Identification of Distributed-Parameter Systems with Missing Data

In this paper we address the identification of linear distributed-parameter systems with missing data. This setting is relevant in, for instance, sensor networks, where data are frequently lost due to transmission errors. We consider an identification problem where the only information available about the system are the input-output measurements from a set of sensors placed at known fixed locations in the distributed-parameter system. The model is represented as a set of coupled multi-input, single-output autoregressive with exogenous input (ARX) submodels. Total least-squares estimation is employed to obtain an unbiased parameter estimate in the presence of sensor noise. The missing samples are reconstructed with the help of an iterative algorithm. To approximate the value of the variables of interest in locations with no sensors, we use cubic B-splines to preserve the continuity of the first-order and second-order spatial derivatives. The method is applied to a simulated one-dimensional heat-conduction process.