System identification with missing data via nuclear norm regularization

The application of nuclear norm regularization to system identification was recently shown to be a useful method for identifying low order linear models. In this paper, we consider nuclear norm regularization for identification of LTI systems with missing data under a total squared error constraint. The missing data problem is of ongoing interest because the need to analyze incomplete data sets arises frequently in diverse fields such as chemistry, psychometrics and satellite imaging. By casting the system identification as a convex optimization problem, nuclear norm regularization can be applied to identify the system in one step, i.e., without imputation of the missing data. Our exploratory work makes use of experimental data sets taken from an open system identification database, DaISy, to compare the proposed method named NucID to the standard techniques N4SID, prediction error minimization and expectation conditional maximization via linear regression. NucID is found to consistently identify systems with missing data within the imposed error tolerance, a task at which the standard methods sometimes fail, and to be particularly effective when the data is missing with patterns, e.g., on multi-rate systems, where it clearly outperforms existing procedures.