Optimal interpolation for linear stochastic systems: The discrete time case

This paper is concerned with least-squares estimation of the state of a linear discrete-time stochastic system when there is a data gap. Our approach, hinging on some basic concepts from stochastic realization theory, allows us to derive compact expressions for the optimal estimate in a more direct and illuminating way than it would be possible via the present smoothing formulae. As a by-product, we also solve the estimation problem for the missing observations.