Exploiting A Priori Time Constant Ratio Information in Difference Equation Two-Thermocouple Sensor Characterization

The characterization of thermocouple sensors for temperature measurement in varying-flow environments is a challenging problem. Recently, the authors introduced novel difference-equation-based algorithms that allow <emphasis emphasistype="boldital">in situ</emphasis> characterization of temperature measurement probes consisting of two-thermocouple sensors with differing time constants. In particular, a linear least squares (LS) <formula formulatype="inline"><tex>$\lambda$</tex></formula> formulation of the characterization problem, which yields unbiased estimates when identified using generalized total LS, was introduced. These algorithms assume that time constants do not change during operation and are, therefore, appropriate for temperature measurement in homogenous constant-velocity liquid or gas flows. This paper develops an alternative <formula formulatype="inline"><tex>$\beta$</tex></formula> formulation of the characterization problem that has the major advantage of allowing exploitation of <emphasis emphasistype="boldital">a priori</emphasis> knowledge of the ratio of the sensor time constants, thereby facilitating the implementation of computationally efficient algorithms that are less sensitive to measurement noise. A number of variants of the <formula formulatype="inline"><tex>$\beta$</tex></formula> formulation are developed, and appropriate unbiased estimators are identified. Monte Carlo simulation results are used to support the analysis.