On generalising difference equation characterisation to higher-order sensor models

The measurement of fast changing temperature fluctuations is a challenging problem in many scientific and engineering disciplines. The limited bandwidth of temperature sensors such as thermocouples and resistance temperature detectors (RTDs) means that measurement errors can be significant during temperature transients. Compensation of the sensor output is therefore necessary in order to provide reliable temperature measurements but requires that a fully parametrised model of the sensor is available. However, parameter estimation is intractable when using only output measurements from a single sensor. Difference equation characterisation provides a solution to this problem by using measurements from two sensors, each represented as first-order models and subject to the same thermal field. Recently the authors have demonstrated that it is possible to extend this method to second-order, resulting in a linear system identification problem for estimation of a set of intermediate parameters which are nonlinearly related to the sensor parameters and which can be solved analytically. The contribution of this paper is to investigate the feasibility of extending the method to higher-order sensor models. It is concluded that while blind characterisation is theoretically possible for higherorder models, it is not practical to implement the approach due to the increasingly complex multimodal cost function that makes identification and isolation of the correct optimum very challenging. Results and conclusions are verified using MonteCarlo simulations.