Time-domain analysis of sensor-to-sensor transmissibility operators

In some applications, multiple measurements are available, but the driving input that gives rise to those outputs may be unknown. This raises the question as to whether it is possible to model the response of a subset of sensors based on the response of the remaining sensors without knowledge of the driving input. To address this issue, we develop time-domain sensor-to-sensor models that account for nonzero initial conditions. The sensor-to-sensor model is in the form of a transmissibility operator that is a rational function of the differentiation operator. The development is carried out for both SISO and MIMO transmissibility operators. These time-domain sensor-to-sensor models can be used for diagnostics and output prediction.