This paper discusses certain aspects of multi-level state estimation. In the first part, the multi-level state estimator of Pearson is considered and it is shown why such filters cannot be used for the practical state estimation of large systems. Then a computationally efficient suboptimal filter formulated by Shah is described and which is then extended to systems with time lags between the subsystems. For large serially connected systems, an even simpler state estimator could be used. A number of numerical studies are given comparing the performance of the two sub-optimal estimators and the overall optimal solution.