  We exploit knowledge of linear substructure in the linear-regression Kalman
filters (LRKFs) to simplify the problem of moment matching. The theoretical
results yield quantifiable and significant computational speedups at no cost of
estimation accuracy, assuming partially linear estimation models. The results
apply to any symmetrical LRKF, and reductions in computational complexity are
stated as a function of the cubature rule, the number of linear and nonlinear
states in the estimation model respectively. The implications for the filtering
problem are illustrated by numerical examples.
