Degree of optimality for mean-square estimation via state-vector partitioning

The problem of minimum mean-square state estimation for linear stationary systems is considered. State-vector partitioning is employed to arrive at a computationally efficient estimate, and a quantitative measure for the degree of optimality for this estimate is derived. This quantitative measure can then be used to relate the degree of optimality to the particular state-vector partition employed, thus providing an ordering over all admissible partitions of the system. A method of selecting the best partition (i.e. the one that maximises the degree of optimality) is outlined.