Identification of sensor-only MIMO pseudo transfer functions

In many applications of system identification, output measurements are available, but measurements of the input are not available. In these cases, sensor-only identification techniques are needed. In the present paper, we define a discrete-time MIMO pseudo transfer function (PTF) between sensor measurements in a sampled-data system with multiple excitation signals. We show that the MIMO PTF does not depend on the unknown initial state or the unknown excitation. We also characterize the order and relative degree of the MIMO PTF. To consistently estimate the Markov parameters of the MIMO PTF in the presence of sensor noise, we use quadratically constrained least squares identification for MIMO systems. We apply this technique to a three-degree-of-freedom mass-spring-damper system to assess the accuracy of the identified PTFs.