysed. It is shown that an alternative normalised cost function formulation, which eliminates the stability problem, results in negatively biased time constant estimates at high noise levels. Further, it is demonstrated that this bias is less significant when temperature variations are broadband. All results are verified using Monte-Carlo simulations.