The most powerful unfalsified model for data with missing values

The notion of the most powerful unfalsified model plays a key role in system identification. Since its introduction in the mid 80s, many methods have been developed for its numerical computation. All currently existing methods, however, assume that the given data is a complete trajectory of the system. Motivated by the practical issues of data corruption due to failing sensors, transmission lines, or storage devices, we study the problem of computing the most powerful unfalsified model from data with missing values. We do not make assumptions about the nature or pattern of the missing values apart from the basic one that they are a part of a trajectory of a linear time-invariant system. The identification problem with missing data is equivalent to a Hankel structured low-rank matrix completion problem. The method proposed selects rank deficient complete submatrices of the incomplete Hankel matrix. Under specified conditions the kernels of the submatrices form a nonminimal kernel representation of the data generating system. The final step of the algorithm is reduction of the nonminimal kernel representation to a minimal one. Apart from its practical relevance in identification, missing data is a useful concept in systems and control. Classic problems, such as simulation, filtering, and tracking control can be viewed as missing data estimation problems for a given system. The corresponding identification problems with missing data are “data-driven” equivalents of the classical simulation, filtering, and tracking control problems.