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

TL;DR

This paper introduces a novel approach for data fusion in stochastic systems with missing data, utilizing time reversal and all-pass extensions to derive symmetric formulas for smoothing and interpolation.

Contribution

It presents a new normalization technique linking forward and backward stochastic models, enabling unified smoothing and interpolation formulas.

Findings

Derived symmetric Mayne-Fraser-like formulas for data fusion.

Established a connection between time reversal and all-pass extensions.

Simplified data fusion mathematics through a new basis normalization.

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.