Both Kalman and Lainiotis filters arise in linear estimation and are associated with linear systems. In this paper, we investigate the partition of linear systems into lower dimensioned independent linear systems. We study the effects of partitioning on filter behaviour and computational burden. It is concluded that the partition does not affect the behaviour of Kalman and Lainiotis filters. Simulation results show that Kalman and Lainiotis filters compute the same outputs (estimation and estimation error covariance), both in the single and in the partitioned model. It is also concluded that the partition leads to significant speedup in both Kalman and Lainiotis filters. Specifically, it is shown that the partition into p independent models leads to super-linear speedup in the range (p, p2) for both filters.