Optimal estimation with missing observations via balanced time-symmetric stochastic models

Abstract: 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.