Approximate system identification with missing data

Linear time-invariant system identification is considered in the behavioral setting. Nonstandard features of the problem are specification of missing and exact variables and identification from multiple time series with different length. The problem is equivalent to mosaic Hankel structured low-rank approximation with element-wise weighted cost function. Zero/infinite weights are assigned to the missing/exact data points. The problem is in general nonconvex. A solution method based on local optimization is outlined and compared with alternative methods on simulation examples. In a stochastic setting, the problem corresponds to errors-invariables identification. A modification of the generic problem considered is presented that is a deterministic equivalent to the classical ARMAX identification. The modification is also a mosaic Hankel structured low-rank approximation problem.