A reduced-order filler algorithm is developed for estimation of the complementary states of a linear system driven by white noise. The estimator gives an unbiased estimate of the states, and the error in the estimate is orthogonal to the subspace of the observations of those states that are common to the observations and the estimated states, The filter performance is suboptimal relative to the full-order optimal linear filter, but benefits are reaped from computational savings in the filtering and associated Riccati equations. The algorithms are developed using a concept of the ‘reduced-order innovation process’. The design uses only a priori information for z, the states to be estimated. The estimator is shown to be unique. The requirements of the stability of the filter are also presented, and its determination can precede its implementation. The basic limitation of this approach is that one is constrained by the minimum order of the filter, because of the assumption in (2.11) that the states to be estimated are complementary to the observed states.