  We consider data fusion for the purpose of smoothing and interpolation based
on observation records with missing data. Stochastic processes are generated by
linear stochastic models. The paper begins by drawing a connection between time
reversal in stochastic systems and all-pass extensions. A particular
normalization (choice of basis) between the two time-directions allows the two
to share the same orthonormalized state process and simplifies the mathematics
of data fusion. In this framework we derive symmetric and balanced
Mayne-Fraser-like formulas that apply simultaneously to smoothing and
interpolation.
