Exact system identification with missing data

The paper presents initial results on a subspace method for exact identification of a linear time-invariant system from data with missing values. The identification problem with missing data is equivalent to a Hankel structured low-rank matrix completion problem. The novel idea is to search systematically and use effectively completely specified submatrices of the incomplete Hankel matrix constructed from the given data. Nontrivial kernels of the rank-deficient completely specified submatrices carry information about the to-be-identified system. Combining this information into a full model of the identified system is a greatest common divisor computation problem. The developed subspace method has linear computational complexity in the number of data points and is therefore an attractive alternative to more expensive methods based on the nuclear norm heuristic.